contributions to the dynamics of south foehn · 2019. 12. 16. · considered in the hydraulic...

Contributions to the Dynamics of

South Foehn:

A Gap Flow Study during the

Mesoscale Alpine Programme

A dissertation submitted to the

Department of Meteorology and Geophysics,

University of Innsbruck

for the degree of

Doctor of Natural Science

presented by

Alexander Gohm

March 2003

Proposal for the composition of the examining committee presented to the dean of

the Faculty of Natural Sciences at the University of Innsbruck as required for the

submission of the dissertation under § 62 (7) UniStG:

Reviewing committee:

1. Ao. Prof. Dr. Georg Mayr (advisor), University of Innsbruck

2. Prof. Dr. Christoph Schär, ETH Zurich

3. Prof. Dr. Stephen Mobbs, University of Leeds

Committee for oral examination:

1. Ao. Prof. Dr. Georg Mayr (advisor), University of Innsbruck

Subject: Dynamics of Mountain Flows

2. Prof. Dr. Laurence Armi, University of California, San Diego

Subject: Oceanography

3. Ao. Prof. Dr. Ignaz Vergeiner, University of Innsbruck

Subject: Atmospheric Waves

Date: March 2003

To my father

wind

heaven

i

”... and last, not least, how to choose among the great many

parameters to be varied and tested, how to look at three-dimensional

flow configurations with our restricted cinemascopic abilities, how to

help being swamped by the mass of data?”

(Vergeiner 1975)

iii

Abstract

Many facets of Alpine foehn winds have been investigated in the past. However,

one which has been neglected so far is the discussion of south foehn as gap flow

through deep incisions in the Alpine chain. The present thesis examines these gap

flows through the Brenner Pass and along the Wipp Valley (Austria/Italy). The

study was motivated by field measurements conducted during the Special Observ-

ing Period (SOP) of the Mesoscale Alpine Programme (MAP) in fall 1999.

The first part examines the applicability of single-layer hydraulic theory to the

Brenner Pass foehn. Numerical shallow-water simulations for a wide range of initial

conditions including shallow and deep foehn cases are discussed and compared with

selected observations of the MAP SOP, such as data from a ground-based scanning

Doppler lidar, an airborne aerosol backscatter lidar, radiosoundings, and automatic

weather stations. Radiosoundings reveal that the average MAP SOP foehn case had

subcritical flow south and nearly critical flow north of the Brenner. The hydraulic

model indicates flow transition to a supercritical state near the pass, and at least

nearly critical conditions in the northern part of the Wipp Valley. Prominent loca-

tions for hydraulic jumps are 2 km north of the pass and near the exit of the Wipp

Valley. The vertical topographic contraction exerts stronger control for the flow at

the Brenner gap than the lateral contraction. The observed and simulated across-

valley asymmetry in the strength of the foehn flow is a result of the complex valley

geometry rather than the influence of upper-level synoptic winds as suggested in a

previous study. Limitations of the applicability of the single-layer hydraulic concept

arise from the fact that foehn cases have been observed with no distinct inversion

or with an inversion depth comparable to the depth of the foehn flow. For such

cases the foehn cannot be described as a flowing layer being separated by a sharp

density step from a passive layer aloft. Further, turbulent entrainment processes

along the inversion layer, which change the reduced gravity across the pass, are not

considered in the hydraulic model. Nevertheless, the model captures essential flow

patterns such as the location of the pressure minimum, wind speed maxima, and

steeply amplified or breaking gravity waves resembled by hydraulic jumps.

The second part presents a case study of a deep south foehn, the MAP IOP 10

v

vi

event (24–25 October 1999), based on a detailed comparison and verification of

high-resolution numerical simulations with observations. The simulations were per-

formed with the Penn State/NCAR mesoscale model MM5. The observational data

sources were the same as in the first part and additionally contained a Doppler sodar.

As a first step, the study provides a synoptic-scale and mesoscale overview of the

event. The quantitative agreement between the numerical results and the observa-

tions is discussed in terms of root-mean square error and mean error. Discrepancies

detected at the beginning of the event are related to an unrealistic upstream profile

in the model which leads to the simulation of a spuriously extended shallow foehn

phase prior to the deep foehn stage. Evidence is found for the overestimation of

the mass flux through the lower Brenner gap and subsequent underestimation of

the flow descent on the leeward side of the pass. Nevertheless, the model captures

several of the striking foehn features: Simulated isentropes and aerosol backscatter

measurements both indicate regions of flow descent, across-valley flow asymmetries,

and hydraulic-jump-like features.

Contents

Abstract v

Contents vii

1 General introduction 1

1.1 Alpine foehn studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Gap flow studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Goals and outline of the thesis . . . . . . . . . . . . . . . . . . . . . . 9

2 Hydraulic aspects of foehn 11

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.1 Topographic environment . . . . . . . . . . . . . . . . . . . . 14

2.1.2 Types of foehn . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.3 Gap flow studies . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Model and measurement description . . . . . . . . . . . . . . . . . . . 20

2.2.1 The shallow-water model . . . . . . . . . . . . . . . . . . . . . 20

2.2.2 Weather stations and radiosoundings . . . . . . . . . . . . . . 21

2.2.3 Lidars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Motivation for hydraulic solutions . . . . . . . . . . . . . . . . . . . . 23

2.3.1 Vertical structure of foehn winds . . . . . . . . . . . . . . . . 23

2.3.2 An exemplary case . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.3 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Numerical solutions for different upstream conditions . . . . . . . . . 26

2.4.1 Condition upstream of the pass . . . . . . . . . . . . . . . . . 26

2.4.2 Flow pattern along the Wipp Valley . . . . . . . . . . . . . . . 28

2.4.3 Flow pattern in the Wipp and Inn Valley . . . . . . . . . . . . 31

2.4.4 Statistical analysis of the flow structure . . . . . . . . . . . . . 34

2.5 Comparison of model flow fields with observations . . . . . . . . . . . 36

2.5.1 Flow condition up- and downstream of the pass . . . . . . . . 37

2.5.2 Flow pattern along the Wipp Valley . . . . . . . . . . . . . . . 38

vii

viii CONTENTS

2.5.3 Flow pattern in and across the Wipp Valley . . . . . . . . . . 43

2.5.4 Flow pattern across the Inn Valley . . . . . . . . . . . . . . . 46

2.6 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . 48

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3 Mesoscale model verification: Case study of a deep foehn 53

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.2 Model and measurement description . . . . . . . . . . . . . . . . . . . 59

3.2.1 The mesoscale model MM5 . . . . . . . . . . . . . . . . . . . 59

3.2.2 Weather stations and radiosoundings . . . . . . . . . . . . . . 60

3.2.3 The NOAA/ETL Doppler lidar . . . . . . . . . . . . . . . . . 60

3.2.4 The ZAMG Doppler sodar . . . . . . . . . . . . . . . . . . . . 61

3.2.5 The NCAR airborne backscatter lidar . . . . . . . . . . . . . . 61

3.3 Overview of the event . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3.1 Synoptic-scale environment . . . . . . . . . . . . . . . . . . . 62

3.3.2 Mesoscale structure . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 Comparison methodology . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5 Comparison with observations . . . . . . . . . . . . . . . . . . . . . . 71

3.5.1 Surface data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.5.2 Vertical profiles of the horizontal wind . . . . . . . . . . . . . 74

3.5.3 Backscatter intensities versus potential temperature . . . . . . 77

3.5.4 Spatial distribution of radial wind velocities . . . . . . . . . . 81

3.6 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 89

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4 Conclusions and outlook 93

Bibliography 97

Acknowledgments 107

Curriculum Vitae 109

Epilogue 111

Chapter 1

General introduction

The present thesis is a contribution to the understanding of the dynamics of foehn

in an Alpine valley. It specifically investigates south foehn occurring in the Wipp

Valley near the Brenner Pass region (Austria/Italy). The emphasis is placed on the

discussion of foehn as gap flow through this pass and along the associated valley.

The study was motivated by field measurements during the Special Observing Period

(SOP) of the Mesoscale Alpine Programme (MAP) in fall 1999. The introductory

part contains a review of relevant foehn literature (section 1.1) and of gap wind

studies (section 1.2) and presents the major goals and the outline of the dissertation

(section 1.3).

1.1 Alpine foehn studies

The research on Alpine foehn has now a history of more than hundred years. The

earliest works go back to the middle of the 19th century (e.g. Hann 1866; Wild

1868). An extensive body of literature is available on many aspects of foehn, includ-

ing theories and concepts, synoptics and statistics, observational analyses as well

as climatic, physiological, and neurological effects (see e.g. Lehmann 1937; Ficker

and de Rudder 1943; Kuhn 1989). Referring to a bibliography compiled by Schlegel

(1975), Seibert (1985) mentioned a remarkable number of 139 foehn studies con-

ducted solely within the period of 1945–1975. A more recent foehn bibliography

compiled by Dürr (1999, 2000) contains more than 150 entries.

Foehn winds in the Innsbruck area (Inn and Wipp Valley) have been investigated

based on various approaches and theories. The results and ideas were not applied

exclusively to this region but also to other mountainous areas. Without trying to

be exhaustive, some of these studies are mentioned in the next few paragraphs.

1

2 General introduction

In a series of four papers with the title ”Innsbruck foehn studies I–IV” Ficker (1906,

1910) investigated the dynamics of foehn based on observational case studies, Defant

(1907) searched for the explanation of periodic temperature fluctuations observed

at the beginning of foehn and during foehn breaks, and Trabert (1908) studied the

physiological influence of foehn on the human condition.

Worth mentioning are the foehn studies conducted by Ficker (1912, 1913, 1931)

based on several gas balloon flights with Innsbruck as take-off site. He reported

strong descent of the foehn flow to the lee of the mountain range north of Innsbruck

(”Karwendel”) on the order of 1500–2000 m. Frequent up- and downdrafts above

the jagged terrain were a typical feature, whereby the perturbations decayed with

increasing height. With the background of Billwiller’s (1899, 1903) studies and

based on his own observations, Ficker explained the reason for the foehn descent

into the valleys to be a compensating effect for the cold low-level air which drains

off the valleys into the Alpine foreland due to a depression northwest of the Alps (the

”aspirating” effect of the cyclone; see Billwiller 1899, Ficker and de Rudder 1943).

With this theory, he was in heavy dispute with Streiff-Becker (1931b, 1931a), who

explained the reason for the foehn descent as follows: A strong jet crossing the

mountain ridges sucks up air from the underlying stagnant cold layer embedded in

the valleys and consequently has to descend to compensate the mass deficit, i.e. to

fill the ”air hole” (”vacuum theory”; see Streiff-Becker 1931a).

Pibal soundings by Kanitscheider (1932, 1938) during foehn conditions in the vicin-

ity of Innsbruck yielded remarkable results. Based on two sets of ascents with a total

of 147 balloon trajectories, Kanitscheider found regions of flow splitting as well as

strong updrafts near the mountain range north of Innsbruck and flow separation

of the descending foehn winds to the lee of the mountains south of Innsbruck. He

classified some cases as ”shallow foehn” for which the southerly flow was only a few

100 m deep and the flow aloft turned to westerly directions. In a third paper, Kan-

itscheider (1939) investigated the flow pattern in the upper Inn Valley 23 km west

of Innsbruck (Telfs) at a location without a north–south aligned valley extending

towards the main Alpine crest.

A popular concept to explain the warming effect of the foehn flow on the leeward side

of mountains, not solely in the Alps, was the thermodynamic foehn theory. It goes

back to Hann (1866) and was discussed e.g. in Ficker and de Rudder (1943), however,

its origin can be traced back even to Espy (1841) (see Hann 1885). The key point

in this theory is that the difference in temperature is gained by a moist-adiabatic

ascent upstream of the barrier and a dry-adiabatic descent to the lee. This theory

1.1 Alpine foehn studies 3

was reviewed and vigorously confuted by Seibert (1985, 1990). The concept relies on

the occurrence of precipitation on the windward side, whereas foehn cases have been

observed without an upstream cloud cover. Based on observations collected during

the Alpine Experiment (ALPEX) in 1982, Seibert rehabilitates a different and a

today widely accepted explanation for the temperature difference across the Alps

during south foehn: It is mainly caused by the warming of the air on the leeward

side due to the descent of the flow from the crest level into the valleys, whereas

upstream of the Alpine ridge the stable stratification favors low-level blocking and

the formation of cold pools. A contribution to the warming by latent heat release

may be not unlikely but is of minor importance.

An interesting approach to explain the dynamics of foehn, which is specifically rel-

evant to the present thesis, is the one by Schweitzer (1953). He compared foehn

winds with a hydraulic flow of a single layer with a free surface. In the stratified

atmosphere this free surface would be represented by a temperature inversion, i.e.

an interface forming a density step between a lower and an upper layer. Foehn was

explained as the flow of the lower layer which has a supercritical velocity, i.e. a flow

speed exceeding the velocity of linear shallow-water gravity waves. Rotors occurring

in the flow were interpreted as hydraulic jumps. As one specific example, Schweitzer

mentioned the foehn which originates at the Brenner Pass and develops into a strong

supercritical flow along the Wipp Valley.

Two publications investigated foehn in a theoretical/analytical manner. Mayr (1987)

studied the dynamics of shallow foehn along theWipp Valley cross-section based on a

linearized two-dimensional model with an isentropic coordinate system, whereby the

mass-flux into the Inn Valley was parameterized. Sensitivity studies showed that a

reduction of the stability increases the amount of flow over the mountain range north

of Innsbruck, i.e. decreases the amount of mass deflected into the Inn Valley, but

also increases the strength of the flow descent above the Inn Valley. Vergeiner (1996)

presented a conceptual dynamic model for the foehn penetration into an idealized

two-dimensional valley filled with a cold pool. He derived a regime diagram for the

total flow penetration with two Froude numbers based on the buoyancy frequency

of the free air stream and of the valley atmosphere. Vergeiner noted the limited

suitability of his 2D model for the application to the Inn Valley due to the (highly

3D) gap-like topography of the Wipp–Inn Valley intersection.

During recent years the early conceptual models and theories of Alpine foehn were

supplemented by a series of three-dimensional numerical simulations of the flow

field. Vergeiner (1975, 1976) developed a linearized model for wavelength scales


between 10 and 100 km and applied it to the mountain-induced gravity wave flow

in the Innsbruck area. In agreement with the observations by Kanitscheider (1932,

1938), the simulated surface wind pattern reveals flow divergence at the exit of the

Wipp Valley. For various different initial conditions, orographically induced gravity

waves produced flow patterns with topographically fixed features, such as updraft

regions. The simulations revealed typical magnitudes of the vertical velocities of

≈ 5–10 m s−1 at about 1 km above the mountain summits. Although the linearizedmodel provides valuable insight into the foehn dynamics, it obviously has to fail if

the gravity wave amplitudes become large, i.e. if non-linear effects become relevant.

Zängl (1999) used a non-linear mesoscale model to study the foehn structure

based on a highly idealized Wipp Valley–Inn Valley terrain configuration. He noted

the importance of the westerly outflow of cold low-level air from the Inn Valley into

the Alpine forelands in order to observe a foehn breakthrough in the Inn Valley. Fur-

ther, he showed that both surface friction and positive vertical wind shear decrease

the likelihood or intensity of wave breaking and that the shape of the Wipp Valley,

i.e. whether it widens north of the pass or not, considerably influences the gravity

wave pattern above the valley and the strength of the foehn near the pass. Recently,

Zängl (2003) and Zängl et al. (2003b) performed high-resolution numerical simula-

tions for the foehn flow over realistic orography. In the first work, idealized initial

and boundary conditions for shallow and deep foehn were used and the results were

compared with surface observations from the MAP SOP. A gravity wave asymmetry

was found in the Inn Valley with stronger wave amplitudes to the east of Innsbruck

than to the west causing a local pressure gradient along the Inn Valley which seems

to drive the usually observed westerly pre-foehn at Innsbruck. The second paper

is a case study of the MAP Intensive Observing Period (IOP) 10 deep foehn event,

which was conducted in order to assess whether it is possible to reproduce the tem-

poral evolution and the spatial structure of a south foehn with a high-resolution

model having a mesh size of ≈800 m. Model data were compared with observationsfrom automatic weather stations and radiosoundings. The study showed encourag-

ing results but also revealed discrepancies concerning, e.g., the small-scale structure

of the wind field near Innsbruck, the amount of turbulent vertical mixing along the

Wipp Valley, and the intensity of precipitation on the southern side of the Alps.

Flamant et al. (2002) presented a simulation with a non-hydrostatic mesoscale

model as part of an extensive study of the MAP IOP 12 foehn case (see below).

The spatial resolution was rather coarse (≈2 km) in the face of the details of theBrenner gap. Nevertheless, the results were useful to complement the flow picture

drawn from the observational analysis.

Two field experiments, ALPEX and MAP, stimulated several observational studies of

1.2 Gap flow studies 5

the foehn in the Brenner Pass region. Seibert (1985) presented analyses of potential

temperature and pressure at the surface, isentropic cross-sections, and investigations

of the wind field of several ALPEX foehn cases for a regional scale (Innsbruck area)

and a larger scale (Alps) and conducted statistical foehn investigations for a period

of four years. The main results were summarized in Seibert (1990). For a south

(and a north) foehn case prior to ALPEX, Steinacker (1983) compiled analyses of the

pressure pattern on isentropic surfaces and showed vertical transects of potential and

equivalent-potential temperatures across the Alps near the Brenner Pass. Fine-scale

pressure and wind analyses in the Inn andWipp Valley of an ALPEX deep foehn case

were published by Vergeiner et al. (1982). Hoinka (1985, 1990) presented airborne

observations of the potential temperature and wind field for ALPEX foehn flights.

Since the MAP SOP in 1999, a few observational studies have been published.

Mayr et al. (2002) discussed observations taken with a car-based platform along

the Brenner Pass transect for the 30 October 1999 (MAP IOP 12) foehn case.

These surface measurements revealed locations of hydraulic jumps and were useful

to extend aircraft observations to the ground. The same event was discussed in an

exemplary manner by Mayr et al. (2003a, 2003b) and studied in detail by Flamant

et al. (2002) based on Doppler lidar data, airborne backscatter lidar observations,

airborne in situ measurements, radiosoundings, and data from automatic weather

stations. Durran et al. (2003) compared ground-based Doppler lidar and airborne in

situ wind measurements for three different MAP foehn events and calculated RMS

errors and bias to estimate the differences between the two data sources.

With the background of this bulk of Alpine foehn literature, the legitimate question

arises if further research on foehn is necessary. We have learned from these studies

that the dynamics of foehn has many different facets. Some of them have been

neglected in the past and therefore gaps – especially orographic ones – have to

be ”filled”. The concept of gap flows has been applied to the Wipp Valley foehn

particularly since the planning phase of the Mesoscale Alpine Programme (MAP)

field experiment (Bougeault et al. 1998). Since the major aim of the present thesis

is to discuss foehn winds as a gap flow phenomenon, a short review of its literature

deserves a separate section.

1.2 Gap flow studies

Gap winds have been observed in many parts of the globe – wherever an incision oc-

curs in the orography and allows the flow to pass through it. Examples are manifold:

winds in the Strait of Gibraltar (Scorer 1952; Dorman et al. 1995), the Mistral in the

French Rhône Valley (Pettre 1982), strong winds near Hokkaidō in Japan (Arakawa


1969), airflow near Unimak Island in the Aleutian Chain (Pan and Smith 1999),

winds in the Howe Sound of British Columbia (Jackson and Steyn 1994a, 1994b;

Finnigan et al. 1994), winds in straits and gaps formed by the Coast/Cascade

Mountains between British Columbia and Washington State (Reed 1931; Overland

and Walter 1981; Mass et al. 1995; Colle and Mass 2000; Doyle and Bond 2001),

airflow through gaps embedded in the Washington Cascade Mountains (Cameron

1931; Mass and Albright 1995; Colle and Mass 1998a, 1998b; Sharp and Mass 2002),

winds in straits, inlets, and gaps near the coast of Alaska (Lackmann and Overland

1989; Macklin et al. 1990; Colman and Dierking 1992; Bond and Stabeno 1998),

winds near a Swedish lake embedded in high mountains (Smedman and Bergström

1995), the outflow over the Gulf of Tehuantepec in Mexico (Schultz et al. 1997;

Steenburgh et al. 1998), a coastal jet with partly gap-flow characteristics at Spits-

bergen (Sandvik and Furevik 2002), intense upvalley winds in the Himalayan Kali

Gandaki Valley (Egger et al. 2000, 2002; Zängl et al. 2001), and the foehn across

the Brenner Pass in the Alps (Flamant et al. 2002; Mayr et al. 2003a).

In many of these cases, especially for gaps embedded in elongated barriers, the gap

flows are highly ageostrophic and follow the pressure gradient force along the gap axis

(e.g. Overland and Walter 1981). The pressure difference is frequently associated

with a pool of cold air upstream of the barrier (e.g. Sharp and Mass 2002). In other

cases the large-scale geostrophic flow is perpendicular to the mountain ridge and

thus aligned parallel to the gap winds (e.g. Pan and Smith 1999). The theories for

the strength of the gap flow were diverse. In the early days, Reed (1931) explained

the gap winds in the Strait of Juan the Fuca as a Venturi effect due to the horizontal

contraction of the sidewalls. Such an effect would place the strongest wind at the

narrowest section. However, it was shown later that the velocity maximum occurred

further downstream (e.g. Colle and Mass 2000). Gap winds driven by the outflow of

cold air along a channel showed characteristics of hydraulic flow (e.g. Jackson and

Steyn 1994b). Even for the airflow through gaps formed by isolated hills with no

stagnant cold pool upstream, shallow-water dynamics seemed to capture the essence

of the phenomenon (Pan and Smith 1999). In these cases, gap winds extending

downstream of the obstacle occur since they avoid Bernoulli loss and maintain their

velocity whereas the adjacent strong flow over the hills soon becomes subcritical and

forms a wake with weaker winds (see discussion in chapter 2). Related to gap winds

is the phenomenon of channeling such as observed in the German Upper Rhine

Valley. The key feature here is the decoupling of the flow in the valley from the

upper-level flow as the valley winds follow the pressure gradient force imposed by

the geostrophic wind balance (e.g. Wippermann 1984; Kalthoff and Vogel 1992).

1.2 Gap flow studies 7

The hydraulic aspects of flow through a horizontal contraction have been investi-

gated by several studies in a theoretical framework for continously stratified fluids as

well as single-layer shallow-water fluids. As an extension of Long’s 1954 theory and

Houghton and Kasahara’s 1968 numerical solutions for the shallow-water flow over

an infinitely long ridge, Arakawa (1969) developed the theory for a single-layer flow

in a rectangular channel through a combined lateral and vertical contraction. The

non-dimensional parameter defining the state of the flow is the local Froude number

F = U/√g∗H, with U and H being the fluid velocity and depth, respectively, and

g∗ being the reduced gravity. F describes the ratio between the fluid speed and the

velocity of linear shallow-water gravity waves. If an initially subcritical flow (F < 1),

i.e. a flow with relatively small velocities and substantial fluid depth, impinges on

a topographic contraction, i.e. rising terrain and/or narrowing channel, it can be

brought to a critical state (F = 1) at the highest and narrowest section – the ”point

of control”. The flow will become asymmetric with respect to the control, i.e. the

fluid will continously accelerate and reduce its free surface height across the contrac-

tion and will become supercritical (F > 1) to the lee. A hydraulic jump will occur

further downstream as an adjustment to the far-downstream subcritical condition.

The jump is an dissipative process which destroys kinetic energy and thus reduces

total energy (Bernoulli head). Since the control fixes the layer depth for a given

flow rate, partial blocking will occur on the windward side of the control with a bore

propagating upstream. If the highest and narrowest section of the channel do not

coincide, the location of the control is not uniquely specified by the geometry of the

channel alone but also depends upon the flow rate (Armi 1986).

The extension of the steady single-layer dynamics to the one of a stably stratified

fluid flowing through a contraction was made e.g. by Wood (1968). He studied

the flow from a stagnant reservoir through a horizontal contraction. The bottom

(top) of the lowest (uppermost) flowing layer was bounded by a stagnant fluid and

represented a surface along which the pressure gradient was zero. For two flowing

layers, he found a solution for which the velocity and density distributions are self

similar (which means e.g. that the relative change of the layer depth is the same in

each layer). Critical flow may occur at other points than the narrowest section, i.e.

at a virtual control (see also Armi 1986). For a multi-layered system the accelerating

flow is controlled at the narrowest point in the channel and through a succession of

virtual controls, at each of which the flow passes from subcritical to supercritical with

respect to a particular wave mode (see also Armi and Williams 1993). Økland (1985)

took Wood’s idea and applied it to the atmosphere, i.e. used isentropic surfaces

instead of density surfaces as streamlines. Vergeiner et al. (2003) recently tackled

the problem of adding a vertical constriction to the horizontal one (resembling the


geometry of a mountain pass) and allowing for the pressure gradient to be non-zero

at the surface (for a realistic case the pressure decreases along the valley bottom

upstream of the pass). They took Wood’s model only to a certain distance upstream

of the pass, from which on they continued with a single-layer model. In this setup

the acceleration of the flow was enough to reach a critical Froude number near the

pass height and supercritical speeds beyond. As a first step, however, this model

was designed to represent the conditions only upstream of the pass.

Recently, several three-dimensional numerical modeling studies investigated gap

wind dynamics in an idealized framework. They assumed idealized ridge-like to-

pographies having embedded gaps, and idealized initial and boundary conditions.

The influence of ambient rotation on the formation of gap flows based on a back-

ground flow mainly parallel to the ridge was studied by Sprenger and Schär (2001)

and Zängl (2002a). Such a configuration resembles e.g. the one of shallow foehn

in the Alps. Gaberšek (2002) and Zängl (2002c) investigated gap flows evolving

from a background flow which was basically normal to the ridge, i.e. had a major

component parallel to the gap axis. Such a setup might represent e.g. the one

of the Mistral winds in the French Rhône Valley. A more thorough discussion of

theses studies is given in chapter 2. Ross and Vosper (2003) investigated the role

of surface friction in stratified flow for two types of topographies: the flow through

an infinitely long valley (2D) and through a mountain pass embedded in a ridge

(3D). Outside the boundary layer the background flow was along the valley (normal

to the ridge), whereas inside the boundary layer the flow had a cross-valley (ridge-

parallel) component due to surface friction. For the 2D valley setup, separation

of the boundary-layer flow from the valley surface and the formation of a blocked

region in the valley was observed for sufficiently small Froude numbers (based on

the valley depth). For the 3D pass setup and for sufficiently strong flow, potential

vorticity generated within the boundary layer by surface friction was advected into

the interior of the flow downwind of the mountain by a hydraulic jump and thus

provided a mechanism for the formation of potential vorticity banners.

1.3 Goals and outline of the thesis 9

1.3 Goals and outline of the thesis

The aims of this dissertation are closely related to two of the five scientific objectives

of the Mesoscale Alpine Programme (MAP) as stated in the MAP Design Proposal

(Binder and Schär 1996; see also Bougeault et al. 2001):

(2a) To improve the understanding and forecasting of the life cycle of Foehn-related

phenomena, including their three-dimensional structure and associated bound-

ary layer processes.

(3) To provide data sets for the validation and improvement of high-resolution

numerical weather prediction, hydrological and coupled models in mountainous

terrain.

Further, the thesis addresses two of the three scientific questions which were formu-

lated in the MAP Science Plan (Bougeault et al. 1998) for the gap flow project P4

in the Brenner Pass region:

(1) To determine the relative importance of gap width versus terrain elevation

changes along the floor axis on deep, continuously stratified flow through real-

istic topography.

(3) To study the vertical and cross-gap distribution of wind speed and thermody-

namic properties. These are controlled by inviscid stratified dynamics together

with surface friction along the valley floor and side walls. The frictional effects

as well as dissipation and mixing of the low-level high speed flow need to be

included in realistic models.

As mentioned in the MAP Science Plan, the flow beneath a strong low-level in-

version may, in a first approximation, be studied using single-layer reduced-gravity

hydraulics. Following this idea, the first part of this thesis (chapter 2) investigates

the hydraulic aspects of the gap winds in the Wipp Valley for south foehn conditions.

The main aim is to determine how well single-layer hydraulics captures the essence

of the foehn dynamics manifested e.g. in the structure of the flow descent and in

the locations of local wind maxima, hydraulic jumps, and flow splitting. A further

aim is to find the reason for across-valley asymmetries of the flow strength and to

determine the relative importance of the vertical versus the lateral contraction of

the Brenner Pass. For this purpose, a numerical single-layer shallow-water model

designed by Schär and Smith (1993a, 1993b) is applied to the foehn flow in the Bren-

ner Pass region for various initial foehn conditions, i.e. different upstream Froude

numbers and fluid layer heights. The model version used in this study assumes a

two-dimensional hydrostatic flow over realistic orography neglecting surface friction


and ambient rotation. The model fields are compared with measurements from the

MAP SOP. The results of this study were submitted to the Quarterly Journal of the

Royal Meteorological Society.

The second part (chapter 3) provides verification of a specific deep foehn simulation

conducted with a high-resolution three-dimensional numerical weather prediction

system, the Penn State/NCAR mesoscale model MM5. The verification is based on

a detailed comparison of the model fields with remote sensing observations (lidar

and sodar), surface measurements, and radiosoundings, which were collected during

the MAP IOP 10. The aims are to assess the quality of a high-resolution simulation

with a state-of-the-art model concerning details of the flow structure, try to quantify

differences between predicted and observed fields based on error measures, as well

as to illuminate the reasons for these discrepancies. The results of this investigation

were submitted to the Monthly Weather Review.

The last part (chapter 4) briefly summarizes the main results from the previous two

studies, whereby more detailed conclusions are given in section 2.6 and 3.6. This

chapter also provides an outlook for future work to address remaining questions.

Chapter 2

Hydraulic aspects of foehn

11

Hydraulic aspects of foehn winds in an Alpinevalley ∗

Alexander Gohm † and Georg J. Mayr

Department of Meteorology and Geophysics, University of Innsbruck, Austria

Summary

This study examines the applicability of single-layer hydraulic theory to Alpine foehn

winds for the example of the flow in the Brenner Pass region (Austria/Italy). South foehn

is described as gap flow over the pass and along the associated Wipp Valley. Numerical

shallow-water simulations for a wide range of initial conditions including shallow and deep

foehn cases are discussed and compared with selected measurements collected within the

Mesoscale Alpine Programme (MAP). The observational analyses are based on Doppler

and aerosol backscatter lidar data for a specific foehn case and on surface observations

and radiosoundings for all foehn cases observed within the 70-day MAP Special Observing

Period (SOP).

Radiosoundings at a location up- (south) and downstream (north) of the pass reveal

that the average MAP SOP foehn case had subcritical flow south and nearly critical flow

north of the Brenner. The hydraulic model indicates flow transition to a supercritical

state near the pass, a hydraulic jump 2 km further north, mainly subcritical flow in the

upper Wipp Valley except near the Brenner, and especially for shallow foehn a tendency

for becoming supercritical in the lower Wipp Valley. The model results suggest that the

vertical topographic contraction exerts stronger control for the flow at the Brenner gap

than the lateral contraction. In accordance with Doppler lidar measurements the hydraulic

model captures the decrease of the wind speed in across-valley direction from east to west

in the northern part of the valley. This asymmetric flow pattern is a result of the complex

valley geometry rather than the influence of upper-level synoptic winds as suggested in a

previous study.

For some observed cases the strength of the temperature inversion on top of the foehn

layer decreased across the pass presumably due to entrainment processes. Consequently,

the reduced gravity decreased as well. The less than perfect agreement between the hy-

draulic parameters retrieved from soundings and those provided by the model has two

major reasons: The model assumes a constant reduced gravity and the calculation of hy-

draulic parameters for foehn cases without a strong and sharp temperature inversion is

ambiguous. Essential flow patterns in the simulated fields, such as the location of the pres-

sure minimum and wind speed maxima, compare well with the surface observations along

a valley transect. Indications for a steeply amplified or breaking gravity wave resembled

by a hydraulic jump to the lee of two mountain ridges are found in lidar observations as

well as simulations.

∗Submitted to Quarterly Journal of the Royal Meteorological Society, February 2003†Corresponding author: Department of Meteorology, University of Innsbruck, Innrain 52, A-

6020 Innsbruck, Austria; e-mail: [email protected]

13

14 Hydraulic aspects of foehn

2.1 Introduction

The goal of this study is to elucidate the dynamics of south foehn winds in an

Alpine valley by means of single-layer hydraulic theory. We address the question

how well hydraulics captures the features of gap winds using the example of the

foehn flow over the Brenner Pass (Austria/Italy) and along the associated Wipp

Valley. The work is part of extensive research activities which have been carried out

within the framework of the Mesoscale Alpine Programme (MAP). Our investigation

incorporates part of the data set collected during the 70-day MAP Special Observing

Period (SOP) in fall 1999 (Bougeault et al. 2001). The observational analysis

complements the numerical results of a shallow-water model.

2.1.1 Topographic environment

The European Alps act as a major obstacle for the impinging large-scale atmospheric

flow. Instead of being simply an elongated, arc-shaped barrier with a smooth surface,

the Alpine massif has a complex structure with many embedded valleys (Fig. 2.1).

Some of them are aligned towards the main Alpine crest where they form more or less

deep incisions in the crest line. These usually very narrow mountain passes are not

only hot spots for the channelling of transalpine traffic causing air quality problems

and noise pollution, but also for the channelling of airflow leading to the formation of

gap flows with partly severe winds. The Brenner Pass (BRE), located in the central-

northeastern part of the Alps, is at 1373 m MSL one of the deepest incisions in the

Alpine chain. The associated valley is the Wipp Valley which stretches in a south-

north direction from the Italian town Sterzing (STZ) to the Austrian city Innsbruck

(IBK) where it merges with the east-west aligned Inn Valley (Fig. 2.2(a)). To the

north, the Inn Valley is bounded by the mountain range Nordkette. The Wipp

Valley has several tributaries with the largest being the Stubai and the Gschnitz

Valley. The pass has a double-gap structure (Fig. 2.2(b)). The base heights (central

widths) are approximately 1.4 km MSL (2 km) for the lower gap and 2.1 km MSL

(15 km) for the upper gap.

2.1.2 Types of foehn

Describing Alpine south foehn as gap flow is a new concept which has been applied

especially since MAP. However, ”gap flow” and ”foehn” are not synonyms. The

former is a rather distinctive description for the below-crest-level flow through the

Brenner gap and along the Wipp Valley. South foehn includes the low-level gap flow

but is a rather general description for the mountain induced downslope windstorm

to the lee of the Alps. It is therefore not necessarily restricted to the locations of

2.1 Introduction 15

Longitude (deg E)

Latit

ude

(deg

N)

Gulf ofGenoa

AdriaticSea

Po Valley

(a)

4 6 8 10 12 14 1643

44

45

46

47

48

49

x (km)

y (k

m)

(b)

BRE

ZUGInn Valley

WippValley

P1

P2

P3

P4

−40 −20 0 20 40

−40

−20

0

20

40

60

Figure 2.1: Topographic map of the European Alps (a) and the MAP Brenner Pass

target area (b). The rectangle in (a) shows the location of the full SWM domain which is

displayed in (b). In (b) the solid rectangle indicates the subdomain of Figs. 2.2(a), 2.6–

2.8 and the two dotted rectangles show the subdomains of Figs. 2.13–2.14. Grey shaded

elevation contours in (a) start at 0 m with increments of 600 m and in (b) at 900 m with

increments of 300 m. The 600-m contour line in (b) is light grey. The dashed line in (b)

denotes the cross-section of Fig. 2.5. The solid line P1P2 indicates one flight leg of the

NCAR Electra aircraft on 20 October 1999 as shown in Fig. 2.15. The solid line P3P4

denotes the cross-section of Fig. 2.12. Filled circles mark the Brenner Pass (BRE, 1373 m)

and the mountain peak Zugspitze (ZUG, 2962 m).

topographic gaps. South foehn is usually divided into a shallow and a deep type

depending on the structure of the above-crest level winds (e.g. Kanitscheider 1932;

Seibert 1990). For the shallow foehn case geostrophic winds have rather westerly

directions and are therefore aligned parallel to the main Alpine ridge or upper-level

winds may be weak at all. The driving force for the cross-Alpine flow through

the gaps is a northward-pointing pressure gradient force which has basically two

potential sources: a synoptic-scale pressure difference due to a depression north of

the Alps and a hydrostatically induced pressure difference on the mesoscale due to

air mass differences north and south of the Alps. The southerly flow is confined to

below the main Alpine crest height at approximately 3 km MSL. For the deep foehn

case the geostrophic wind direction above the crest has a component perpendicular to

the Alpine ridge and the forcing for cross-barrier flow is therefore stronger. The Alps

are on the leading edge of a synoptic-scale pressure trough and southerly winds are


x (km)

y (k

m)

(a)

STZ

IBK

SER

NOS

SAB BRE

ELB GED

STE

PAK

IV

SV

GV

WV

NK

−30 −20 −10 0 10

−10

0

10

20

30

40

−30 −20 −10 0 10

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

Hei

ght (

km M

SL)

x (km)

(b)

SWMHigh Resolution

Figure 2.2: Topographic map of the Wipp Valley region (a) and height of the main

Alpine crest across the Brenner Pass (b). Elevation contours in (a) are shaded as in

Fig. 2.1(b). The white dashed line in (a) indicates the crest line shown in (b). The black

dotted line in (a) denotes the cross-section of Fig. 2.5. The solid and dashed lines in

(b) are the crest lines as represented by the SWM orography and by a 30-m-resolution

orography, respectively. Crosses in (a) indicate automatic weather stations, among others,

at Sterzing (STZ, 944 m), Brenner (BRE, 1373 m), Steinach (STE, 1116 m), Gedeir (GED,

1084 m), Ellbögen (ELB, 1080 m), and Innsbruck (IBK, 609 m). Filled circles in (a) mark

the mountain peaks Sattelberg (SAB, 2107 m), Nösslachjoch (NOS, 2231 m), Serles (SER,

2717 m), and Patscherkofel (PAK, 2252 m). Italic letters in (a) denote the location of the

Wipp Valley (WV ), Inn Valley (IV ), Stubai Valley (SV ), Gschnitz Valley (GV ), and the

northern range Nordkette (NK ).

therefore present at least throughout the lower troposphere. Downslope windstorms

to the lee may be observed even in valleys which have no origin at the main crest,

i.e. which are rather west-east aligned. In the Wipp Valley a low-level gap flow is

embedded in the deep foehn flow.

2.1.3 Gap flow studies

Gap flows occur in many mountainous parts of the world. Pan and Smith (1999)

compiled an extensive list of literature about gap wind observations. They also

reviewed two analytical models, linear theory of continuously stratified flow and

non-linear shallow-water flow, for the application to gap winds.

2.1 Introduction 17

Continuously stratified gap flows

Armi and Williams (1993) studied the steady hydraulics of a continuously stratified

fluid flowing through a horizontal contraction in an experimental and theoretical

manner. Their results showed that the flow passes from sub- to supercritical (with

respect to a particular wave mode) at a succession of virtual controls as the flow

accelerates through the contraction. Recently, several numerical studies treated gap

winds as stratified flow past idealised gap-like topographies (Sprenger and Schär

2001; Zängl 2002a, 2002c; Gaberšek 2002). Sprenger and Schär (2001) investigated

the role of earth’s rotation assuming a geostrophically balanced westerly flow par-

allel to an infinitely long ridge with an embedded gap excluding surface friction.

This setup resembles idealized conditions for shallow south foehn in the Alps. The

proposed mechanism for the formation of the gap winds is the decoupling of the flow

within the gap from the geostrophic flow aloft. The southerly gap flow is then driven

by the geostrophic pressure gradient across the ridge. Zängl (2002a) showed that

the replacement of this infinite ridge by an isolated one fundamentally changes the

gap flow pattern. Flow splitting on the upstream edge of the isolated mountain and

Coriolis effects can even result in a weak northerly gap flow since the geostrophic

pressure gradient is compensated or even reversed by potentially cold low-level air

which is piled up along the northern side of the mountain. Simulations with an

arc-shaped mountain similar to the real Alps showed that a southerly component in

the large-scale flow appears to be necessary to obtain southerly gap flows. In such

a case a hydrostatic pressure difference across the Alps forms as potentially cold

low-level air is piled up on the southern side of the Alps. Two studies discussed,

among other details, gap winds arising in a non-rotating environment for large-scale

flow perpendicular to an elongated mountain with an embedded level gap (Zängl

2002c; Gaberšek 2002). Zängl (2002c) noted that in the linear regime wind and

pressure perturbations along the gap are caused by gravity waves radiating from

the mountain towards the gap axis, and by low-level confluence within the gap.

In the non-linear regime, however, confluence becomes negligible due to upstream

blocking and the amplitude of the vertically propagating gravity waves is reduced

due to low-level wave breaking. In this regime the driving force for the gap flow

is the low-level pressure difference across the mountain. Similar to Zängl’s results,

Gaberšek (2002) identified two mechanism responsible for gap flow enhancement de-

pending on the non-dimensional ridge height ε = Nh/U (which describes the degree

of non-linearity), with h being the obstacle height, U the uniform fluid velocity, and

N the buoyancy frequency. The first one is characterized by a mountain lee-wave

(ε ∼ 1) and the second one by upstream flow blocking (ε ≥∼ 5).


Single-layer hydraulic gap flows

The simplified problem of a single-layer fluid with a free surface flowing through a

gap is related to the problem of a single-layer shallow-water flow over a ridge (see

the review of its theory e.g. in Henderson 1966; Baines 1995; Durran 1990). The

continuous acceleration of the flow across the ridge is related to the transition from

a subcritical into a supercritical state at the summit where the local Froude number

F = U/√g∗H becomes unity, i.e. where the speed of the flow U equals the speed

of linear shallow-water gravity waves√g∗H (with g∗ being the reduced gravity and

H the fluid layer depth). Further downstream of the obstacle, a hydraulic jump

causes the transition back into a subcritical state. Dissipation of energy in the jump

reduces the Bernoulli function. The two parameters controlling the flow are the

upstream Froude number F∞ = U∞/√g∗H∞ and the non-dimensional mountain

height M = hm/H∞ (ratio between the ridge height and the upstream depth of

the fluid layer). Arakawa (1969) presented a theory which combines the effects of a

lateral and a vertical contraction of the orography for the flow through a channel.

He applied it to gap winds occurring in Hokkaidō, Japan. A lateral contraction

due to a gap has a similar effect as a vertical contraction due to a ridge or as a

combination of both (rising terrain height and decreasing channel width). All three

configurations favour flow transition from a sub- to a supercritical state at the point

of control which is at the narrowest and highest part of the orography. A more

complicated situation occurs if the highest and narrowest section do not coincide.

In such a case critical flow will occur somewhere in between and the exact location of

the control depends not only on the geometry of the channel but also on the flow rate

(Armi 1986). Applications of the single-layer hydraulic concept with a comparison

to observations include studies of gap winds in the Rhône Valley (Pettre 1982), near

the Howe Sound (Jackson and Steyn 1994b; Finnigan et al. 1994), in the Strait

of Gibraltar (Dorman et al. 1995), and near the Aleutian Chain (Pan and Smith

1999). The shallow-water simulations of Pan and Smith (1999) showed qualitative

agreement with the flow field derived from satellite-borne synthetic aperture radar

(SAR) images. Their numerical results obtained for real terrain geometry (mountain

gaps in Unimak Island) as well as for a family of idealized gap topographies (gap

formed by two bell-shaped hills) showed that critical conditions always occurred first

at the mountain peaks. They concluded that the effect of rising terrain dominates

over the effect of difluence (near a peak) and confluence (near a saddle). The authors

describe gap winds as streams of air that have avoided Bernoulli loss over the terrain

by passing through gaps and thus have maintained their strength in the wake – in

contrast to the airflow over the adjacent hills that has experienced strong Bernoulli

loss in hydraulic jumps leading to weak flow in the wake.

To our knowledge, the first work which discussed the similarity between the

2.1 Introduction 19

dynamics of south foehn in the Wipp Valley and the one of a hydraulic flow with a

free surface was by Schweitzer (1953). His interpretation of south foehn was the one

of a shooting flow with supercritical velocity, i.e. with fluid velocities exceeding the

linear gravity wave speed. These gravity waves are excited at an internal interface

formed by a temperature inversion. Such an inversion layer is a frequently observed

foehn property (e.g. Seibert 1990). Schweitzer explained the observed rotors in the

foehn flow as hydraulic jumps. The description of foehn by means of hydraulic theory

experienced a renaissance during the planning phase of the MAP SOP (Bougeault

et al. 1998). It was noted that the flow beneath a strong low-level inversion may

be studied, in a first approximation, using single-layer reduced-gravity hydraulics.

Flamant et al. (2002) followed this idea in a study of a shallow foehn event observed

during the MAP Intensive Observing Period (IOP) 12. A quasi two-dimensional

steady-state hydraulic model was used for the calculation of the Froude number along

the Wipp Valley. Essentially, this model describes the flow through a rectangular

channel having rigid side walls with varying channel width and bottom height, and

with constant fluid layer height across the valley. The underlying concept is similar

to the one used in Jackson and Steyn (1994b) for the Howe Sound, except that the

latter included the effect of an external large-scale pressure gradient and of surface

friction. The change of the channel width along the Wipp Valley was idealized with

a parabolic function. There are several problems connected to this simplified quasi

two-dimensional consideration: The concept neglects the effects of the tributary

valleys, which is justified for cases only where the flow into the Wipp Valley is

weak. The definition of the channel width at locations where tributary valleys

merge with the Wipp Valley seems to be problematic and to some extent arbitrary.

As mentioned also by the authors, the treatment of the flow to be homogeneous in

across-valley direction (which arises from the definition of a rectangular geometry

of the valley) has its limitations since the real valley topography has a complex

structure favouring across-valley variations of the flow. Finally, cases where the

fluid height exceeds the height of the sidewalls cannot be treated and therefore the

quasi two-dimensional concept is limited to very shallow foehn cases.

Our approach of the problem differs from the quasi two-dimensional concept in

the point that we solved the time-dependent hydraulic equations for a truly two-

dimensional single-layer shallow-water flow over realistic orography. It is therefore

similar to the approach in Pan and Smith (1999) and avoids the above mentioned

problems of the quasi two-dimensional concept. The paper is organized as follows:

Section 2.2 introduces the hydraulic model and describes the observational data

set. Section 2.3 gives a motivation for the application of hydraulic theory to foehn

winds in the Wipp Valley. The numerical results for various upstream conditions are

discussed in section 2.4. Section 2.5 presents a comparison of the hydraulic solution


with observations. The study concludes with a summary in section 2.6.

2.2 Model and measurement description

2.2.1 The shallow-water model

The numerical shallow-water model (SWM) used in this work was developed by

Schär and Smith (1993a, 1993b). Applications of the SWM include e.g. the study

of bottom friction for the flow past an isolated obstacle (Grubǐsić et al. 1995), wake

formation by mountains (Smith and Smith 1995; Smith et al. 1997), gap winds

in the Aleutian Chain (Pan and Smith 1999), and the generation of shocks in a

single-layer (Jiang and Smith 2000) and a two-layer (Jiang and Smith 2001a, 2001b)

flow. The reader is referred to these studies for a detailed description of the model.

Our version of the SWM is based on the two-dimensional governing equations for a

single-layer hydrostatic flow without ambient rotation and surface friction:

Dû

Dt̂+∂(ĥ + Ĥ)

∂x̂= 0, (2.1)

Dv̂

Dt̂+∂(ĥ + Ĥ)

∂ŷ= 0, (2.2)

∂Ĥ

∂t̂+∂(ûĤ)

∂x̂+∂(v̂Ĥ)

∂ŷ= 0, (2.3)

with the non-dimensional variables (henceforth generally labelled with hats) û and v̂

as the two horizontal velocity components, Ĥ and ĥ as fluid layer depth and terrain

height, respectively, Ẑ = ĥ+Ĥ as fluid layer height, and t̂ as time. Equations (2.1)–

(2.3) are non-dimensionalised with the following scales: a typical length L for the

horizontal length scale, the initial far-upstream depth of the fluid layer H∞ (with

h∞ = 0) for the vertical length scale, the phase speed of linear gravity waves√g∗H∞

for the velocity scale, and the time scale L/√g∗H∞. The reduced gravity is defined

as g∗ = g∆ρ/ρ with ρ being the density of the fluid and ∆ρ being the density

difference across the free surface. With a typical wind speed of the foehn flow of

U = 15 m s−1, a length scale of L = 50 km (length of the Wipp Valley between

STZ and IBK), and a Coriolis parameter of f = 1.1× 10−4 s−1, the typical Rossbynumber is Ro = U/(fL) ≈ 2.7. Thus, the neglect of Coriolis effects is justified to afirst approximation. The SWM solves Eqs. (2.1)–(2.3) in the momentum flux form.

Its numerical scheme conserves mass and momentum but allows energy dissipation

such as the destruction of kinetic energy in hydraulic jumps. The model has the

capability of handling material surfaces collapsing to zero-mass layers at regions

where the topography pierces the fluid (Schär and Smolarkiewicz 1996). This is

2.2 Model and measurement description 21

of particular importance for the simulation of shallow foehn cases where the flow

through the Brenner gap is confined to heights below the main Alpine crest and

therefore mountains may protrude through the top of the fluid.

The total domain of the SWM orography is shown in Fig. 2.1(b). It is centred

near the Brenner Pass and covers the Wipp Valley and major parts of the Inn Valley.

The domain is resolved with 233 (259) grid points in west–east (south–north) direc-

tion and with a mesh size of 500 m. As shown in Fig. 2.2(b) the essentially structure

of the Brenner gap in the Alpine ridge is well resolved in the SWM orography, al-

though the heights of the pass and of individual mountain peaks are off by an order

of 200 m compared to a high-resolution elevation model. The choice of the horizontal

length scale L does not affect the general type of the solutions of the shallow-water

equations. For example, a doubling of the non-dimensional mesh sizes ∆x̂ and ∆ŷ

will only stretch the flow but will not change its regime and general pattern. For

convenience, we chose L = 1 km which gives a grid spacing of ∆x̂ = ∆ŷ = 0.5. The

non-dimensional time step was ∆t̂ = 0.1. The initial flow, having a horizontally

homogeneous layer height and constant southerly velocity, was introduced as an im-

pulsive start from rest. The model was integrated with 3000 iterations (t̂ = 300) to

obtain a quasi-steady state. Near the lateral boundaries the flow was relaxed to the

initial values within a region spanning over 8 grid points. This boundary condition

effectively removes propagating disturbances, such as hydraulic jumps, impinging

on the boundaries from the model domain interior without noticeable reflections.

For an initial fluid layer height Z0 and velocity U0 being horizontally homoge-

neous and for a specific topography, the solution of the flow is determined by Z0

and the initial local Froude number F(0,X) at an arbitrary place X (such as at the

upstream location STZ with F(0,STZ) = U0/√

g∗H(0,STZ)). We performed a total of

35 simulations with the control parameters Z(0,STZ) = 2, 2.5, 3, 3.5, 4 km MSL

and F(0,STZ) = 0.25, 0.5, 0.75, 1, 1.25, 1.5, 2. For the sake of clarity the name of

the simulations include these two parameters, e.g. Z20F025 denoting the simula-

tion with Z(0,STZ) = 2 km MSL and F(0,STZ) = 0.25. At t̂ = 300 two simulations,

Z35F200 and Z40F200, had still supercritical flow at Sterzing (F(300,STZ) > 1; see

Fig. 2.4(a)). Such cases are rather unlikely to be observed (see section 2.3) and they

are therefore skipped in the following discussion. Based on the flow field at t̂ = 300,

the remaining 33 numerical experiments are divided into 10 shallow foehn cases with

Z(300,STZ) < 3.2 km MSL and 23 deep foehn cases with Z(300,STZ) ≥ 3.2 km MSL.

2.2.2 Weather stations and radiosoundings

During the MAP SOP the Wipp and Inn Valley were instrumented with a total

of 35 automatic weather stations. Mayr et al. (2003a) give a detailed description


of the gap flow measurements during MAP. In our study we used the 10-minutes-

average data set from a subset of 16 stations aligned along the Wipp Valley floor

between STZ and IBK (see Fig. 2.2(a)). During south foehn conditions radiosondes

were released, among other places, at STZ and Gedeir (GED) (see Fig. 2.2(a)) to

record the vertical conditions up- and downstream of the pass. From a total of 17

IOPs, soundings were made during 11 IOPs at STZ and during 7 IOPs at GED. We

used the whole data set of these two stations for the statistical analysis of hydraulic

parameters.

2.2.3 Lidars

During the MAP SOP, the National Oceanic and Atmospheric Administration’s

Environmental Technology Laboratory (NOAA/ETL) operated a scanning Doppler

lidar (TEACO2) in the Wipp Valley at Gedeir (GED) about half way between the

Brenner Pass and Innsbruck (see Fig. 2.2(a)). The system is described in Post and

Cupp (1990). Recent analyses of its MAP data set are presented in Gohm et al.

(2003), Flamant et al. (2002), and Durran et al. (2003). Other studies containing

TEACO2 observations involve e.g. the investigation of flows in the Grand Canyon

(Banta et al. 1999), on the Colorado Front Range (Neiman et al. 1988; Darby

et al. 1999), and at the Monterey Bay (Darby et al. 2002b). The lidar emits

pulses of infrared light at 10.59 µm. The signal is backscattered from aerosols

which move with the flow. The Doppler-shifted frequency of the received signal

reveals the radial wind velocity component along the direction of the lidar beam. In

our definition, winds towards (away from) the lidar have positive (negative) radial

velocities. Various types of elevation and azimuthal scans were conducted, typically

within two sectors centred at an azimuth angle up-valley (178◦) and down-valley

(320◦) of the lidar site.

The Scanning Aerosol Backscatter Lidar (SABL) of the National Center for

Atmospheric Research (NCAR) was operated during several MAP foehn cases on

board the NCAR Electra aircraft in a nadir-pointing mode. A brief description of

the system is given e.g. in Rogers et al. (1998). SABL data were recently used in

a study of a deep foehn event which was part of the MAP IOP 10 (Gohm et al.

2003). The lidar emits pulses of light at 532 nm (green) and 1064 nm (infrared) and

detects the signal backscattered from aerosols, air molecules, and hydrometeors.

The backscattered signal describes the aerosol structure in the lower troposphere

along the trajectory of the aircraft. In our study we used the 1-Hz data set of the

green channel with a resolution of 7.5 m along the lidar beam. The top of multiple

aerosol layers can be estimated from backscatter intensity profiles with a simple

gradient-method described by Gohm et al. (2003).

2.3 Motivation for hydraulic solutions 23

The analysis of lidar data presented herein focuses on the foehn event of 20

October 1999 (MAP IOP 8). Investigated TEACO2 data include scans performed

within one hour centred at 14 UTC. SABL data are used from one short flight leg

flown near 14 UTC across the Inn Valley at a cruising altitude of 5.2 km MSL (see

Fig. 2.1(b)).

2.3 Motivation for hydraulic solutions

2.3.1 Vertical structure of foehn winds

The vertical structure of Alpine south foehn is usually associated with a more or less

pronounced stable layer (in frequent cases a temperature inversion) on top of the less

stably stratified foehn flow (see e.g. Fig. 2.3). Within this layer winds frequently

change from across-barrier (southerly) direction near its bottom to along-barrier

(westerly) direction near its top. The wind shift is most pronounced for shallow

foehn for which the cross-mountain flow is confined to below the main Alpine crest

level (and therefore restricted to major gaps in the Alpine topography) and where the

prevailing synoptic winds are westerly. Vertically propagating gravity waves excited

by the orography decay as they pass the zone of turning winds due to 3D-critical-

level absorption (e.g. Shutts 1995). The directional wind shear and the density step

(caused by the stability change) across the transition zone decouples the underlying

foehn winds from the upper-level flow. Through the decoupling the influence of

the terrain is essentially restricted to the foehn layer and not transmitted to the

upper-level flow. Therefore, the dynamics of foehn, especially the one of the shallow

type, may be governed to a certain extent by reduced-gravity single-layer shallow-

water hydraulics. Consequently, the free surface height of the single-layer system

would represent the centre height of the stable layer. The former is an infinitely

thin boundary between the lower flowing fluid and some passive fluid aloft, whereas

the latter is a boundary of finite depth between the foehn layer and the upper-

tropospheric flow. For a well-developed deep foehn the shift to westerly winds

rather occurs in the upper troposphere or even near the tropopause and no distinct

temperature inversion may be found. Thus, the decoupling is not as pronounced as

for shallow foehn.

2.3.2 An exemplary case

Figure 2.3 depicts the vertical structure of a foehn event observed during the MAP

IOP 8. In its early stage it was a pure shallow foehn which became deeper in the

afternoon of 20 October 1999. Data were taken from two radiosonde ascents at

Sterzing and Gedeir on 12 UTC 20 October 1999. These two soundings illustrate


0 5 10 15 201

1.5

2

2.5

3

3.5

4

4.5

5

Wind Speed (m/s)

Hei

ght (

km M

SL)

(b)

90 135 180 225 2701

1.5

2

2.5

3

3.5

4

4.5

5

Wind Direction (deg)

Hei

ght (

km M

SL)

(c)

285 290 295 300 305 3101

1.5

2

2.5

3

3.5

4

4.5

5

Potential Temperature (K)

Hei

ght (

km M

SL)

(a)

STZGED

Figure 2.3: Vertical profiles from radiosonde ascents at Sterzing (940 m MSL; solid line)

and Gedeir (1070 m MSL; dashed line) on 12 UTC 20 October 1999. Potential temperature

in K (a), wind speed in m s−1 (b), and wind direction in degrees (c). Stars and crosses

denote the bottom and the top of the foehn flow, respectively. Upward and downward

pointing triangles indicate the bottom and the top of the strongly stable layer, respectively.

hb Z ∆Z H U ∆θ θ g∗ c

Location (m MSL) (m MSL) (m) (m) (m s−1) (K) (K) (m s−2) (m s−1) F

Sterzing 2010 2900 650 890 6 6.4 290 0.22 14 0.4

Gedeir 1110 2390 540 1280 14 6.6 293 0.22 17 0.8

Table 2.1: Hydraulic parameters calculated from two radiosoundings. Radiosonde ascents

at Sterzing and Gedeir on 12 UTC 20 October 1999. See text for further explanation.

the basic features of the foehn flow and the modification which the flow experiences

as it crosses the Brenner Pass. The centre height of the stable layer Z, which

marks the top of the foehn flow, is located at 2900 m MSL at STZ and descends

to 2390 m MSL at GED. The depth of the temperature inversion ∆Z reduces from

650 m upstream to 540 m downstream of the pass. Flow descent and vertical mixing

causes warming of the foehn air and the formation of a jet with velocities exceeding

15 m s−1 to the lee of the pass. In both profiles, winds change across the stable layer

from southerly to westerly directions. Upstream of the pass the bottom height of

the foehn flow hb does not coincide with the ground level. The flow is nearly blocked

to a height of 2010 m MSL which is the base height of the upper Brenner gap (see

Fig. 2.2(b)). For the calculation of the local Froude number of the foehn layer the

following parameters have to be retrieved from the two soundings: the depth of

the foehn layer H defined as the depth between hb and Z, the mean wind speed U

averaged vertically over H , the difference of potential temperature ∆θ across the

stable layer, and the average potential temperature of the foehn layer θ. Based

2.3 Motivation for hydraulic solutions 25

hb Z ∆Z H U ∆θ g∗ c

Location Measure (m MSL) (m MSL) (m) (m) (m s−1) (K) (m s−2) (m s−1) F

Sterzing Average 1400 3730 970 2330 7 9 0.29 26 0.3

Minimum 940 2700 90 890 2 3 0.09 11 0.1

Maximum 2040 5590 2870 4550 17 19 0.60 46 0.7

Gedeir Average 1120 2660 630 1540 14 5 0.17 16 0.9

Minimum 1070 2010 180 910 7 2 0.06 9 0.5

Maximum 1400 3510 2070 2440 22 11 0.36 28 1.3

Table 2.2: Statistical analysis of hydraulic parameters. Calculated from 49 radiosonde

ascents at Sterzing and 23 at Gedeir during south foehn conditions within the MAP SOP.

See text for further explanation.

on these parameters the reduced gravitational acceleration g∗ = g∆θ/θ, the local

gravity wave speed c =√g∗H , and finally the local Froude number F = U/

√g∗H

can be derived. Table 2.1 lists these parameters for the two soundings. The observed

flow is clearly subcritical at STZ (F = 0.4). At GED the mean wind speed is close

to the local gravity wave speed and therefore the flow is nearly critical (F = 0.8).

Transition to supercritical flow (F > 1) in between these two locations, i.e. near the

pass, and further downstream of GED are likely to occur as we will see in section 2.4.

2.3.3 Statistical analysis

Table 2.2 provides a statistical analysis of the MAP SOP radiosonde data set col-

lected during south foehn conditions. The analysis is based on 49 soundings from

STZ and 23 from GED. Wind data, and thus local Froude numbers, are available

only for 41 soundings from STZ and 21 from GED. Orographic blocking in the

basin of STZ occurred in many foehn cases. On average, however, the height of the

blocked layer was lower than in the discussed IOP 8 case. It coincided with the base

height of the lower Brenner gap at 1400 m MSL. At GED the foehn flow typically

reached the surface with the exception of a few cases where it was lifted a few 100 m

off the ground. At STZ the centre height of the stable layer Z marking the top of

the upstream foehn flow ranged between 2700 and 5590 m MSL with an average

of 3730 m MSL. The stable layer usually had a depth ∆Z of several 100 m. The

potential temperature step ∆θ across the stable layer (corresponding to a vertical

density step) was on average lower at GED (5 K) than at STZ (9 K). The hori-

zontally varying density step led to a on-average reduction of the reduced gravity

between STZ and GED from 0.29 to 0.17 m s−2 and thus also to a reduction of the

gravity wave speed from 26 to 16 m s−1. Farmer and Armi (1999) observed such a

decrease of the density difference along the flow trajectory for stratified flow over a

sill in the Ocean and discussed its effects on the modification of the hydraulic solu-


tion. The decrease was by a factor of four between an upstream location and the sill

crest. They explained it to be caused by entrainment processes which continuously

eroded the stable layer. It is likely that for south foehn in the Wipp Valley a similar

mechanism occurs. However, the effect is certainly smaller than in the Oceanic case

since the on-average change is less than a factor of two and in cases as the IOP 8

(see Table 2.1) and IOP 12 (see Flamant et al. 2002) even negligible. In these two

events the potential temperature step was basically constant along the Wipp Valley

cross-section. The flow at STZ during MAP SOP south foehn conditions was always

subcritical with an average local Froude number of 0.3. The average wind speed at

GED of 14 m s−1 was close to the value of the gravity wave speed, which means that

the flow was nearly critical on average. However, the maximum of F = 1.3 indicates

that at least in some cases the flow became supercritical at GED. The numerical

simulations in section 2.4 will identify potential locations for supercritical flow.

2.4 Numerical solutions for different upstream

conditions

2.4.1 Condition upstream of the pass

Figure 2.4(a) depicts the flow conditions at the upstream location Sterzing for all

35 simulations at the initial state (t̂ = 0) and the quasi-steady state (t̂ = 300). All

simulations except two (Z35F200 and Z40F200) have subcritical flow upstream of

the pass at t̂ = 300. This is due to the ridge-like geometry of the Brenner Pass

orography, which causes partial blocking of the upstream flow with lifting of the free

surface and a reduction of the fluid velocity (Long 1970). The difference between

the initial and final layer height at STZ is therefore a measure for the amount

of upstream blocking. While the upstream reservoir height is lifted by blocking,

the downstream reservoir height is reduced due to the Bernoulli loss in a series of

hydraulic jumps. This reservoir difference can be interpreted as a pressure gradient

across the Alps. For the 33 simulations with subcritical upstream flow at t̂ = 300,

29 cases had critical flow near the Brenner Pass. In four cases (Z25F025, Z30F025,

Z35F025, and Z40F025) the flow remained subcritical there (Fig. 2.4(b)). In the

former cases the pass is controlling the flow rate through the gap by adjusting the

layer height to a specific value. This explains the non-linear relation between the

final layer height ZSTZ and the final Froude number FSTZ in Fig. 2.4(a)–(b). Such

a non-linear relation was derived by Arakawa (1969) (as an extension of Long’s

1954 result) for the critical non-dimensional mountain height Mc = hc/H∞ (ratio

between critical ridge height and upstream layer depth) of a ridge in a rectangular

channel with variable channel width d. For steady-state conditions a subcritical flow

2.4 Numerical solutions for different upstream conditions 27

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5Initial and Final Conditions

Upstream Froude Number

Laye

r H

eigh

t (km

MS

L)

←subcritical supercritical→

(a) InitialFinal

C1

S1 S2

S3 S4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5Final Conditions

Upstream Froude Number

Laye

r H

eigh

t (km

MS

L)

(b) F=1 near BREF


result, since it basically says that the flow over the Brenner Pass is mainly controlled

by the vertical topographic contraction of the gap, i.e. the effect of the lateral

contraction is minor. The effective controlling mountain height is at 1900 m MSL

greater than the actual height of the pass but slightly below the base height of

upper gap (see Fig. 2.2(b)). The slight deviation of the model conditions to the left

of curve C1 in Fig. 2.3(b) might indicate some influence of the lateral contraction

at least for intermediate upstream fluid layer heights (≈3.5–4.5 km MSL). Some ofthe simulations with lower ZSTZ deviate to the right of C1, suggesting that the flow

is controlled by a lower effective mountain height. This might be a result of the

double-gap structure of the pass, which means that for rather deep (rather shallow)

foehn the upper (lower) gap is mainly controlling the flow.

2.4.2 Flow pattern along the Wipp Valley

To illustrate the overall similarities and local differences among the bulk of nu-

merical experiments we show four simulations which are typical for shallow foehn

(Z20F075 and Z20F125 in Fig. 2.5(a)–(b)) and deep foehn (Z25F100 and Z25F150 in

Fig. 2.5(c)–(d)). Table 2.3 lists their initial conditions at STZ and their steady-state

conditions at STZ (see also Fig. 2.4(b)) and GED. For the classification of ”shal-

low” and ”deep” we chose a threshold value for the steady-state fluid layer height

at STZ of ZSTZ = 3.2 km MSL which is close to the maximum crest height in the

Brenner region (see Fig. 2.2(b)). For cases with ZSTZ lower than this value, fluid

can only flow through the Brenner gap. High mountain peaks west and east of the

pass pierce the fluid surface and stay ”dry”. We will see that the features of shallow

foehn change rather smoothly into the ones of deep foehn as ZSTZ increases beyond

3.2 km MSL.

Figure 2.5 illustrates the flow pattern along the axis of the Wipp Valley. A

common feature in all four numerical experiments is an overall decrease of the free

surface height and an increase of the wind speed from south to north. The flow

becomes critical near the pass and stays supercritical for about 2 km, where a

Z(0,STZ) Z(300,STZ) Z(300,GED) Foehn

Simulation (km MSL) F(0,STZ) (km MSL) F(300,STZ) (km MSL) F(300,GED) type Figure

Z20F075 2.0 0.75 2.5 0.17 2.0 0.99 shallow 2.5–2.7

Z20F125 2.0 1.25 3.0 0.34 2.3 0.87 shallow 2.5–2.7

Z20F150 2.0 1.50 3.1 0.35 2.4 0.91 shallow 2.12,2.15

Z20F200 2.0 2.00 3.5 0.50 2.7 0.95 deep 2.12–2.15

Z25F075 2.5 0.75 3.1 0.06 2.5 0.97 shallow 2.12,2.15

Z25F100 2.5 1.00 3.4 0.28 2.7 0.88 deep 2.5–2.7,2.12,2.15

Z25F150 2.5 1.50 4.0 0.34 3.1 0.92 deep 2.5–2.7

Table 2.3: Parameters for selected SWM simulations. See text for further explanation.


Fwspd

0

0.5

1

1.5

2

F, w

spd

Z20F075

(a)

−10 −5 0 5 10 15 20 25 30 35 400

1

2

3

4

Hei

ght (

km M

SL)

Distance (km)

STZ BRE STE ELB IBKSTZ BRE STE ELB IBKSTZ BRE STE ELB IBKSTZ BRE STE ELB IBKSTZ BRE STE ELB IBK

Fwspd

0

0.5

1

1.5

2

F, w

spd

Z20F125

(b)

−10 −5 0 5 10 15 20 25 30 35 400

1

2

3

4

Hei

ght (

km M

SL)

Distance (km)


Fwspd

0

0.5

1

1.5

2

F, w

spd

Z25F100

(c)

−10 −5 0 5 10 15 20 25 30 35 400

1

2

3

4

Hei

ght (

km M

SL)

Distance (km)


Fwspd

0

0.5

1

1.5

2

F, w

spd

Z25F150

(d)

−10 −5 0 5 10 15 20 25 30 35 400

1

2

3

4

Hei

ght (

km M

SL)

Distance (km)


Figure 2.5: Vertical cross-section along the Wipp Valley (indicated in Figs. 2.1(b) and

2.2(a)) for the simulation Z20F075 (a), Z20F125 (b), Z25F100 (c), and Z25F150 (d) at t̂ =

300. Top panel: local Froude number (solid) and non-dimensional wind speed (dashed).

Bottom panel: fluid layer height (solid) and topography (grey-shaded) in kmMSL. Markers

indicate the location of Sterzing (STZ), Brenner (BRE), Steinach (STE), Ellbögen (ELB),

and Innsbruck (IBK).


hydraulic jump causes the flow to become subcritical again. The location of the

jump is related to the widening of the valley immediately north of BRE, but also

to the influence of a smaller ridge protruding into the valley from the eastern side.

This ridge causes the valley to bend westward for about 4 km (see Fig. 2.2(a)). In

the upper part of the Wipp Valley, except for the pass region, the flow along the

valley axis is subcritical at least to the south of Steinach (STE) with only moderate

velocities, however, it is generally stronger for deep foehn cases. While for deep

foehn cases the wind speed in the central part of the Wipp Valley shows weak

variability, for shallow foehn cases the flow continuously accelerates north of STE

and becomes supercritical a few kilometres south of Ellbögen (ELB). In nearly all

simulations the wind speed maximum along the valley axis is located in the northern

part of the Wipp Valley – frequently near ELB. For very shallow foehn cases, such

as shown in Fig. 2.5(a), a hydraulic jump occurs near ELB where the Wipp Valley

widens as it merges with the Stubai Valley. For these cases the flow along the

valley axis north of ELB is weak due to the blocking effect of the mountain range

north of IBK (Nordkette). The mass flux over the Nordkette is zero as the flow

is completely deflected into the Inn Valley. For the shallow foehn case shown in

Fig. 2.5(b) the upstream layer height ZSTZ is high enough so that part of the fluid

is able to flow over the Nordkette. In this simulation the region of supercritical flow

north of ELB extends from the Wipp Valley into the Inn Valley and at least two

hydraulic jumps can be identified between ELB and IBK. Increasing the upstream

layer height only slightly affects the magnitude of the non-dimensional wind speed

in the northern part of the Wipp Valley (see Fig. 2.5(b)–(d)). However, an increase

of the layer depth increases the gravity wave speed and therefore reduces the local

Froude number. Thus, a transition from a rather shallow to a rather deep foehn

changes the flow regime in the northern part of the transect from a supercritical

state into a nearly critical or even subcritical state. At least for the flow along the

valley axis and except for the pass region, hydraulic jumps seem to be less likely for

deep foehn cases. However, local variations of the free surface height (which would

correspond to local up- and downdrafts) are at least as strong for deep foehn cases as

for shallow foehn cases. The effect of the narrowing of the valley immediately north

of STE and the subsequent widening near the next eastern tributary valley (see

Fig.2.2(a)) is much stronger for deep foehn. In the experiment Z25F150 this lateral

contraction causes a sharp descent of the free surface height near STE together with

F > 1, an effect which is basically absent in the shallow foehn simulations.


2.4.3 Flow pattern in the Wipp and Inn Valley

The flow varies not only along the valley axis but also across. Therefore, we now

discuss the flow structure based on plan-view illustrations which cover the whole

Wipp Valley and part of the Inn Valley. Figure 2.6 displays regions with sub- and

supercritical flow. Hydraulic jumps are apparent at locations where the wind vector

crosses the ”F = 1”-contour line pointing to a region with F < 1. Figure 2.7

illustrates the wind field with horizontal wind barbs, whereby the non-dimensional

velocity was scaled with a gravity wave speed of 20 m s−1 which is close to the

average values listed in Table 2.2.

While the flow along the valley axis in the southern part of the Wipp Valley

may stay subcrit

contributions to the dynamics of south foehn · 2019. 12. 16. · considered in the hydraulic...

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