Thermally-Driven Circulations in Mountain Terrain

Slope Winds

Terminology of slope winds

Upslope winds and downslope winds

Upslope winds are often called ‘anabatic winds’

Downslope winds also called: drainage winds, katabatic winds

Theory of air drainage has a long history

Fleagle (1950) derived momentum equations for A fluid cooling at the bottom of a sloped surface.

Manins and Sawford (1979)

Horst and Doran (1986)

x

p

1

1T1 2T2

cold warm

x

z

2

21 )(

T

TTg

T1 < T2

PGF

1 > 2

=

Buoyancy

Figure 1. Basic mechanisms of downslope winds (Adapted from Atkinson, 1981)

I

z

wudg

x

p

z

uw

x

uu

t

u

rr

sin

1

where u and w are velocity components in the x and z directions, r is a reference density, p is the pressure, g is gravitational force, d is the potential temperature deficit in the flow, r is the reference potential temperature, and is the slope angle.

Term I is the storage of momentum, term II is advection, term III is the horizontal pressure gradient force, term IV is the buoyancy force, term V is the turbulent momentum flux.

Momentum budget for slope flow

II III IV V

I

where v is virtual potential temperature, Cp is the gas constant for dry air at constant pressure, R is the outgoing radiation flux, and is the turbulent sensible heat flux.

The local rate of heat storage (term I) results from an imbalance of convergence of virtual potential temperature by advection (term II), radiative flux divergence (term III), and the divergence of turbulent sensible heat flux (term IV).

Heat budget for slope flow

II III IV

z

w

z

R

Czw

xu

tv

pr

vvv

1

The budget equations for pure katabatic flow have been derived for simple situations assuming horizontally homogenous depth along a slope of infinite length.

The slope angle for katabatic flows has been assumed to be very small in the theoretical framework, and thus the flow to be in hydrostatic balance.

Manins and Sawford (1979b) suggested that even in very mountainous terrain, ‘extensive’ slopes were rarely above 10. Furthermore, the cooling is based on the three terms (II, III, and IV) in (1.2).

Horst and Doran 1986

Downslope flows (drainage flows)

Meteor Crater 2006

Campfire smoke plume-Shallow inversion Layer

Whiteman(2000)