jim o’donnell university of connecticut · 2007-08-09 · plume. journal of geophysical research...

PASI Lectures on Fronts I: Jim O’Donnell

University of Connecticut

Outline

1. History, Phenomenology and Anatomy2. Classification3. Laboratory and Numerical Analogs4. Quantitative Predictions and

Observations5. Open Questions6. Summary

The Ocean Off Montauk Point

NYRADAR View

• Uda, M. 1938. Researches on”siome” or current rip in the seas and oceans. Geophys. Mag. 11, 307-372.

• Cromwell, T. and J.L. Reid. A study of oceanic fronts. Tellus, 8, 94-101.

• Voorhis, A.D. 1969. The horizontal extent and persistance of thermal fronts in the Sargasso Sea. Deep Sea Res. 16, Suppl. 331-337.

• Zaneveld, J.R.V., M. Andrade and G.F. Beardsley, 1969. Measurements of optical properties at an oceanic front observed near the Gallapagos Islands. J. Geophys. Res. 74, 5540-5541.

Early Scientific Descriptions of Ocean Fronts

From Simpson (2006)Shelf Sea/ Tidal Mixing Front

Chlorophyll and Temperature

From Garvine, 1975River Plume Front

Old observations of the ConnecticutRiver Plume (Garvine, 1974)

•The general structure of surface salinity

•SigmaT Cross Section

Connecticut River

Long Island Sound Ebb

Across Front Section

River Plume Front

Tidal Intrusion Front

Simpson, J.H. and R.A. Nunes, 1981

00 /)( ρρρ −=b

Consider the conservation of MASS in a moving. turbulent Incompressible fluid subject to heating, then defining the buoyancy

),,,( tzyxBDtDb

Σ+∇=

),,,( tzyxzB

tb z Σ+

∂∂

+∂∂

−∂∂

−=∂∂

Which, assuming that only the vertical turbulent flux component is significant, can be written as

2. Front Classification

⎭⎬⎫

⎩⎨⎧

∂∂

+∂∂

∂∂

⎭⎬⎫

⎩⎨⎧ Σ+∂∂

∂∂

⎭⎬⎫

⎩⎨⎧

∂∂

+∂∂

−=∂∂

∂∂

tzyxzB

z ),,,(

Consider now the evolution of the spatial gradient in the x direction and by differentiating the previous equation, we get

Propagation of an existing gradient-Plume FrontSpatial gradient of heating or vertical mixing-Tidal Mixing FrontDifferential advection of a lateral gradient-Shear FrontCon/divergence and down/upwelling –upwelling front

⎭⎬⎫

⎩⎨⎧

∂∂

+∂∂

∂∂

⎭⎬⎫

⎩⎨⎧ Σ+∂∂

∂∂

⎭⎬⎫

⎩⎨⎧

∂∂

+∂∂

−=∂∂

∂∂

tzyxzB

z ),,,(

Consider now the evolution of the spatial gradient in the x direction and by differentiating the previous equation, we get

Plume /Tidal Intrusion Front

Mixing Front

Shear Front

Upwelling front

• Note that this “classification” is just superficial

• Persistence requires a dynamic balance as well as scalar flux balances.

• Note that unsteady behavior is documented in smaller fronts; there is some work on coastal current fronts and there is very little know about tranientbehavior in large scale fronts.

Important points so far…

• The term “front” is ill-defined.• Estuaries are full of them • Estuarine Fronts: How Important Are

They? Largier, 1993. Estuaries Vol. 16, No. I , p. 1-1 1 March 1993

• A classification scheme helps isolate “frontogenesis” mechanisms

• Evolution takes place and that hasn’t been fully described yet.

3. Lab and Numerical Experiments

• To build intuition it is best to remove complexity.

• Lab experiments and simple models can illustrate processes and consequences of interactions

• Gravity current adjustments• The effect of mixing

The leading edge of the Chesapeake Plume at Duck,. NC.Photo from William Birkemeier, US Army Corps of Engineers (via S. Lentz)

From J. E. Simpson and R. E. Britter, 1980:A Laboratory Model of an Atmospheric Mesofront, Quarterly Journal of the Royal Meteorological Society.

The Simpson-Britter Experiments

Laboratory measurements of mixing in a turbulent gravity current. This gravity current was produced by releasing dense fluid from a lock at one end of a rectangular channel. The false coloursand contours show across-channel averaged density structure. Contours are at levels of 80%, 60%, 40%, 20%, and 5% of the intialdensity, respectively, with the 5% contour outermost. For more information see: Hacker, J., Linden, P.F., & Dalziel, S.B. 1996 Mixing in lock-release gravity currents. Dyn. Atmos. Oceans.24, 183-195.

Benjamin’s (1968) view

When a gravity current moves into a stationary, immiscible, deep, ambient fluid, von Karman (1940) and Benjamin (1968) showed the speed of the front should be

aaghU ρρρ /)(2 001 −=i.e. proportional to the internal wave speed behind the front.

The proportionality depends on the relative depth of the layers.

Britter and Simpson (1978)

B&S 78 added the effects of mixing in the leading edge and did a pile of lab experiments.

Britter and Simpson (1978)

Layer Depth Ratio

L&I 87

Benjamin

BENJAMIN, T. B. 1968. Gravity currents and related phenomena. Journal of Fluid Mechanics 31:209-243.

BRITTER, R. E. AND J. E. SIMPSON. 1978. Experiments on thedynamics of a gravity current head. Journal of Fluid Mechanics88:223-240.

LUKETINA, D. A. AND J. IMBERGER. 1987. Characteristics of asurface buoyant jet. Journal of Geophysical Research 2:5435-5447.

LUKETINA, D. A. AND J. IMBERGER. 1989. Turbulence and entrainment in a buoyant surface plume. Journal of Geophysical Research 94:12619-12636.

Marmorino G.O. and C.F. Trump, 2000.Gravity current structure of the Chesapeake outflow plume. JGR 105, 28,847-28,861.

O’Donnell, J., G.O. Marmorino, and C.F. Trump (Convergence and Downwelling at the Connecticut River plume Front. JPO, 28, 1481-1495.

Increa

sing M

=Rate at which fluid behind the front catches up with the front

=Ambient Flow

Met data

Layer Depth Ratio

Increased mixing

• Increases the convergence

• And increases the frontal velocity

Summary so far

• The frontal propagation is about right• The entrainment is not well measured and

theory is essentially untested• A discussion of several formulations is in

O’Donnell (1993).• A three layer approximation is probably

better• Three dimensional effects are not

understood.

Axial Convergence Front

Nunes, R.A. and J.H. Simpson, 1985

Columbia River Mouth: Jonathan Nash and Jim Moum

Plume Front Observations

Connecticut River

•The general structure

Connecticut River

Across Front Section

•The effect of the tides

• Observed Cross-front circulation Front location

Model of Garvine 1974

field pressure thePRESCRIBE These

riation.density va surface theis )( andcontrasdensity maximum theis where

ρργ

γρρ

−<≤≤−

⎪⎩

⎪⎨⎧ +−=

∂∂

+∂∂

−=∂∂

+∂∂

=∂∂

+∂∂

τρρ

Hydrostatic

Volume conservation

steady inertia = HPG + Friction

friction linterfaciaby dragfield pressureby on accelerati

tentrainmen todue loss force) (flowflux momentum of Divergence

headaches) some(after yeilds momentum x ofn Integratio

tentrainmenflux mass of divergencedxd

yields continuity ofn integratio The

∞∞−

∞−

uCrDgEuSdzu

EuSqudz

Parameterization/specification of mixing and friction

Yet More Model Details

z)u(x, and D(x)for equations aldifferentinonlinear coupled, in tworesult These

faexfaTCaexaTE

Note: This model prescribes the shape of the density field and seeks the interface shape and circulation consistent with the assumed dynamics.

Require Mixing and Friction to be maximum at the front

Note that this is analogous to the familiar “method of dynamic sections”

• Coriolis force = horizontal pressure gradient.• Pressure is hydrostatic• Measure density

Section across Gulf Stream

at Cape Hatterass

Old observations of the Connecticut River Plume (Garvine, 1974)

•Measured density field •Modeled field

• Observed Cross-front circulation• and some model predictions

Sample locations

Old observations of the Connecticut River Plume (Garvine, 1974)

•Measured density field •Modeled field

• Observed Cross-front circulation• and some model predictions

Sample locations Model with S=0

Model with S=+1

Time for a Break

Surface Current and Density Array

1000 1500 2000 25004500

East (m)

12:56:29

13:00:46

13:15:40

13:18:46

Ship track & front locations

Model Density and Across-front velocity (cm/s)4 4 4 4

6 6 6 68 8 8 810 10 10 1012 12 12 1214 14 14 1416 16 16 1618 18 18 18

-40 -20 0 20 40 60 80-9

-30 -30 -30 -30-20 -20 -20 -20-10 -10 -10 -100 0 0 010 10 10 1020 20 20 2030 30 30 3040 40 40 40

Density (sigma-t) and Across-front velocity (cm/s)444 6 6 68

10 10 10 101212 12 12

14 14 14 1416

1616 16

18 18 18

-20 0 20 40 60 80-9

-20 -20

20 2020

40 4040

-4 -2 0 2 4 6

East (km)

1000 1500 2000 25004500

East (m)

12:56:29

13:00:46

13:15:40

13:18:46

Ship track & front locations

10 10 10 101212 12 12

14 14 14 1416

1616 16

18 18 18

-20 0 20 40 60 80-9

-20 -20

20 2020

40 4040

Observations With SCUD and TOAD – O’Donnell et al. 1998

10 10 10 101212 12 12

14 14 14 1416

1616 16

18 18 18

0 0 20 40 60 80

-20 -20

20 2020

40 4040

Observations With SCUD and TOAD – O’Donnell et al. 1998sity and Across-front velocity (cm/s)

4 4 4 46 6 6 68 8 8 810 10 10 1012 12 12 1214 14 14 1416 16 16 1618 18 18 18

0 20 40 60 80

-30 -30 -30 -30-20 -20 -20 -20-10 -10 -10 -100 0 0 010 10 10 1020 20 20 2030 30 30 3040 40 40 40

Model of Garvine 1974:density and vertical velocity

Salinity

Backscatter

Vertical velocityIn the Plume In the front

Comparison of model w to data

-40 -20 0 20 40 60 80-60

Acrossfront (m)

ModelBinned Data

Binned model

Summary so far

• Plume and fronts are everywhere• They have very small scales• Garvine’s model for the velocity looked OK• But the length scale for mixing was

arbitary• And the Overturning regions was missing.

Overturning,the Ozmidov Scale ,the Thorpe Scale and the Ellison Scale

//'adjustment

frequencybuoyancy or Vaisala the:

Vertical displacement

To scale the salinity fluctuations so sections can be compared we normalize by the local vertical gradient to produce the distance that a parcel would have to be displaced along the gradient to create the observed salinity fluctuation.

The scale can’t be greater than the distance to the boundary so the normalized scale is

The RMS of this is the turbulence scale of Ellison (1957) 2/12

sdzdsl

⎭⎬⎫

⎩⎨⎧

−−

⎭⎬⎫

⎩⎨⎧

−−

⎭⎬⎫

⎩⎨⎧=

Stillinger Tank

Front Scales: width

Lab experiments: Itsweire, E.C., K. Helland, and C. Van Atta (1986). “The evolution of grid-generated turbulence in a

stably-stratified fluid,” J. Fluid Mech. 162, 299.Rohr, J.J., E.C. Itsweire, K.N. Helland, and C.W. Van Atta (1988). “Growth and decay of turbulence

in a stably stratified shear flow”. J. Fluid Mech. 195, 77-111.Itsweire, E., J. Koseff, D. Briggs & J. Ferziger, 1993, "Turbulence in stratified shear flows:

Implications for interpreting shear-induced mixing in the ocean", J. Phys. Oceanogr. 23, 508-

Suggest that for

5at ,suppressed is Mixing4/12

≈>= NtSNRi

Assuming a “frozen field” then

NULUNLNt

22 ⎟

⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

dzduNand

O'Donnell & Ackleson: Figure 3

Ship track and front crossings with the local frontal coordinates

East (km)

Start: 11:04

End: 11:09

1 1.5 2 2.5 3 3.5 45

May 2006 Ship Track

Ebb current

3 survey runs22 total front crossingsaverage boat speed: 2 ms-1

Front Structure

-100 -80 -60 -40 -20 0 20 40 60 80 1000

Across Front Distance (m)

-100 -50 0 50 100

Section 2

-2002040

-100 -50 0 50 100

-40-20020

-100 -80 -60 -40 -20 0 20 40 60 80 10010-2

Across front distance (m)

-100 -80 -60 -40 -20 0 20 40 60 80 1000

Across-front (m)

0 10 20 30 40 50 60 70 80 90 10010-2

across front distance (m)

Lfit=33 (m)

0 10 20 30 40 50 60 70 80 90 10010

-100 -80 -60 -40 -20 0 20 40 60 80 10010-2

Across front variation in Richardson number

-100 -80 -60 -40 -20 0 20 40 60 80 1000

Across front variation of L

0 10 20 30 40 50 60 70 80 90 10010-2

across front distance (m)

Lfit=33 (m)

Across Front Decay of L/D

Scale ComparisonS1 S3 S4 S5

Itsweire: LI= 23.5 26.7 38.6 26.9

Lfit ~ 33

Comments

Bay Koombanain 10got )1989(Imberger and LuketinaRiver Columbiain 10 found (2005)Jay andOrton

)/(1010~ front, plume CT at the obtained valuesFor the

40~ so

4/1for 5.1/suggest (1988) al.et Rohr of sexperiment Lab

)/( is scale (1965) Ozmidov The

−− −

kgWatts

Orton and Jay, GRL 2005 – Columbia River Plume

0 10 20 30 40 50 60 70 80 90 10010

)15/exp( x−

From, Levine, Goodman, O’Donnell (2006) – JMS.

Across front variation of

dissipation rate estimates (W/kg)

)15/exp( x−

Scale Comparison

Section: S1 S3 S4 S5CTR Front: LI=5U/N 23.5 26.7 38.6 26.9

Lfit ~ 15

Level (m): 3.7 7.2 9.1 11.7 14.7FRONT Front L=5U/N 74 81

Lfit ~ 60 71 60 91 75

Conclusions– There is a leading edge with

horizontal scale of order of the depth

– A second scale ~ 30m is consistent with the decay of sheared stratified turbulence

– If current parameterizations are to be employed the 30m scale must be resolved.

– Dissipation rate decays across front and maximum decreases along front (maybe)

– Maximum estimate (10-5) may be biased low due to underestimate of vertical gradient in S

faexfaTCaexaTE

Not such a bad idea after all.

south of Long Sand Shoal,convergence and downwellingintensify

front deepens dramatically but little change in size of mixing region

Survey 3 – Transect K

From Houk 2007

X = 42 m

The Start…..

•Bumpus, D.F. (1973) A description of the circulation on the shelf of the east coast of the United States. Prog. Oceanogr. 6, 111-157.•Beardsley R. C. and C.N. Flagg (1976). The water structure mean Currents and shelf/slope water front in the New England continental shelf. Mem. Soc. R. Sci. Liege, 6, 209-225.•Beardsley, R.C. and W.C. Boicourt (1981). On the estuarine and continental shelf circulation in the Middle Atlantic Bight, in Evolution of Physical Oceanography, B.A. Warren and C. Wunsch.•Beardsley et al. (1985). The Nantucket Shoals Flux Experiment (NSFE79), I, A basic description of the current and temperature variability, J. Phys. Oceanogr. 15, 713-748.•Aikman, F., III, H.W. Ou and R.W. Houghton, (1988). Current variability across the New England continental shelf-break and slope. Cont. Shelf Res. 8, 625-651.•Houghton, R.W., F. Aikman III, and H.W. Ou(1988).Shelf-slope water frontal structure and cross-shelf exchange at the New England shelfbreak. Cont. Shelf Res. 8, 687-710.•Chapman, D.C. and R.C. Beardsley (1989). On the origin of the shelf water in the Middle Atlantic Bight. J. Phys. Oceanogr. 19, 384-391.•Linder C.A, and G. Gawarkiewicz, (1998). A climatology of the shelfbreak front in the Middle Atlantic Bight. J. Geophys. Res. 103, 18405-18423.

Surface Salinity

Low discharge High Discharge

Bottom Salinity

Low discharge High Discharge

Low Discharge Cross-section - 1

High Discharge Cross-section - 1

Low Discharge Cross-section - 1

N.B. Higher Stratification on the inner-inner shelf

N.B. Overall Stratification is of similar magnitude

32 Isohaline intrusion

Wind Effect during High Discharge- Section 3Upwelling Favorable Light & Variable

Interim Summary

• The thinner, broader, more stratified surface layer during upwelling favorable winds appears to be consistent with the Ekmanstraining idea of Fong and Geyer, 2000.

• The mid water salinity intrusion has not been reported on the inner shelf before. (High resolution surveys reveal more detailed structure.

The Short Towed Array on the Connecticut’s fantail

5 CTDs

Depressor fin

One of the LIS Outflow Fronts

Freshwater in the Coastal Oceanseawifs

SeaWiFS image of Chesapeake and Delaware Bays

estuary(mixing)

Chesapeake Bay buoyant coastal current- far field

SAR image: Donato and Marmorino, Continental Shelf Research 22, 2002

Buoyant coastal current : 4 km wide, 5 m deepcw/cα ~ 0.2 consistent with

Wα/Ww (surface trapped)

Griffiths &Hopfinger, JFM 1983

Buoyant current in a rotating tank

~4m/day

Important papers about bottom BEL control of Coastal Currents

• Trowbridge, J. H. and S.J. Lentz (1991) Assymetric behavior of an oceanic boundary layer above a sloping bottom. J. Phys. Oceanogr. 21. 1171-1185

• Lentz, S. J. and J.H. Trowbridge (1991) The bottom boundary layer over the northern California shelf. J. Phys Oceanogr. 21, 1186-1201.

• Gawarkiewicz, G. and D.C. Chapman (1991) The formation and maintainance of shelfbreak fronts in an unstratified flow. J. Phys. Oceanogr. 21. 1225-1239.

• Chapman D.C. and S. J. Lentz, 1994: Trapping of a coastal density front by the bottom boundary layer. J. Phys. Oceanogr., 24, 1464–1479.

• Gawarkiewicz, G. and D.C. Chapman (1992) The role of stratification in the formation and maintainance of shelfbreak fronts. J. Phys. Oceanogr. 22. 753-772.

• MacReady, P. and P.B. Rhines (1991). Buoyant inhibition of Ekmantransport on a slope and its effect on stratified spin-up. J. Fluid Mech. 223. 631-661.

• Chapman, D.C. and S.J. Lentz (1994). Trapping of a coastal density front by the bottom boundary layer. J. Phys. Oceanogr. 24. 1464-1479.

• Yankovsky, A. E., and D. C. Chapman, 1997: A simple theory for the fate of buoyant coastal discharges. J. Phys. Oceanogr., 27, 1386–1401.

hρo-Δρ

geometry

Chapman 2002

From geometry:

hρo-Δρ

∂∂

=∂∂

∂−=

∂∂

ρρρ

Assume geostrophic and hydrostatic then

And get thermal wind

hρo-Δρ

Offshore BEL transport:

bbx ruLinearized bottom stress:

Approximate

Wyρρ Δ

≈∂∂

and integrating thermal wind

hzfWguu

fWhguC

CzfWgu

=∂∂ ρ

hρo-Δρ

)(' hzfWguu b ++=Using

and assuming that the offshore transport has widened the current to the point where h is such that 0=bu

and set the horizontal integral to the along shore flux

hzzfWgudz

−−⎥⎦

⎤⎢⎣

⎡+=∫

And then integrate vertically to obtain

fhgdyh

fWgdyudzQ

≈== ∫∫ ∫−

The depth and location of foot of the front is 2/1

⎟⎟⎠

⎞⎜⎜⎝

gQfh α/hW =&

Recent Observations evaluating the BEL Coastal Current Control Theory

• Houghton, R. (1997), Lagrangian flow at the foot of a shelfbreak front using a dye tracer injected into the bottom boundary layer, Geophys. Res. Lett., 24, 2035–2038.

• Houghton, R., and M. Visbeck (1998), Upwelling and convergence in the Middle Atlantic Bight shelf break front, Geophys. Res. Lett., 25, 2765–2768.

• Barth, J. A., D. Bogucki, S. D. Pierce, and P. M. Korso (1998), Secondary circulation associated with a shelfbreak front, Geophys. Res. Lett., 25, 2761–2764.

• Pickart, R. S. (2000), Bottom boundary layer structure and detachment in the shelfbreak jet of the Middle Atlantic Bight, J. Phys. Oceanogr., 30, 2668– 2686.

• Linder, C.A., G.G. Gawarkiewicz and R.S. Pickart (2004), Seasonal characteristics of bottom boundary layer detachment at the shelfbreak front in the Middle Atlantic Bight, J. Geophys. Res., 109, C03049, doi:10.1029/2003JC002032

From Pickart 2000, The Accumulated Temperature Change Method (AMT)

From Linder, C.A., G.G. Gawarkiewiczand R.S. Pickart(2004)

From Houghton (2006)

Upwelling wind response of coastal current fronts

• Based on Fong and Geyer (2000)• Houghton, Tilburg Garvine (2004)

Figure 4. Contours of stress and salinity for t = 0, 12, 24, 48, and 72 hours. Shaded contours are used to indicate salinity contours in intervals of 0.5 psu. Superimposed on the shading are contours of magnitude of the total stress in solid contour lines (0.01 Pa intervals). The thick contour line is stress, which is 10% of the applied surface stress.

Figure 7. Contours of vertical salt flux and salinity for t = 0, 12, 24, 48, and 72 hours. Shaded contours are used to indicate salinity contours in intervals of 0.5 psu. Superimposed on the shading are contours of vertical salt flux in solid contour lines (10 -5 psu m s -1 intervals). The cross-shore-integrated mean vertical salt flux is indicated in the lower left corner of each panel.

Summary of the upwelling wind response

• Mixing persists at the seaward plume front because of an Ekmanstraining mechanism in which there is a balance between the

advection of cross-shore salinity gradients and vertical mixing.

Dye (colors) and Salinity

Houghton, R. W., C. E. Tilburg, R. W. Garvine, and A. Fong (2004), Delaware River 23 plume response to a strong upwelling-favorable wind event, Geophys. Res. Lett., 31, L07302,doi:10.1029/2003GL018988.

Important Points

• Fronts are everywhere on the shelf• There are plume fronts, mixing fronts and

shear fronts• The location of the shelfbreak fronts and

coastal current fronts are generally consistent the Chapman-Lentz idea

• Transient wind events play a big role in offshore transport through straining and vertical mixing

jim o’donnell university of connecticut · 2007-08-09 · plume. journal of geophysical research...

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