Capes and form drag: the role of stratification Marcello G. Magaldi 1, Tamay M. Özgökmen 1,...
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Transcript of Capes and form drag: the role of stratification Marcello G. Magaldi 1, Tamay M. Özgökmen 1,...
Capes and form drag: the role of stratification
Marcello G. Magaldi1, Tamay M. Özgökmen1, Annalisa Griffa1, Eric P. Chassignet2, Hartmut Peters1 and Mohamed Iskandarani1
1 RSMAS, University of Miami2 COAPS, Florida State University
10/02/2007
Outline
• Motivation and open questions
• Numerical setup
• Results and form drag
• Conclusions and future work
10/02/2007
Why studying capes?
10/02/2007
One of many capes in Puget Sound, (WA)
A case of current separation?
1. Current separation and eddy formation (Signell and Geyer, 1991)
2. Lee wave generation (MacCready and Pawlak, 2001)
3. Vortex tilting and stretching (Farmer et al., 2002)
4. Secondary circulations (Geyer, 1993)
5. Upwelling (Alee et al., 2004)
6. High values of dissipation and mixing (Pawlak et al., 2003)
• Movie for a no sloping case
Eddy generation 10/02/2007
CyclonesPositive vorticity
AnticyclonesNegative vorticity
Red conesFlow visualization
No slope
Bu = 0.10
τ = 25.92
Eddy generation 10/02/2007
No slope
Bu = 0.10
Dissipation dilemma 10/02/2007
(Lavelle et al, 1988)
More than the 70% of the whole energy
loss
Bottom drag coefficients are
210 times larger than usual in order to match observations
(Lavelle et al, 1988; Foreman et al, 1995)
Eddy generation 10/02/2007
Re = 28.4
Van Dyke, 1982
Re = 0.16
Re = 140
We know the role of lateral friction...
Dong et al., 2007
Re*
Eddy generation 10/02/2007
We know the role of bottom friction...
Doglioli, A. M., Griffa, A., Magaldi, M. G., 2004. JGR.
Increasing Ref
Main controlling parameter
Ref = H / CD D
Equivalent Reynolds Number
Advection / bottom friction
Open questions 10/02/2007
...but what is the role of stratification in the generation of eddies behind capes?
Only three papers:
• Boyer and Tao, 1987; big aspect ratio (1:1), not realistic (ocean 1:10 is steep)
• Davies et al., 1990;
• MacCready and Pawlak, 2001No rotation
Aims of the study
• Identify how stratification affects the eddy regime
• Understand how this translates in terms of dissipation (and mixing)
10/02/2007
Numerical setup 10/02/2007
Boyer and Tao, 1987
Initial condition:
fluid in motion, linearly stratified
(U= - 0.078 m/s, V= 0.0 m/s, η = geos.)
U
Open BCs:
M2 Flather, Chapman, M3 and Tracer radiation relaxation on tracers to the initial value on 6 pts
f = 10 - 2 s – 1, CD = 3*10 - 3
H = 81m Ref ≈ 207
Along-shore extent = 1760m
Cross-shore extent = 320 m
T = 12.5 °, initial flat isopyc.
Scale 1:103
1 cm = 10 m
Interior: ∆x = ∆y = 2m = D/65285x100x20 pts, k-ε closure
Regional Ocean Modeling System (ROMS)
Lab Experiments 10/02/2007
Burger NumberBu=(N2H2)/(f2D2)
At different depths ( τ = t U/D = 9.6)
z*= 0.25
z*= 0.50
z*= 0.75
At different times ( z* = z/H = 0.50)
τ = 3.8
τ = 7.3
τ = 10.6
τ = 1.0
τ = 5.0
τ = 8.9
Bu= 0.15 Bu= 0.31 Bu= 6.48
fully attached regime eddy attached regime eddy shedding regime
Boyer and Tao, 1987
Results 10/02/2007
Ro = 0.06, Implicit Diffusion, τ = t U/D = 9.936 z* = z/H = 0.5
Bu = 0.05
Bu = 1.00
Bu = 0.30
Bu = 6.48
Slope 1:1, D = 130 m
meters
meters
meters
meters
met
ers
met
ers
met
ers
met
ers
Vorticity field: eddies are shed for higher Bu
Results 10/02/2007
1:1
1:100
1:50
meters
met
ers
kilo
met
ers
kilo
met
ers
Low stratified waters, Bu = 0.05
kilometers
1:200
Ro = 0.06, Implicit Diffusion, τ = t U/D = 9.936 z* = z/H = 0.5
kilometers
kilometers
kilo
met
ers
Vorticity field
Form drag 10/02/2007
z
xb(x,y)
η(x,y,t)
U
F1F2
12
Drag
Form Drag 10/02/2007
Ro = 0.06,
Implicit Diffusion
Bu = 0.05
Bu = 0.70
Bu = 0.30
Bu = 6.48
1:1 slope case
Internal DragExternal Drag
Total DragSkin Drag
Total Drag Coef. = 0.24
Total Drag Coef. = 1.86Total Drag Coef. = 1.24
Total Drag Coef. = 0.83
Drag coefficients in
function of time
Form Drag 10/02/2007
Ro = 0.06,
Implicit Diffusion
Drag coefficients in
function of stratification
and for different slopes
CdTot (Bu)
Cd T
ot
Internal Form Drag 10/02/2007
Ro = 0.06, Implicit Diffusion, τ = 4.752
Low Stratification, Bu = 0.05
Slope 1:50Slope 1:1
Slope 1:100
Pa
Pa
Pa
Slope 1:200
Pa
pint – p0int Cd Int (y)
3D view 10/02/2007
Slope 1:200Ro = 0.06,
Implicit Diffusion,
τ = 0 and 4.752
Low Stratification,
Bu = 0.05
Salinity
Conclusions 10/02/2007
1. We are able to reproduce 2 of the 3 regimes by Boyer and Tao (1987). We are not able to reproduce the eddy attached regime (non-hydrostatic implications, top lid?)
2. The eddy shedding regime is enhanced by larger Burger numbers more horizontal flow, more tendency of separation stronger and more coherent vortices
3. Flow regimes do not significantly change for gentler and more realistic slopes (less inertial for bottom friction!)
4. The form drag coefficients change with Bu and increase significantly for gentler slopes (equal increase keeping a constant slope)
Future work 10/02/2007
• Quantification of mixing (energetic approach,
open boundary conditions)
• Application to the Gargano Cape
The Gargano Cape 10/02/2007
MODIS-Aqua Chlorophyll ConcentrationDaily average
NCOM surface velocity
Courtesy of Dr. Angelique Haza
Dynamics of the Adriatic in Real-Time (DART project)
Questions? 10/02/2007
Please ask my Italian friends...
Thank you!!!
Results 10/02/2007
1:1
1:100
1:50
kilometers
meters
met
ers
kilo
met
ers
kilo
met
ers
High stratified waters, Bu = 1.00
Ro = 0.06, Implicit Diffusion, τ = t U/D = 9.936 z* = z/H = 0.5
1:200
kilometers
kilometers
kilo
met
ers
Vorticity field
Internal Form Drag 10/02/2007
Ro = 0.06, Implicit Diffusion, τ = 4.752
High Stratification, Bu = 6.48
Slope 1:50Slope 1:1
Slope 1:100
Pa
Pa
Pa
pint – p0int Cd Int (y)
3D view 10/02/2007
Slope 1:1Ro = 0.06,
Implicit Diffusion,
τ = 0 and 4.752
Low Stratification,
Bu = 0.05
3D view 10/02/2007
Slope 1:50Ro = 0.06,
Implicit Diffusion,
τ = 0 and 4.752
Low Stratification,
Bu = 0.05
Numerical grid 10/02/2007
Plotting every 3 grid points
Implicit viscosity
#define ANA_GRID#define MASKING#define UV_VIS2#define TS_DIF2
Viscosity is scaled by grid size
#define VISC_GRID#define DIFF_GRID
TNU2 == 0.0d0 0.0d0 VISC2 == 0.0d0Resolution: Interior ∆x = ∆y = 2m = D/65
West, ∆x = 24 x interior resolutionEast, ∆x = 8 x interior resolution
South, ∆y = 8 x interior resolutionr = 0.33, n = 3.26
Motivation 10/02/2007
COASTAL MANAGEMENT
impact on transport of sediments, pollutants, nutrients,
phytoplankton and larvae
(Bastos et al., 2003)
Portland Bill (UK)
Sewages
Portofino Cape
(Doglioli et al., 2004)
Capes vs islands 10/02/2007
Why don’t we use the literature dealing with isles?
1. presence of coast
• reduced eddy shedding (Verron, 1991)
2. sloping bottom
• reduced eddy shedding (Klinger, 1994)
• topographic Rossby waves (Freeland, 1990)
• lee waves (MacCready and Pawlak, 2001)
Re* = 200
Re* = 1200
( Verron,1991 )
QG model
Eddy generation 10/02/2007
• Movie for a no sloping case
CyclonesPositive vorticity
AnticyclonesNegative vorticity
Red conesFlow visualization
Bu = 6.48
D = 13 km