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