1. Capes and form drag: the role of stratification Marcello G. Magaldi 1, Tamay M. Özgökmen 1, Annalisa Griffa 1, Eric P. Chassignet 2, Hartmut Peters 1 and Mohamed Iskandarani 1 1 RSMAS, University of Miami 2 COAPS, Florida State University 10/02/2007

2. Outline Motivation and open questions Numerical setup Results and form drag Conclusions and future work 10/02/2007

3. 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)

4. Movie for a no sloping case Movie for a no sloping case Eddy generation 10/02/2007 Cyclones Positive vorticity Anticyclones Negative vorticity Red cones Flow visualization No slope Bu = 0.10 τ = 25.92

5. Eddy generation 10/02/2007 No slope Bu = 0.10

6. Dissipation dilemma 10/02/2007 (Lavelle et al, 1988) More than the 70% of the whole energy loss Bottom drag coefficients are 2  10 times larger than usual in order to match observations (Lavelle et al, 1988; Foreman et al, 1995)

7. 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*

8. Eddy generation 10/02/2007 We know the role of bottom friction... Doglioli, A. M., Griffa, A., Magaldi, M. G., 2004. JGR. Increasing Re f Main controlling parameter Re f = H / C D D Equivalent Reynolds Number Advection / bottom friction

9. 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, 2001 No rotation

10. Aims of the study Identify how stratification affects the eddy regime Understand how this translates in terms of dissipation (and mixing) 10/02/2007

11. 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, C D = 3*10 - 3 H = 81m  Re f ≈ 207 Along-shore extent = 1760m Cross-shore extent = 320 m T = 12.5 °, initial flat isopyc. Scale 1:10 3 1 cm = 10 m Interior: ∆x = ∆y = 2m = D/65 285x100x20 pts, k-ε closure Regional Ocean Modeling System (ROMS)

12. Lab Experiments 10/02/2007 Burger Number Bu=(N 2 H 2 )/(f 2 D 2 ) 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= 0.15Bu= 0.31Bu= 6.48 fully attached regimeeddy attached regimeeddy shedding regime Boyer and Tao, 1987

13. 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 Vorticity field: eddies are shed for higher Bu

14. Results 10/02/2007 1:1 1:100 1:50 meters kilometers 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 Vorticity field

15. Form drag 10/02/2007 z x b(x,y) η(x,y,t) U F1F1 F2F2 1 2 Drag

16. 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 Drag External Drag Total Drag Skin 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

17. Form Drag 10/02/2007 Ro = 0.06, Implicit Diffusion Drag coefficients in function of stratification and for different slopes Cd Tot (Bu) Cd Tot

18. 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 Slope 1:200 Pa p int – p 0 int Cd Int (y)

19. 3D view 10/02/2007 Slope 1:200 Ro = 0.06, Implicit Diffusion, τ = 0 and 4.752 Low Stratification, Bu = 0.05 Salinity

20. 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)

21. Future work 10/02/2007 Quantification of mixing (energetic approach, open boundary conditions) Application to the Gargano Cape

22. The Gargano Cape 10/02/2007 MODIS-Aqua Chlorophyll Concentration Daily average NCOM surface velocity Courtesy of Dr. Angelique Haza Dynamics of the Adriatic in Real-Time (DART project)

23. Questions? 10/02/2007 Please ask my Italian friends... Thank you!!!

24. Results 10/02/2007 1:1 1:100 1:50 kilometers meters kilometers 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 Vorticity field

25. 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 p int – p 0 int Cd Int (y)

26. 3D view 10/02/2007 Slope 1:1 Ro = 0.06, Implicit Diffusion, τ = 0 and 4.752 Low Stratification, Bu = 0.05

27. 3D view 10/02/2007 Slope 1:50 Ro = 0.06, Implicit Diffusion, τ = 0 and 4.752 Low Stratification, Bu = 0.05

28. 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 == 0.0d0 Resolution: Interior ∆x = ∆y = 2m = D/65 West, ∆x = 24 x interior resolution East, ∆x = 8 x interior resolution South, ∆y = 8 x interior resolution r = 0.33, n = 3.26

29. 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)

30. 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

31. Eddy generation 10/02/2007 Movie for a no sloping case Cyclones Positive vorticity Anticyclones Negative vorticity Red cones Flow visualization Bu = 6.48 D = 13 km