1. Wave-current Interaction (WEC) in the COAWST Modeling System Nirnimesh Kumar, SIO with J.C. Warner, G. Voulgaris, M. Olabarrieta *see Kumar et al., 2012 (might be in your booklet) Implementation of the vortex force formalism in the coupled ocean-atmosphere- wave-sediment transport (COAWST) modeling system for inner shelf and surf zone applications, Ocean Modelling, Volume 47, 2012, Pages 65-95. *also see Olabarrieta et al., 2012

4. Momentum Balance Continuity Governing Equations Radiation Stress Vortex Force Formalism This term on phase averaging gives vortex force Recipes for Wave-Current Interaction

5. Radiation Stress 2-D Radiation Stress Equations (Longuet-Higgins, 1962, 1964) Excess flux of momentum due to presence of waves. Explains wave setup, wave setdown, generation of longshore currents, rip currents. Breaker Zone Surf Zone set-up MWL set-down Swash Beach Profile Wave Setup: Balance between quasi-static pressure and radiation stress divergence Longshore Currents: Generated due to gradient of radiation stress in longshore direction

6. Adapted from Smith (2006, JPO) Cross-shore Alongshore Product of Stokes drift and mean flow vorticity (Craik and Leibovich, 1976). Physically representative of wave refraction due to current shear Vortex Force (VF)

7. Wave Rollers

8. Stokes-Coriolis Force, Surface and Bottom Streaming Cross-shore Vel.Alongshore Vel. From Lentz et al., 2008 Wave-propagation direction

9. Wave-averaged Eqns. Local Acc. Advective accn. Coriolis + Stokes-Coriolis Pressure Gradient Radiation Stress Bottom Stress Radiation Stress Accounts for wave breaking Local Acc. Advective accn. Stokes -Coriolis Pressure Gradient Vortex ForceBottom Stress Coriolis Non-conservative forcing Vortex Force Formalism Accounts for wave breaking

10. Wave-averaged Eqns. Local Acc. Advective accn. Stokes -Coriolis Pressure Gradient Vortex ForceBottom Stress Coriolis Non-conservative forcing Vortex Force Formalism Accounts for wave breaking Surface Streaming Bottom Streaming Whitecapping Wave Rollers Depth-limited breaking

11. Depth-limited Breaking Surface Intensified

12. Integrate oceanic, atmospheric, wave and morphological processes in the coastal ocean (Warner et al., 2010) Coupled-Ocean-Atmosphere-Wave-Sediment-Transport (COAWST) modeling system Methodology ROMS SWAN WRF CSTMS http://woodshole.er.usgs.gov/operations/modeling/COAWST/index.html

13. cppdefs.h (COAWST/ROMS/Include) WEC_MELLOR + Activates the Mellor (2011) method for WEC WEC_VF (preferred method for 3D) Activate WEC using the Vortex Force formalism ( Uchiyama et al., 2010 ) Wave-current Interaction (WEC) WEC_MELLOR (Mellor, 2011) WEC_VF (Uchiyama et al., 10) + Roller Model + Streaming + Dissipation (depth) + Roller Model + Wave mixing + Streaming Implemented in Kumar et al., 2011 Implemented in Kumar et al., 2012 *Processes in italics are optional

14. Dissipation (Depth-limited wave breaking) WDISS_THORGUZA Wave dissipation based on Thornton and Guza (1983). See Eqn. (31), pg-71 WDISS_CHURTHOR Wave dissipation based on Church and Thornton (1993). See Eqn. (32), pg-71 WDISS_WAVEMOD Activate wave-dissipation from a wave model. If using SWAN wave model, use INRHOG=1 for correct units of wave dissipation Note: (a)Use WDISS_THORGUZA/CHURTHOR if no information about wave dissipation is present, and you can’t run the wave model to obtain depth-limited dissipation (b)If you do not define any of these options, and still define WEC_VF, the model expects a forcing file with information about dissipation

15. ROLLER MODEL (for Wave Rollers) ROLLER_SVENDSEN Wave roller based on Svendsen (1984). See Warner et al. (2008), Eqn. 7 and Eqn. 10. ROLLLER_MONO Wave roller for monochromatic waves from REF-DIF. See Haas and Warner, 2009. ROLLER_RENIERS Activate wave roller based on Reniers et al. (2004). See Eqn. 34-37 (Advection-Diffusion) Note: If defining ROLLER_RENIERS, you must specify the parameter wec_alpha (α r in Eqn. 34, varying from 0-1) in the INPUT file. Here 0 means no percentage of wave dissipation goes into creating wave rollers, while 1 means all the wave dissipation creates wave rollers.

16. Wave breaking induced mixing TKE_WAVEDISS ZOS_HSIG Enhanced vertical mixing from waves within framework of GLS. See Eq. 44, 46 and 47. Based on Feddersen and Trowbridge, 05 The parameter α w in Eq. 46 can be specified in the INPUT file as ZOS_HSIG_ALPHA (roughness from wave amplitude) Parameter C ew in Eqn. 47 is specified in the INPUT file as SZ_ALPHA (roughness from wave dissipation)

17. Bottom and Surface Streaming BOTTOM_STREAMING Bottom streaming due to waves using Uchiyama et al. (2010) methodology. See Eqn. 22-26. This method requires dissipation due to bottom friction. If not using a wave model, then uses empirical Eq. 22. BOTTOM_STREAMING _XU_BOWEN Bottom streaming due to waves based on methodology of Xu and Bowen, 1994. See Eq. 27. SURFACE_STREAMING Surface streaming using Xu and Bowen, 1994. See Eq. 28. Note: (a)BOTTOM_STREAMING_XU_BOWEN was tested in Kumar et al. (2012). It requires very high resolution close to bottom layer. Suggested Vtransform=2 and Vstretching=3

18. [0,0] [1000,-12] z x y H sig = 2m T p = 10s θ = 10 o Shoreface Test Case (Obliquely incident waves on a planar beach)  Wave field computed using SWAN  One way coupling (only WEC)  Application Name: SHOREFACE  Header file: COAWST/ROMS/Include/shoreface.h  Input file: COAWST/ROMS/External/ocean_shoreface.in

19. Header File (COAWST/ROMS/Include)

20. Input File (COAWST/ROMS/External)

21. Requires a wave forcing file as one way coupling only

22. Forcing file for one way coupling Data/ROMS/Forcing/swan_shoreface_angle_forc.nc Should contain the following variables Wave HeightHwave Wave DirectionDwave Wave LengthLwave Bottom Orbital Vel.Ub_Swan Depth-limited breakingDissip_break Whitecapping induced breakingDissip_wcap Bottom friction induced dissip.Dissip_fric Time PeriodPwave_top/Pwave_bot

23. WEC Related Output

24. Results (I of III) Significant Wave Height Sea surface elevation

25. Results (II of III) Depth-averaged Velocities Cross-shore Vel.Longshore Vel.

26. Results (III of III) Cross-shore Longshore Vertical EulerianStokes

27. WEC related Diagnostics Terms (i.e., contribution to momentum balance) Terms in momentum balance DefinitionOutput Variable Local Acc. u_accel/ ubar_accel Horizontal Advection u_hadv/ubar_hadv Vertical Advection u_vadv Coriolis Forceu_cor/ubar_cor Stokes-Coriolisu_stcor/ubar_stcor Pressure Gradient u_prsgrd/ubar_prs grd Vortex Forceu_hjvf/ubar_hjvf Vortex Forceu_vjvf

28. Terms in momentum balanceDefinitionOutput Var. Breaking + Roller Acceleration + Streaming u_wbrk/ubar_wbrku_wrol/ub ar_wrol u_bstm/ubar_bstmu_sstm/ub ar_sstm BREAKING THE PRESSURE GRADIENT TERM Pressure Gradientu_prsgrd/ubar_prsgrd Eulerian Contributionubar_zeta Quasi-static response, Eqn. 7 ubar_zetw Bernoulli-head contribution, Eqn. 5 ubar_zbeh Surface pressure boundary, Eqn. 9 ubar_zqsp

29. Vertical profile of terms in momentum balance Alongshore Cross-shore

30. DUCK’ 94, NC-Nearshore Experiment DUCK’ 94- Nearshore Experiment

31. Obliquely incident waves on a barred beach (DUCK’ 94 Experiment) Experiment conducted Oct. 12, 1994 (Elgar et al., 97; Garcez-Faria et al., 98, 00) Wave field from SWAN. One way coupling.

32. Sea Surface Elevation Depth averaged cross-shore velocity Depth averaged longshore velocity Wave Height Wave Parameters, Depth-Averaged Flows η u v H rms εbεb

33. Vertical profile of Cross-shore & Longshore Vel. Cross-shore Alongshore Eulerian Kumar et al., 2012 Stokes Drift Vertical Distribution of Wave Dissipation

34. Comparison to Field Observations Cross-shore Alongshore Obs from Garcez-Faria et al., 1998, 2000Kumar et al., 2012

35. Alongshore Cross-shore Vertical profile of terms in momentum balance Notes: Over the bar (a) VF balances Breaking (b) VM balances Advection