Wave-current Interaction (WEC) in the COAWST Modeling System Nirnimesh Kumar with John Warner, George Voulgaris, Maitane Olabarrieta *see Kumar et al., 2012 (third paper 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, 10.1016/j.ocemod.2012.01.003. *also see Olabarrieta et al., 2012 (fourth paper for applications)

Wave-averaged Equations Wave-Current Interaction Description StCOR Stokes-Coriolis Force/Hasselmann Stress PG Pressure Gradient (Includes Bernoulli head, quasi-static pressure and vertical vortex force, Eqn. 5, 7, 9 and 13) HVF Horizontal Vortex Force BA+RA Breaking & Roller Acceleration (Wave dissipation and roller induced flows) BtSt+SuSt Bottom & Surface Streaming (Can act as stress in bottom and surface layer)

Exchange of Data Field http://woodshole.er.usgs.gov/operations/modeling/COAWST/index.html

Wave-current Interaction (WEC) WEC_MELLOR (Mellor, 2011) WEC_VF (Uchiyama et al., 10) Implemented in Kumar et al., 2011 + Dissipation (depth) + Roller Model + Wave mixing + Streaming + Roller Model + Streaming Implemented in Kumar et al., 2012 *Processes in italics are optional 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)

Dissipation (Depth-limited wave breaking) WDISS_THORGUZA Use depth-limited wave dissipation based on Thornton and Guza (1983). See Eqn. (31), pg-71 WDISS_CHURTHOR Activate depth-limited 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: 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 If you do not define any of these options, and still define WEC_VF, the model expects a forcing file with information about dissipation

ROLLER MODEL (for Wave Rollers) ROLLER_SVENDSEN Activate wave roller based on Svendsen (1984). See Warner et al. (2008), Eqn. 7 and Eqn. 10. ROLLLER_MONO Activate 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 (αr 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.

Wave breaking induced mixing TKE_WAVEDISS ZOS_HSIG Activate enhance vertical viscosity mixing from waves within framework of GLS. See Eq. 44, 46 and 47. The parameter αw in Eq. 46 can be specified in the INPUT file as ZOS_HSIG_ALPHA (roughness from wave amplitude) Parameter Cew in Eqn. 47 is specified in the INPUT file as SZ_ALPHA (roughness from wave dissipation) Note: Sensitivity tests for wave-mixing were done in Kumar et al. (2012). The enhanced mixing is sensitive to Cew

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. _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: 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

Shoreface Test Case (Obliquely incident waves on a planar beach) [0,0] [1000,-12] z x y Hsig= 2m Tp = 10s θ = 10o 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

Header File (COAWST/ROMS/Include)

Input File (COAWST/ROMS/External)

Input File (COAWST/ROMS/External) Requires a wave forcing file as one way coupling only

WEC Related Output Dissip_roller / Eqn. 37 rollA / Eqn. 35 Zetaw / Eqn. 7 qsp / Eqn. 9 bh / Eqn. 5

Should contain the following variables Forcing file for one way coupling Data/ROMS/Forcing/swan_shoreface_angle_forc.nc Should contain the following variables Wave Height Hwave Wave Direction Dwave Wave Length Lwave Bottom Orbital Vel. Ub_Swan Depth-limited breaking Dissip_break Whitecapping induced breaking Dissip_wcap Bottom friction induced dissip. Dissip_fric Time Period Pwave_top/Pwave_bot

Code Compilation:coawst.bash Application Name Number of Nested Grids ROOT and Project Directory Define Message Passage Interface (MPI), Fortran Compiler, NETCDF4 Header (*.h) & Analytical (ana_*.h) Files ./coawst.bash –j N

Running the Shoreface Test Case np = number of processors coawstM = Executable created after compilation Input file = ROMS/External/ocean_shoreface.in Serial ./coawstS.exe ROMS/External/ocean_shoreface.in Parallel mpiexec/run -np 4 ./coawstM.exe ROMS/External/ocean_shoreface.in

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

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

Results (III of III) Eulerian Stokes Cross-shore Longshore Vertical

WEC related Diagnostics Terms (i.e., contribution to momentum balance) Terms in momentum balance Definition Output Variable 𝜕 𝜕𝑡 𝐻 𝑧 ⋅𝑢 Local Acc. u_accel/ ubar_accel 𝜕 𝜕𝑥 𝐻 𝑧 𝑢𝑢 + 𝜕 𝜕𝑦 𝐻 𝑧 𝑣𝑢 +𝑢 𝜕 𝜕𝑥 𝐻 𝑧 𝑢 𝑆𝑡 +𝑢 𝜕 𝜕𝑦 𝐻 𝑧 𝑣 𝑆𝑡 Horizontal Advection u_hadv/ubar_hadv 𝜕 𝜕𝑠 𝜔 𝑠 𝑢 +𝑢 𝜕 𝜕𝑠 𝜔 𝑠 𝑆𝑡 Vertical Advection u_vadv 𝐻 𝑧 ⋅𝑓⋅𝑣 Coriolis Force u_cor/ubar_cor 𝐻 𝑧 ⋅𝑓⋅ 𝑣 𝑠𝑡 Stokes-Coriolis u_stcor/ubar_stcor − 𝐻 𝑧 ⋅ 𝜕 𝜑 𝑐 𝜕𝑥 | 𝑧 Pressure Gradient u_prsgrd/ubar_prsgrd 𝐻 𝑧 𝑣 𝑠𝑡 𝜕𝑣 𝜕𝑥 − 𝜕𝑢 𝜕𝑦 Vortex Force u_hjvf/ubar_hjvf 𝜔 𝑠 𝑆𝑡 𝜕𝑢 𝜕𝑠 u_vjvf

Terms in momentum balance Definition Output Var. 𝐻 𝑧 ℱ 𝑤𝜉 (see Eqn. 21) Breaking + Roller Acceleration + Streaming u_wbrk/ubar_wbrk u_wrol/ubar_wrol u_bstm/ubar_bstm u_sstm/ubar_sstm BREAKING THE PRESSURE GRADIENT TERM 𝜑 𝑐 =𝑔 𝜁 𝑐 − 𝜁 − 𝑔−𝒦 | 𝜁 𝑐 + 0 𝑠 𝑔𝜌 𝜌 0 −𝐾 𝐻 𝑧 𝑑𝑠 (𝐄𝐪𝐧. 𝟏𝟑, 𝟒𝟗, 𝐓𝐚𝐛𝐥𝐞 𝟐) − 𝐻 𝑧 ⋅ 𝜕 𝜑 𝑐 𝜕𝑥 | 𝑧 Pressure Gradient u_prsgrd/ubar_prsgrd − 𝛻 ⊥ 𝑔 𝜁 𝑐 + −ℎ 𝜍 𝑐 𝑔𝜌 𝜌 0 𝑑𝑧 Eulerian Contribution ubar_zeta 𝑔 𝛻 ⊥ 𝜁 Quasi-static response, Eqn. 7 ubar_zetw 𝛻 ⊥ 𝒦| 𝜁 𝑐 Bernoulli-head contribution, Eqn. 5 ubar_zbeh 𝑔 𝛻 ⊥ 𝒫| 𝜁 𝑐 Surface pressure boundary, Eqn. 9 ubar_zqsp

Inlet Test Case (WEC in a tidal inlet) Wave field computed using SWAN Two way coupling (WEC and CEW) Application Name: INLET_TEST Header file: COAWST/Projects/Inlet_test/Coupled/inlet_test.h Input file: COAWST/Projects/Inlet_test/Coupled/ocean_inlet_test.in COAWST/Projects/Inlet_test/Coupled/swan_inlet_test.in COAWST/Projects/Inlet_test/Coupled/coupling_inlet_test.h NORTH SOUTH

Header File (COAWST/Projects/Inlet_test/Coupled)

Input File (COAWST/Projects/Coupled/ocean_inlet_test.in ROMS/Functionals/ana_fsobc.h

Input File (COAWST/Projects/Coupled/swan_inlet_test.in INRHOG should be 1 for correct units of wave dissipation Example of TEST Command TEST 120 {} TEST 0

Input File (COAWST/Projects/Coupled/swan_inlet_test.in

Input File (COAWST/Projects/Coupled/coupling_inlet_test.in

Code Compilation:coawst.bash ./coawst.bash –j N

Running the Inlet_Test Case np = number of processors coawstM = Executable created after compilation Input file = Projects/Inlet_Test/Coupled/coupling_inlet_test.in Serial ./coawstS.exe Projects/Inlet_test/Coupled/coupling_inlet_test.in Parallel mpiexec/run -np 4 ./coawstM.exe Projects/Inlet_test/Coupled/coupling_inlet_test.in

Results Hsig

References Kumar et al., 2012: 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, 10.1016/j.ocemod.2012.01.003. Kumar et al., 2011: Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications, Coastal Engineering, Volume 58, Issue 12, December 2011, Pages 1097-1117, 10.1016/j.coastaleng.2011.06.009. Olabarrieta, M., J. C. Warner, and N. Kumar (2011), Wave-current interaction in Willapa Bay, J. Geophys. Res., 116, C12014, doi:10.1029/2011JC007387. Warner et al., 2008: Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model, Computers & Geosciences, Volume 34, Issue 10, October 2008, Pages 1284-1306, ISSN 0098-3004, 10.1016/j.cageo.2008.02.012. Haas and Warner, 2009: Comparing a quasi-3D to a full 3D nearshore circulation model: SHORECIRC and ROMS, Ocean Modelling, Volume 26, Issues 1–2, 2009, Pages 91-103, ISSN 1463-5003, 10.1016/j.ocemod.2008.09.003.