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-atmospherewave-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 t H z u x H z u u y H z v u u ACC s s St s H z f v H z f v VA BF H x z u St u y H z v St HA s u u H zF x COR H zF w B A R A B tSt SuSt Hz c x v H z v st z PG x u u s y s St HVF ' ' v u u w s H z s VM Wave-Current Interaction StCOR StC O R H zD HM st Description 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) + Roller Model + Streaming Implemented in Kumar et al., 2011 Implemented in Kumar et al., 2012 *Processes in italics are optional WEC_VF (Uchiyama et al., 10) + Dissipation (depth) + Roller Model + Wave mixing + Streaming cppdefs.h (COAWST/ROMS/Include) WEC_MELLOR+ WEC_VF (preferred method for 3D) Activates the Mellor (2011) method for WEC 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: (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 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 REFDIF. See Haas and Warner, 2009. ROLLER_RENIERS Activate wave roller based on Reniers et al. (2004). See Eqn. 34-37 (Advection-Diffusion) Note: (a)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 • 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 TKE_WAVEDISS INPUT file as ZOS_HSIG_ALPHA (roughness from ZOS_HSIG 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. 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 Shoreface Test Case (Obliquely incident waves on a planar beach) Hsig= 2m Tp = 10s θ = 10o [0,0] z y x [1000,-12] 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 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 ./coawst.bash –j N Header (*.h) & Analytical (ana_*.h) Files 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 Cross-shore Longshore Vertical Stokes WEC related Diagnostics Terms (i.e., contribution to momentum balance) Terms in momentum balance 𝜕 𝐻 ⋅𝑢 𝜕𝑡 𝑧 𝜕 𝜕 𝜕 𝜕 𝐻𝑧 𝑢𝑢 + 𝐻𝑧 𝑣𝑢 + 𝑢 𝐻𝑧 𝑢 𝑆𝑡 + 𝑢 𝐻𝑧 𝑣 𝑆𝑡 𝜕𝑥 𝜕𝑦 𝜕𝑥 𝜕𝑦 𝜕 𝜕 𝜔𝑠 𝑢 + 𝑢 𝜔𝑠𝑆𝑡 𝜕𝑠 𝜕𝑠 𝐻𝑧 ⋅ 𝑓 ⋅ 𝑣 𝐻𝑧 ⋅ 𝑓 ⋅ 𝑣 𝑠𝑡 𝜕𝜑𝑐 −𝐻𝑧 ⋅ | 𝜕𝑥 𝑧 𝜕𝑣 𝜕𝑢 𝐻𝑧 𝑣 𝑠𝑡 − 𝜕𝑥 𝜕𝑦 𝜔𝑠𝑆𝑡 𝜕𝑢 𝜕𝑠 Definition Output Variable Local Acc. u_accel/ ubar_accel Horizontal Advection u_hadv/ubar_hadv Vertical Advection u_vadv Coriolis Force u_cor/ubar_cor Stokes-Coriolis u_stcor/ubar_stcor Pressure Gradient u_prsgrd/ubar_prs grd Vortex Force u_hjvf/ubar_hjvf Vortex Force u_vjvf Terms in momentum balance Definition Breaking + Roller Acceleration + Streaming 𝐻𝑧 ℱ 𝑤𝜉 (see Eqn. 21) Output Var. u_wbrk/ubar_wbrk u_wrol/ubar_wrol u_bstm/ubar_bstm u_sstm/ubar_sstm BREAKING THE PRESSURE GRADIENT TERM 𝜑𝑐 =𝑔 𝜁𝑐 𝑠 − 𝜁 − 𝑔 − 𝒦 |𝜁 𝑐 + 𝜕𝜑 𝑐 −𝐻𝑧 ⋅ | 𝜕𝑥 𝑧 Pressure Gradient u_prsgrd/ubar_prsgrd Eulerian Contribution ubar_zeta 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 𝜍𝑐 −𝛻⊥ 0 𝑔𝜌 − 𝐾 𝐻𝑧 𝑑𝑠 (𝐄𝐪𝐧. 𝟏𝟑, 𝟒𝟗, 𝐓𝐚𝐛𝐥𝐞 𝟐) 𝜌0 𝑔𝜁 𝑐 + −ℎ 𝑔𝛻⊥ 𝜁 𝑔𝜌 𝑑𝑧 𝜌0 Inlet Test Case (WEC in a tidal inlet) Wave field computed using NORTH SWAN Two way coupling (WEC and CEW) Application Name: INLET_TEST Header file: COAWST/Projects/Inlet_test/Coupled/ inlet_test.h Input file: SOUTH 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 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 oceanatmosphere-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.