Report

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-atmospherewave-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 Governing Equations Momentum Balance + . + − ℬ + × = Continuity ⋅= Eulerian Mean Flow () + Oscillatory Flow ( ) Recipes for Wave-Current Interaction Radiation Stress ⋅ = ⋅ + ⋅ ;with ⋅ = Vortex Force Formalism ⋅ = + × × This term on phase averaging gives vortex force Radiation Stress Excess flux of momentum due to presence of waves. Explains wave setup, wave setdown, generation of longshore currents, rip currents. 2-D Radiation Stress Equations (Longuet-Higgins, 1962, 1964) = = Swash ∙ 2 + 1 − 0.5 ∙ 2 2 ∙ 2 2 . 2 + 1 − 0.5 Wave Setup: Balance between quasi-static pressure and radiation stress divergence Breaker Zone Surf Zone set-up set-down MWL Longshore Currents: Generated due to gradient of radiation Beach Profile stress in longshore direction Vortex Force (VF) Product of Stokes drift and mean flow vorticity (Craik and Leibovich, 1976). Alongshore Physically representative of wave refraction due to current shear × = Stokes drift = Depth-mean ambient flow = () − + − Cross-shore Adapted from Smith (2006, JPO) Wave Rollers Stokes-Coriolis Force, Surface and Bottom Streaming Cross-shore Vel. Wave-propagation direction From Lentz et al., 2008 Alongshore Vel. Wave-averaged Eqns. Radiation Stress + + + Local Acc. Advective accn. − = − Coriolis + Stokes-Coriolis 1 0 Pressure Gradient − + + Radiation Stress Bottom Stress Accounts for wave breaking Vortex Force Formalism 1 + + + + + + − − = − 0 Local Coriolis Stokes Pressure Advective accn. Acc. -Coriolis Gradient + − − + + ℱ Accounts for wave breaking Vortex Force Bottom Non-conservative Stress forcing Wave-averaged Eqns. Vortex Force Formalism 1 + + + + + + − − = − 0 Local Coriolis Stokes Pressure Advective accn. Acc. -Coriolis Gradient + − − + + ℱ Accounts for wave breaking Vortex Force Bottom Non-conservative Stress forcing Depth-limited breaking Whitecapping Wave Rollers Bottom Streaming Surface Streaming Depth-limited Breaking 1 − α ) ⋅ = 0 ⋅ ⋅ = Dissipation due to depth-limited breaking (from empirical formulations or SWAN) = . −ℎ 2 = cosh + Surface Intensified Methodology Coupled-Ocean-Atmosphere-Wave-Sediment-Transport (COAWST) modeling system Integrate oceanic, atmospheric, wave and morphological processes in the coastal ocean (Warner et al., 2010) WRF SWAN ROMS CSTMS 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 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 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 (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 • Enhanced vertical mixing from waves within framework of GLS. See Eq. 44, 46 and 47. Based on Feddersen and Trowbridge, 05 • 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) Bottom and Surface Streaming Bottom streaming due to waves using Uchiyama et al. (2010) methodology. See Eqn. 22-26. This method BOTTOM_STREAMING requires dissipation due to bottom friction. If not using a wave model, then uses empirical Eq. 22. BOTTOM_STREAMING Bottom streaming due to waves based on methodology of Xu and Bowen, 1994. See Eq. 27. _XU_BOWEN Surface streaming using Xu and Bowen, 1994. See Eq. SURFACE_STREAMING 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 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 WEC Related Output 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 ⋅ + + + + ⋅ ⋅ ⋅ ⋅ − ⋅ | − 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 ℱ (see Eqn. 21) Output Var. u_wbrk/ubar_wbrku_wrol/ub ar_wrol u_bstm/ubar_bstmu_sstm/ub ar_sstm BREAKING THE PRESSURE GRADIENT TERM = − − − | + − ⋅ | Pressure Gradient u_prsgrd/ubar_prsgrd Eulerian Contribution ubar_zeta Quasi-static response, Eqn. 7 ubar_zetw ⊥ | Bernoulli-head contribution, Eqn. 5 ubar_zbeh ⊥ | Surface pressure boundary, Eqn. 9 ubar_zqsp −⊥ 0 − (. , , ) 0 + −ℎ ⊥ 0 Vertical profile of terms in momentum balance Cross-shore Breaking Acc. Hor. Advection ⋅ + Hor. VF Pressure Gradient − 1 Vertical Mixing ′ ′ − Vertical Advection ⋅ + Alongshore DUCK’ 94- Nearshore Experiment DUCK’ 94, NC-Nearshore Experiment 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. Wave Parameters, Depth-Averaged Flows Hrms Wave Height Sea Surface Elevation εb η Depth averaged cross-shore velocity u v Depth averaged longshore velocity Vertical profile of Cross-shore & Longshore Vel. Cross-shore Eulerian Stokes Drift Notes: = () ≠ () Alongshore Vertical Distribution of Wave Dissipation Kumar et al., 2012 Comparison to Field Observations Cross-shore Alongshore Obs from Garcez-Faria et al., 1998, 2000 Kumar et al., 2012 Vertical profile of terms in momentum balance Cross-shore Breaking Acc. Alongshore Notes: Hor. Advection Over the bar (a) VF balances Breaking Hor. VF (b) VM balances Advection ⋅ + Pressure Gradient − 1 Vertical Mixing ′ ′ − Vertical Advection ⋅ +