1. 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, /j.ocemod
*also see Olabarrieta et al., 2012 (fourth paper for applications)

2. 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)

3. Exchange of Data Field

4. 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)

5. 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

6. 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 (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.

7. 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

8. Bottom and Surface Streaming
BOTTOM_STREAMING
Bottom streaming due to waves using Uchiyama et al. (2010) methodology. See Eqn 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, See Eq. 27.
SURFACE_STREAMING
Surface streaming using Xu and Bowen, 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

9. 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

10. Header File (COAWST/ROMS/Include)

11. Input File (COAWST/ROMS/External)

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

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

14. 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

15. 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

16. 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

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

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

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

20. 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

21. 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

22. 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

23. Header File (COAWST/Projects/Inlet_test/Coupled)

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

25. 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

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

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

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

29. 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

30. Results
Hsig

31. 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, /j.ocemod 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 , /j.coastaleng Olabarrieta, M., J. C. Warner, and N. Kumar (2011), Wave-current interaction in Willapa Bay, J. Geophys. Res., 116, C12014, doi: /2011JC 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 , ISSN , /j.cageo 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 , ISSN , /j.ocemod