Transcript Wave-current Interaction using the Vortex Force Method

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.