wave-current interaction (wec) in the coawst modeling system nirnimesh kumar, sio with j.c. warner,...
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Wave-current Interaction (WEC) in the COAWST Modeling System
Nirnimesh Kumar, SIOwith 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-atmosphere-wave-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
𝜕𝑼𝜕𝑡
+(𝑼 .𝛻 )𝑼+𝟏𝝆𝟎
𝛻𝑝−ℬ 𝒛+ 𝑓 𝒛×𝑼=𝟎Momentum Balance
Continuity 𝛻 ⋅𝑼=𝟎Eulerian
Governing Equations
;withRadiation Stress
Vortex Force Formalism
(𝑼 ⋅ 𝛻 )𝑼=𝛁|𝑼|𝟐 /𝟐+ (𝜵×𝑼 )×𝑼
This term on phase averaging gives vortex force
Recipes for Wave-Current Interaction
Radiation Stress
𝑺=[𝑆 𝑥𝑥 𝑆 𝑥𝑦𝑆 𝑦𝑥 𝑆 𝑦𝑦 ]=𝐸 [𝑛 ∙ (𝑐𝑜𝑠2𝜃+1 )−0.5
𝑛 ∙𝑠𝑖𝑛 2𝜃2
𝑛 ∙𝑠𝑖𝑛2 𝜃2
𝑛 . (𝑠𝑖𝑛2𝜃+1 )−0.5]2-D Radiation Stress Equations (Longuet-Higgins, 1962, 1964)
Excess flux of momentum due to presence of waves. Explains wave setup, wave setdown, generation of longshore currents, rip currents.
Breaker Zone
Surf Zone
set-upMWLset-down
Swash
Beach Profile
Wave Setup:Balance between quasi-static pressure and radiation stress divergence
Longshore Currents:Generated due to gradient of radiation stress in longshore direction
Adapted from Smith (2006, JPO)
𝑼𝑺𝒕 𝑉 (𝑥)𝜵×𝑼
Cross-shore
Alon
gsho
re
Stokes drift
h-mean ambient flow
𝑽𝑭=𝑉 𝑆𝑡(𝜕𝑉𝜕 𝑥 − 𝜕𝑈𝜕𝑦 ) �̂�+𝑈𝑆𝑡 (𝜕𝑉𝜕 𝑥 − 𝜕𝑈
𝜕𝑦 ) �̂�
Product of Stokes drift and mean flow vorticity (Craik and Leibovich, 1976).
Physically representative of wave refraction due to current shear
𝑼𝑺𝒕
Vortex Force (VF)
Wave Rollers
Stokes-Coriolis Force, Surface and Bottom Streaming
Cross-shore Vel. Alongshore Vel.
From Lentz et al., 2008
Wave-propagation direction
Wave-averaged Eqns.
𝜕𝑢𝑙
𝜕𝑡+{𝜕 (𝑢𝑙𝑢𝑙 )
𝜕𝑥+𝜕 (𝑢𝑙𝑣 𝑙 )𝜕 𝑦
+𝜕 (𝜔𝑠𝑢
𝑙 )𝜕𝑠 }− 𝑓𝑣 𝑙=−𝐻 𝑧 ( 1
𝜌0
𝜕𝑃𝜕 𝑥 |
𝑧)−{𝜕𝑆𝑥𝑥
𝜕 𝑥+𝜕𝑆𝑥𝑦
𝜕 𝑦 }+𝐷𝑥
Local Acc.
Advective accn. Coriolis + Stokes-Coriolis
Pressure Gradient
Radiation Stress
Bottom Stress
Radiation Stress
Accounts for wave breaking
+{𝑣𝑆𝑡 ( 𝜕𝑣𝜕 𝑥 − 𝜕𝑢𝜕 𝑦 )−𝜔𝑠
❑𝑆𝑡 𝜕𝑢𝜕𝑠 }+𝐷𝑥+ℱ𝑤𝑥
Local Acc.
Advective accn. Stokes-Coriolis
Pressure Gradient
Vortex Force Bottom Stress
𝜕𝑢𝜕𝑡
+{𝜕 (𝑢𝑢)𝜕 𝑥
+𝜕 (𝑢𝑣 )𝜕 𝑦
+𝑢 (𝜕𝑢𝑆𝑡
𝜕 𝑥+𝜕𝑣 𝑆𝑡
𝜕 𝑦 )+ 𝜕 (𝜔𝑠𝑢)𝜕 𝑠
+𝑢𝜕 (𝜔𝑠
❑𝑆𝑡 )𝜕 𝑠 }− 𝑓𝑣− 𝑓 𝑣𝑆𝑡=−( 1
𝜌 0
𝜕𝜑𝜕 𝑥 |
𝑧)
Coriolis
Non-conservative forcing
Vortex Force Formalism
Accounts for wave breaking
Wave-averaged Eqns.
+{𝑣𝑆𝑡 ( 𝜕𝑣𝜕 𝑥 − 𝜕𝑢𝜕 𝑦 )−𝜔𝑠
❑𝑆𝑡 𝜕𝑢𝜕𝑠 }+𝐷𝑥+ℱ𝑤𝑥
Local Acc.
Advective accn. Stokes-Coriolis
Pressure Gradient
Vortex Force Bottom Stress
𝜕𝑢𝜕𝑡
+{𝜕 (𝑢𝑢)𝜕 𝑥
+𝜕 (𝑢𝑣 )𝜕 𝑦
+𝑢 (𝜕𝑢𝑆𝑡
𝜕 𝑥+𝜕𝑣 𝑆𝑡
𝜕 𝑦 )+ 𝜕 (𝜔𝑠𝑢)𝜕 𝑠
+𝑢𝜕 (𝜔𝑠
❑𝑆𝑡 )𝜕 𝑠 }− 𝑓𝑣− 𝑓 𝑣𝑆𝑡=−( 1
𝜌 0
𝜕𝜑𝜕 𝑥 |
𝑧)
Coriolis
Non-conservative forcing
Vortex Force Formalism
Accounts for wave breaking
Surface Streaming
Bottom Streaming
Whitecapping
Wave Rollers
Depth-limited breaking
Depth-limited Breaking
𝐁𝑏=(1−α𝑟¿⋅ 𝜖𝑏
𝜌 0 ⋅𝜎𝐤 ⋅ 𝑓 𝑏 (𝑧 )
= Dissipation due to depth-limited breaking (from empirical formulations or SWAN)
𝑓 𝑏 (𝑧 )= 𝐹𝐵
∫−h
�̂�
𝐹𝐵 .𝑑𝑧
𝐹𝐵 = cosh ( 2 𝜋𝐻𝑟𝑚𝑠
(𝑧+𝐷 ))
Surface Intensified
Integrate oceanic, atmospheric, wave and morphological processes in the coastal ocean (Warner et al., 2010)
Coupled-Ocean-Atmosphere-Wave-Sediment-Transport (COAWST) modeling system
Methodology
ROMS SWAN
WRF
CSTMShttp://woodshole.er.usgs.gov/operations/modeling/COAWST/index.html
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)
Wave-current Interaction (WEC)
WEC_MELLOR(Mellor, 2011)
WEC_VF(Uchiyama et al., 10)
+ Roller Model+ Streaming
+ Dissipation (depth)+ Roller Model + Wave mixing + Streaming
Implemented in Kumar et al., 2011
Implemented in Kumar et al., 2012
*Processes in italics are optional
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_WAVEMODActivate 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
TKE_WAVEDISSZOS_HSIG
• 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 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)
Bottom and Surface Streaming
BOTTOM_STREAMINGBottom 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
[0,0]
[1000,-12]
z
x
y
Hsig= 2mTp = 10sθ = 10o
Shoreface Test Case (Obliquely incident waves on a planar beach)
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 fileas 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)
Cross-shore
Longshore
Vertical
Eulerian Stokes
WEC related Diagnostics Terms(i.e., contribution to momentum balance)Terms in momentum balance Definition Output
VariableLocal Acc. u_accel/
ubar_accelHorizontal Advection u_hadv/ubar_hadv
Vertical Advection
u_vadv
Coriolis Force u_cor/ubar_cor
Stokes-Coriolis u_stcor/ubar_stcorPressure Gradient
u_prsgrd/ubar_prsgrd
Vortex Force u_hjvf/ubar_hjvf
Vortex Force u_vjvf
Terms in momentum balance Definition Output Var.
(see Eqn. 21)Breaking + Roller Acceleration + Streaming
u_wbrk/ubar_wbrku_wrol/ubar_wrolu_bstm/ubar_bstmu_sstm/ubar_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
Vertical profile of terms in momentum balance
Breaking Acc.
Hor. Advection
Hor. VF
Pressure Gradient
Vertical Mixing
Vertical Advection
Alongshore Cross-shore
DUCK’ 94, NC-Nearshore Experiment
DUCK’ 94- 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.
Sea Surface Elevation
Depth averagedcross-shore velocity
Depth averagedlongshore velocity
Wave Height
Wave Parameters, Depth-Averaged Flows
η
u
v
Hrms
εb
Vertical profile of Cross-shore & Longshore Vel.Cr
oss-
shor
e Al
ongs
hore
Eulerian
Kumar et al., 2012
Stokes Drift
Notes:
Vertical Distribution of Wave Dissipation
Comparison to Field Observations
Cross-shore
Alongshore
Obs from Garcez-Faria et al., 1998, 2000 Kumar et al., 2012
Alongshore Cross-shore
Vertical profile of terms in momentum balance
Breaking Acc.
Hor. Advection
Hor. VF
Pressure Gradient
Vertical Mixing
Vertical Advection
Notes:
Over the bar (a) VF balances Breaking
(b) VM balancesAdvection