[MITgcm-support] Sensitivity of Tidal Forcing on Boundary Conditions

[Ren, Chunyu]

Dear MITgcm community,

I have been running a simple 2D, homogeneous model to test the sensitivity of tidal forcing on boundary conditions. The model setup is quite simple and idealized: it has a flat bottom, a closed inshore boundary (vertical side wall) and an open offshore boundary where a sinusoidal barotropic tide is prescribed (panel a in the attached figure). A negligible linear drag coefficient (1e-12) is employed at the bottom all the time. We ran four simulations with different combinations of the bottom boundary condition (free-slip vs no-slip) and free surface setup (linear vs nonlinear). According to the manual, two of the runs with free-slip have negligible bottom drag, while the other two with no-slip have bottom drag generated from the interior viscosity.

 The simulation results differ dramatically across these cases which is quite confusing. Specifically, we observed very different sea surface height (SSH) tilt in the direction of the tidal flow during equilibrium (panel c). Furthermore, the SSH tilt cannot be explained by the divergence/convergence of the depth-integrated volume transport in the same direction (panel b). I was curious if anyone has seen similar behaviors before or can comment on whether the result is physical or not. An example data file for one of the cases is also attached below. Thanks very much for your time!

Best,
Chunyu
[cid:8133117c-2f2a-4183-a2ac-468f84c8e65e]
Data File for Case 1:
# Model parameters
# Continuous equation parameters
 &PARM01
# Viscosity
 viscAh=3,
 viscAr=3.E-3,
 implicitViscosity=.TRUE.,
# Diffusivity and convection
 diffKhT=3,
 diffKrT=3.E-5,
 ivdc_kappa=0.,
 implicitDiffusion=.TRUE.,
# Coriolis parameter
 f0=1.e-4,
 beta=0.,
 selectCoriScheme=0,
# Density and equation of state
#Momentum
 momTidalForcing=.FALSE.,
# Bottom Conditions
 no_slip_sides=.TRUE.,
 no_slip_bottom=.TRUE.,
 bottomDragLinear=5.E-12,
#bottomDragQuadratic=0.0025,
# Temp only active tracer, no salinity
 rhoConst=1000.,
 rhoNil=1000.,
 eosType='LINEAR',
 tAlpha=2.E-4,
 sBeta =0.E-4,
#tRef= 99*0.,
 tRefFile='TRef.bin',
 saltStepping=.FALSE.,
# activate partial cells
 hFacMinDr=0.2,
 hFacMin=0.2,
# free surface parameters
 rigidLid=.FALSE.,
 implicitFreeSurface=.TRUE.,
 exactConserv=.TRUE.,
 nonlinFreeSurf=4,
 select_rStar=2,
 hFacInf=0.2,
 hFacSup=2.0,
# advection scheme
 tempAdvScheme=3,
 staggerTimeStep=.TRUE.,
 useSingleCpuIO = .TRUE.,
 &
# Elliptic solver parameters
 &PARM02
 cg2dTargetResidual=1.E-7,
 cg2dMaxIters=1000,
 &

# Time stepping parameters
 &PARM03
 nIter0=0,
 nTimeSteps=108000,
 deltaT=30.0,
 pChkptFreq=0.0,
 chkptFreq=0.0,
 dumpFreq=3720.,
 monitorFreq=0.,
 monitorSelect=2,
 tauThetaClimRelax=0.,
 momDissip_In_AB=.TRUE.,
#Forcing for boundary condition files
 periodicExternalForcing=.TRUE.,
# 1/12th M2 tidal period...
 externForcingPeriod = 310.,
 externForcingCycle = 44640.,
 &

# Gridding parameters
 &PARM04
 usingCartesianGrid=.TRUE.,
 delX=1000*150.,
 delY=1*1.E3,
 delR=200*1.,
 &

# Input datasets
 &PARM05
 bathyFile='bathy.50km.bin',
 zonalWindFile=,
 uVelInitFile='uvelocity.bin',
 meridWindFile=,
 hydrogThetaFile='temperature.50km.bin',
 &
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