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Anisotropic viscosity options

The anisotropic viscosity routine computes the viscous terms in the momentum equation as the divergence of a stress tensor, which is linearly related to the rate-of-strain tensor with viscous coefficents visc_para and visc_perp . These coefficients represent energy dissipation in directions parallel and perpendicular to a specified alignment direction which breaks the isotropy of the dissipation. There are three options for choosing the alignment direction: 1) along the local instantaneous flow direction, 2) along the east direction, and 3) along the coordinate directions (note: the viscous operator is invariant under a rotation of the alignment direction by 90 degrees, so for example, choosing the alignment direction as north, south, east or west are all equivalent.). A functional approach is used to derived the discrete operator, which ensures positive-definite energy dissipation, provided visc_para > visc_perp.

Parallel and perpendicular viscosities can vary in space by setting the flag lvariable_hmix_aniso to .true. The spatially-varying viscosities in the parallel and perpendicular directions are read from a file (var_viscosity_infile). A specific form of the viscosities useful for CESM1 coupled simulations can be internally computed if the input filename is 'ccsm-internal'. In such a case, the six viscosity parameters for the form must also be supplied.

The viscosities may optionally (lsmag_aniso = .true.) be evaluated with Smagorinsky-like non-linear dependence on the deformation rate, which is proportional to the norm of the strain tensor. With the Smagorinsky option, the viscosities are evalutated as

ν|| max(c|||D|ds2),u||ds)  
ν max(c|D|ds2),uds) (3.3)

where ds = min(dx,dy), |D| = √2|E| is the deformation rate, |E| is the norm of the strain tensor, c|| and c are dimensionless coefficients of order 1, and u|| and u are velocities associated with the grid Reynolds number which determine minimum background viscosities in regions where the nonlinear viscosities are too small to control grid-point noise. Typically u|| and u are order 1 cm/s. Perpendicular Smagorinsky coefficients can be reduced using a latitudinally-dependent Gaussian function. The form of this function is governed by the three smag_lat parameters.


Table: Anisotropic viscosity namelist
&hmix_aniso_nml LANL default CESM1 gx3 dipole-grid default CESM1 gx1 dipole-grid default CESM1 tx0.1v2 dipole-grid default Anisotropic viscosity
hmix_alignment_choice 'flow' 'grid' 'east' 'east' 'flow', 'grid', 'east' choice for alignment of parallel viscosity component (aligned with local flow, grid lines or east-west direction)
lvariable_hmix_aniso .false. .true. .true. .true. .true., .false. use spatially-varying viscosity
lsmag_aniso .false. .false. .false. .false. .true., .false. compute viscosities using a Smagorinsky formulation
visc_para 0.0 1.0 50.0 x 107 50.0 x 107   parallel viscosity component (cm2/s)
visc_perp 0.0 1.0 50.0 x 107 50.0 x 107   perpendicular viscosity component (cm2/s)
c_para 0.0 0.0 8.0 8.0   dimensionless parallel Smagorinsky coeff
c_perp 0.0 0.0 8.0 8.0   dimensionless perpendicular Smagorinsky coeff
u_para 0.0 0.0 5.0 5.0   velocity (cm/s) for grid Reynolds no. viscous limit in parallel direction
u_perp 0.0 0.0 5.0 5.0   velocity (cm/s) for grid Reynolds no. viscous limit in perpendicular direction
var_viscosity_infile 'unknown_var_viscosity_infile' 'ccsm-internal' 'ccsm-internal' 'ccsm-internal' string ≤ 256 characters name of file containing variable viscosity factors or internal generation of a ccsm-specific form
var_viscosity_infile_fmt 'bin' 'bin' 'bin' 'bin' 'bin', 'nc' viscosity input file format
var_viscosity_outfile 'unknown_var_viscosity_outfile' auto-filled by CESM1 scripts (*pop.v.*) auto-filled by CESM1 scripts (*pop.v.*) auto-filled by CESM1 scripts (*pop.v.*) string ≤ 256 characters output file for writing internally-generated variable viscosity
var_viscosity_outfile_fmt 'bin' 'nc' 'nc' 'nc' 'bin', 'nc' viscosity output file format
vconst_1 1.e7 1.0e7 0.6e7 0.6e7   CESM1 variable viscosity parameter (cm2/sec)
vconst_2 24.5 24.5 0.5 0.5   CESM1 variable viscosity parameter
vconst_3 0.2 0.2 0.16 0.16   CESM1 variable viscosity parameter
vconst_4 1.e-8 1.e-8 2.e-8 2.e-8   CESM1 variable viscosity parameter (1/cm)
vconst_5 3 3 3 3   CESM1 variable viscosity parameter (dimensionless)
vconst_6 1.e7 1.e7 0.6e7 0.6e7   CESM1 variable viscosity parameter (cm2/sec)
vconst_7 N/A 90.0 45.0 45.0   CESM1 variable viscosity parameter (degrees latitude)
smag_lat 20.0 20.0 20.0 20.0   latitude (degrees) for starting variation in Smagorinsky viscosity
smag_lat_fact 0.98 0.98 0.98 0.98   amplitude of Gaussian function for reducing Smagorinsky coefficients
smag_lat_gauss 98.0 98.0 98.0 98.0   width (degrees squared) of Gaussian function for reducing Smagorinsky coefficients



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Physical process options Up: Horizontal mixing parameterizations Previous: Gent-McWilliams isopycnic tracer diffusion   Contents

2010-03-31