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) (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