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 coefficients 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 evaluated as

ν_|| → max(c_|||D|ds²),u_||ds)
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.