PUBLIC INTERFACE ~ PUBLIC ROUTINES ~ NAMELIST

Module ocean_lapcgrid_friction_mod

Contact:  S. M. Griffies
Reviewers: 
Change History: WebCVS Log

OVERVIEW

This module computes the thickness weighted time tendency for horizontal velocity arising from horizontal Laplacian friction. Friction is formulated for the C-grid here.

This module computes the thickness weighted time tendency for horizontal velocity arising from horizontal Laplacian friction. The viscosity used to determine the strength of the tendency can be a general function of space and time as specified by the Smagorinsky approach as well as a grid-scale dependent background viscosity. The form of the friction operator can be isotropic or anisotropic in the horizontal plane. Friction is formulated for the C-grid here.

OTHER MODULES USED

       constants_mod
    diag_manager_mod
             fms_mod
     mpp_domains_mod
             mpp_mod
   ocean_domains_mod
       ocean_obc_mod
 ocean_operators_mod
ocean_parameters_mod
     ocean_types_mod
      ocean_util_mod
 ocean_workspace_mod

PUBLIC INTERFACE

ocean_lapcgrid_friction_init:
lapcgrid_friction:
lapcgrid_viscosity_check:
lapcgrid_reynolds_check:
compute_neptune_velocity:

PUBLIC ROUTINES

  1. ocean_lapcgrid_friction_init

    DESCRIPTION
    Initialize the horizontal Laplacian friction module by registering fields for diagnostic output and performing some numerical checks to see that viscosity is set appropriately.


  2. lapcgrid_friction

    DESCRIPTION
    This routine computes thickness weighted and density weighted time tendency for horizontal velocity arising from horizontal Laplacian friction. The algorithm is derived from a functional approach that ensures kinetic energy is consistenty dissipated for all flow configurations. The stencil is far simpler than the B-grid approach. In particular, there are no triads here for the C-grid. Fundamental to the scheme are the rates of horizontal deformation horizontal tension = DT = (dy)(u/dy)_x - (dx)(v/dx)_y horizontal strain = DS = (dx)(u/dx)_y + (dy)(v/dy)_x Units of the tension and strain are sec^-1.


  3. lapcgrid_viscosity_check

    DESCRIPTION
    Subroutine to perform linear stability check for the Laplacian operator given a value for the horizontal biharmonic viscosity.


  4. lapcgrid_reynolds_check

    DESCRIPTION
    Subroutine to compute the LLaplacian grid Reynolds number. Large Reynolds numbers indicate regions where solution may experience some grid noise due to lack of enough horizontal friction.


    INPUT
    u    Horizontal velocity field at time tau
       [real, dimension(isd:ied,jsd:jed,nk,2)]

  5. compute_neptune_velocity

    DESCRIPTION
    Compute Neptune velocity for c-grid. Method follows that used in MOM2 and MOM3 as implemented by Greg Holloway (zounds@ios.bc.ca) and Michael Eby (eby@uvic.ca) Coded in mom4 by Stephen.Griffies Neptune is calculated as an equilibrium streamfunction given by pnep = -f*snep*snep*ht and is applied through friction whereby the solution is damped towards the equilibrium streamfunction rather than being damped towards zero kinetic energy. hu = depth of B-grid velocity corner snep = spnep + (senep-spnep)*(0.5 + 0.5*cos(2.0*latitude)) Neptune length scale snep has a value of senep at the equator and smoothly changes to spnep at the poles Reference: Holloway, G., 1992: Representing topographic stress for large scale ocean models, J. Phys. Oceanogr., 22, 1033-1046 Eby and Holloway, 1994: Sensitivity of a large scale ocean model to a parameterization of topographic stress. JPO, vol. 24, pages 2577-2588 March 2012 Stephen.Griffies Algorithm updated to Eby and Holloway (1994) May 2012 Stephen.Griffies upgraded to Cgrid


NAMELIST

&ocean_lapcgrid_friction_nml

use_this_module
Must be true to use this module. Default is false.
[logical]
debug_this_module
For debugging by printing checksums.
[logical]
viscosity_scale_by_rossby
To scale down the laplacian viscosity according to the relative scale of the horizontal grid and the first baroclinic Rossby radius. This is a useful scheme for models that resolve the Rossby radius in the lower latitudes, and so presumably do not wish to have much laplacian friction, whereas the higher latitudes need more friction. Default viscosity_scale_by_rossby=.false.
[logical]
viscosity_scale_by_rossby_power
The power used to determine the viscosity scaling function. Default viscosity_scale_by_rossby_power=2.0.
[real]
divergence_damp
To damp the divergence field.
[logical]
divergence_damp_vel_micom
Velocity scale to set the viscosity used with divergence damping.
[real, units: m/s]
k_smag_iso
This is the dimensionless Smagorinsky coefficient used to set the scale of the Smagorinsky isotropic viscosity.
[real, units: dimensionless]
k_smag_aniso
This is the dimensionless Smagorinsky coefficient used to set the scale of the Smagorinsky anisotropic viscosity.
[real, units: dimensionless]
vel_micom_iso
Velocity scale that is used for computing the MICOM isotropic viscosity.
[real, units: m/sec]
vel_micom_aniso
Velocity scale that is used for computing the MICOM anisotropic viscosity.
[real, units: m/sec]
equatorial_zonal
Orient the anisotropic friction within a latitudinal band according to zonal direction.
[logical]
equatorial_zonal_lat
Latitudinal band to use the zonal friction orientation.
[real]
equatorial_no_smag
Turn smag off within equatorial_zonal_lat region.
[logical]
eq_vel_micom_iso
Velocity scale that is used for computing the MICOM isotropic viscosity within a user specified equatorial band.
[real]
eq_vel_micom_aniso
Velocity scale that is used for computing the MICOM anisotropic viscosity within a user specified equatorial band.
[real]
eq_lat_micom
Equatorial latitude band (degrees) within which the MICOM viscosity is set according to eq_vel_micom_iso and eq_vel_micom_aniso.
[real]
restrict_polar_visc
For restricting the background viscosity poleward of a latitude. This method may be useful for coupling to an ice model in which case the horizontal viscosity may need to be a bit smaller to maintain time step constraints. This is because the effective friction is larger than that just within the ocean.
[logical]
restrict_polar_visc_lat
Latitude poleward of which we restrict the viscosity.
[real]
restrict_polar_visc_ratio
Ratio of the normal critical value that we limit the viscosity to be no greater than. If restrict_polar_visc_ratio=1.0 then there is no special limitation of the viscosity beyond that of the one-dimensional stability constraint.
[real]
neptune
Set to true for computing friction relative to Neptune barotropic velocity. Default neptune=.false.
[logical]
neptune_length_eq
Length scale used to compute Neptune velocity at equator.
[real, units: m]
neptune_length_pole
Length scale used to compute Neptune velocity at pole.
[real, units: m]
neptune_depth_min
Minimum depth scale used for computing Neptune velocity. Default neptune_depth_min=100.0
[real, units: m]
neptune_smooth
For doing a horizontal 1-2-1 smoothing on the diagnosed neptune velocity scale. Default neptune_smooth=.true.
[logical]
neptune_smooth_num
Number of smoothing passes for neptune velocity. Default neptune_smooth_num=1.
[integer]
use_side_drag_friction
For converting friction at U-cells next to walls into a drag law, as per Deremble et al. Use cdbot_array from ocean_core/ocean_bbc.F90 to compute drag force. Default use_side_drag_friction=.false.
[logical]
side_drag_friction_scaling
Dimensionless scaling used for cdbot_array when setting side drag friction. So the effective side dragy coefficient is side_drag_friction_scaling*cdbot_array. Default side_drag_friction_scaling=1.0.
[real]
side_drag_friction_uvmag_max
Maximum magnitude of horizontal velocity used to compute the side drag friction. This parameter can be useful especially for pressure models where the bottom cells can be quite thin and subject to sporadic large magnitudes. We do the same thing with bottom drag calculations. Default side_drag_friction_uvmag_max=10.0.
[real, units: m/s]
side_drag_friction_max
Maximum magnitude of the side drag induced friction. This parameter can be useful especially for pressure models where the bottom cells can be quite thin and subject to sporadic large magnitudes. We do the same thing with bottom drag calculations in ocean_bbc. Default side_drag_friction_max=1.0.
[real, units: N/m^2]

REFERENCES

  1. S.M. Griffies and R.W. Hallberg, 2000: Biharmonic friction with a Smagorinsky viscosity for use in large-scale eddy-permitting ocean models Monthly Weather Review, vol. 128, pages 2935-2946
  2. R. D. Smith and J. C. McWilliams, 2003: Anisotropic horizontal viscosity for ocean models, Ocean Modelling, vol. 5, pages 129-156.
  3. Maltrud and Holloway, 2008: Implementing biharmonic neptune in a global eddying ocean model, Ocean Modelling, vol. 21, pages 22-34.
  4. Deremble, Hogg, Berloff, and Dewar, 2011: On the application of no-slip lateral boundary conditions to coarsely resolved ocean models, Ocean Modelling.
  5. Griffies: Elements of MOM (2012)

NOTES

The ocean model can generally run with both Laplacian and biharmonic friction enabled at the same time. Such has been found useful for some eddying ocean simulations.

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