Boundary Conditions on Quasi-Stokes Velocities in Parameterizations

Abstract This paper examines the implications for eddy parameterizations of expressing them in terms of the quasi-Stokes velocity. Another definition of low-passed time-averaged mean density (the modified mean) must be used, which is the inversion of the mean depth of a given isopycnal. This definition naturally yields lighter (denser) fluid at the surface (floor) than the Eulerian mean since fluid with these densities occasionally occurs at these locations. The difference between the two means is second order in perturbation amplitude, and so small, in the fluid interior (where formulas to connect the two exist). Near horizontal boundaries, the differences become first order, and so more severe. Existing formulas for quasi-Stokes velocities and streamfunction also break down here. It is shown that the low-passed time-mean potential energy in a closed box is incorrectly computed from modified mean density, the error term involving averaged quadratic variability. The layer in which the largest differences ...

[1]  Stephen M. Griffies,et al.  The Gent–McWilliams Skew Flux , 1998 .

[2]  Richard J. Greatbatch,et al.  Exploring the Relationship between Eddy-Induced Transport Velocity, Vertical Momentum Transfer, and the Isopycnal Flux of Potential Vorticity , 1998 .

[3]  M. Spall,et al.  Specification of eddy transfer coefficients in coarse resolution ocean circulation models , 1997 .

[4]  T. McDougall,et al.  Isopycnal Averaging and the Residual Mean Circulation , 1996 .

[5]  M. Eby,et al.  Sensitivity of a Large-Scale Ocean Model to a Parameterization of Topographic Stress , 1994 .

[6]  A. Bennett,et al.  Microstructure Fluxes across Density Surfaces , 1993 .

[7]  R. Greatbatch,et al.  On Parameterizing Vertical Mixing of Momentum in Non-eddy Resolving Ocean Models , 1990 .

[8]  B. Hoskins,et al.  Eliassen-Palm Cross Sections for the Troposphere , 1980 .

[9]  D. G. Andrews,et al.  Planetary Waves in Horizontal and Vertical Shear: The Generalized Eliassen-Palm Relation and the Mean Zonal Acceleration , 1976 .

[10]  A. Robinson,et al.  The Baroclinic Instability of the Open Ocean , 1974 .

[11]  J. Green,et al.  Transfer properties of the large‐scale eddies and the general circulation of the atmosphere , 1970 .

[12]  F. Bretherton.  Critical layer instability in baroclinic flows , 1966 .

[13]  E. T. Eady,et al.  Long Waves and Cyclone Waves , 1949 .

[14]  A. M. Treguier,et al.  Evaluating eddy mixing coefficients from eddy-resolving ocean models : A case study , 1999 .

[15]  T. McDougall.  Three-Dimensional Residual-Mean Theory , 1998 .

[16]  P. Gent,et al.  Isopycnal mixing in ocean circulation models , 1990 .