Small-Scale Parameterization in Large-Scale Ocean Models

Abstract

The parameterization of sub-grid scale processes, a necessity in present numerical ocean models, is generally accomplished in terms of eddy diffusion coefficients, usually taken as constants. This note examines two non-constant eddy diffusivities which have recently been suggested for processes associated with the diapycnal transport of mass: internal wave induced diffusion considered by Gargett and Holloway [1984] and boundary mixing considered by Armi [1979]. Two points are made: first that both parameterizations are very model-dependent, requiring careful attention to assumptions incorporated in each; second that both processes, as parameterized, lead to diapyncal mass diffusivities which have inverse power-law dependences upon N, K ^∝_d N^−p, p > 0. It is noted that spatial gradients of diffusion coefficients act like velocities in advection-diffusion balances of conservative scalars, and hence may strongly affect ocean property distributions. In addition, vertical gradients of K_d enter the geostrophic vorticity equation, and hence may have dynamical effects. The actual importance of spatially variable diffusivities to numerical model results should be explored. For a proper assessment, diffusivities should be incorporated as acting along and across isopycnals, instead of locally horizontally and vertically.