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 Kd 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.