Stochastic closure for nonlinear Rossby waves

Abstract

An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for two-dimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.