The statistical dynamics of turbulent Rossby wave flow over topography

Abstract

The statistical dynamics of Rossby wave turbulence is examined by comparing direct numerical simulation of the vorticity form of the 2-D Navier--Stokes equation with a non-Markovian statistical closure theory for inhomogeneous flow over mean topography. The quasi-diagonal direct interaction approximation closure theory is formulated for the interaction of mean fields, Rossby waves and inhomogeneous turbulence over topography on a generalized ?-plane. The competing effects of nonlinear waves at the large scales and fully developed turbulence at the small scales is examined by comparing closure theory with ensemble averaged results from direct numerical simulation at resolution k=48 for circularly truncated wavenumber space. This work builds on the low resolution ?-plane studies of Frederiksen and O'Kane (2005) and extends the high resolution f-plane studies of O'Kane and Frederiksen (2004) to incorporate waves. We also examine the performance of a computationally efficient restart or cumulant update procedure at moderate Reynolds number in the presence of waves.