Numerical experiments on the behavior of Rossby waves in the critical layer

Abstract

The barotropic vorticity equation is numerically integrated in time to study the behavior of Rossby waves in the vicinity of the critical latitude. The integrations are conducted with linear, quasi-linear (wave-mean flow interaction), and nonlinear models on a sphere for both the inviscid and viscous cases. The meridional resolution required for the correct representation of a vorticity overturning is determined for both the inviscid and viscous cases. The Stewartson–Warn–Warn (SWW) analytical solution is reexamined by comparison with the present numerical results. The cat's eye represented by the closed streamfunction is tilted in the present model results, unlike that in a ‘scaled model’ based on the SWW solution. It is shown that this discrepancy is due to the omission of the meridional structure of the disturbance in the first-order matched asymptotic expansions in the SWW solutions.