The Effect of Nonlinearities on the Evolution of Barotropic Easterly Waves in a Nonuniform Environment

Abstract

The nonlinear evolution of a barotropic Rossby wave in a nonuniform basic state is studied numerically. The simulations are designed to isolate and clarify the role of advective nonlinearities in the development process. The model is barotropic, nondivergent and inviscid, on a beta-plane. The steady basic flow is zonally and meridionally nonuniform, and is maintained by a specified steady vorticity source. The wave propagates through an isolated inhomogeneity and interacts with the basic flow. Nonlinear effects are isolated by suppressing the nonlinear terms in the equations. Two sets of experiments have been carried out. In the first the basic state is an isolated steady vortex embedded in a uniform easterly flow. A single plane wave propagates through the isolated vortex inhomogeneity. In the second the basic state is a zonally varying unstable easterly jet. The inhomogeneity is an isolated region of enhanced instability of the jet. The linearly most unstable wave mode is allowed to evolve to finite amplitude in a uniform region of the jet. The wave then propagates through the isolated region of enhanced instability. It is found that advective nonlinearities enhance the development of the waves evolving in a nonuniform environment by allowing more effective use of sources of vorticity associated with the inhomogeneity. The nonlinearities allow fluid parcels to move more slowly and/or more directly through the vorticity source. The results are compared with both the observed development of tropical storms and previous theoretical results.