Planetary Waves in Horizontal and Vertical Shear: Asymptotic Theory for Equatorial Waves in Weak Shear

Abstract

A simple multiple-scale expansion procedure is given for calculating corrections to the structure of equatorial planetary waves in the presence of weak shear and dissipation. For upward-propapting Rossby-gravity (Yanai-Maruyama) and Kelvin (Wallace-Kousky) waves, explicit results are obtained for the case of Newtonian cooling and Rayleigh friction, correct to the first two orders in the ratio μ of wave to mean-flow height scales. The results are used in a direct calculation of the horizontal Reynolds stress u′v′¯ and demonstrate the strong dependence of u&primev′¯ on the ratio of friction to cooling coefficients. In certain parameter regimes of interest in the tropical stratosphere, a slight north-south asymmetry in the y profile of ū can cause changes in the wave structure such that the mean zonal acceleration ∂ū/∂t tends to have the same asymmetry. That is, there may be a tendency for asymmetries in ū(y) to amplify in the presence of dissipating waves.