Generalized Hough Modes: The Structure of Damped Global-Scale Waves Propagating on a Mean Flow with Horizontal and Vertical Shear

Abstract

The technique of classical tidal theory in which linear disturbances to a background flow at rest are expanded in terms of Hough modes is generalized for damped disturbances to a general zonal mean state under the assumption that the vertical scale of the background flow is longer than the vertical scale of the disturbance. Generalized Hough modes provide an alternative to the concept of mode coupling between classical modes as a means of describing how the mean flow and damping affect the wave structure. Generalized modes take into account the horizontal shear of the mean flow and damping at lowest order. Effects of vertical shear in the mean flow only arise as first-order corrections, and hence generalized modes provide exact modal solutions to the linearized primitive equations when the mean flow only varies with latitude.