Energy Relations of Atmospheric Tides and Their Significance to Approximate Methods of Solution for Tides with Dissipative Forces

Abstract

The concepts of kinetic energy, potential energy and energy flux are clarified and quantified for atmospheric tides. An understanding of the tidal energy relations provides physical insight into the problem of dissipative effects an tidal structure. It is shown that mode coupling effects due to dissipative forces are related to the coupling of kinetic energy between different tidal modes, and the mode-coupling coefficients are computed for several tidal modes. A relation is derived linking energy density and variations of the eigenvalues of Laplace's tidal equation with frequency. A formalism of ?analogous atmospheric oscillations? in a plane-parallel, uniformly rotating atmosphere is proposed to provide an approximate method of computing tidal structure in the presence of dissipative forces.