Atmospheric oscillations—I

Abstract

A general theory of atmospheric oscillations is developed in which, by expanding in a complete set of vector harmonics, the system of differential equations for the motion can be reformulated, giving a system of matrix differential equations in the vertical variable. General formulae are derived for the matrix elements using group-theoretical methods. The separable case is considered in detail and a matrix representation of the Hough functions and associated eigenvalues is obtained, from which the orthogonality property follows directly; detailed calculations of these eigenfunctions and eigenvalues are made for the lunar diurnal and semi-diurnal oscillations. In Paper II the method will include the determination of the forced tidal oscillations of the combined atmosphere-ionosphere system, with the full Coriolis force.