Equivalent gravity modes—An interim evaluation

Abstract

The behavior of the main solar semidiurnal tidal mode in a dissipative atmosphere is studied both in a rotating spherical atmosphere and by means of the equivalent gravity mode approximation. The former involves the neumerical solution of a two dimensional partial differential equation which (due to the presence of friction) is non-separable. The latter involves approximating the tidal mode at the equator by means of an internal gravity wave on a non-rotating plane; this approximation has been used extensively in earlier studies of the behavior of atmospheric tides in the thermosphere where viscosity assumes dominant importance. In the present study, dissipation is modelled by Newtonian cooling and Rayleigh. friction, both of which are taken to increase inversely with mean density. Coefficients are chosen to crudely simulate the effects of molecular viscosity and conductivity. The results of this study provide an opportunity to evaluate the equivalent gravity mode formalism. Our main findings are:

(i) Below 130 km, where friction is unimportant, equivalent gravity mode results are, for all practical purposes, identical to those at the equator obtained from a spherical calculation.

(ii) Above 130 km amplitudes over the equator obtained from the spherical calculation are about 30% smaller than those obtained from the equivalent gravity mode calculations. Also, there is a 15°xs (½ hour) difference in phase.

(iii) The amplitude reduction over the equator, cited above, is associated with a broadening of the latitude distribution of amplitude for the oscillatory pressure and temperature fields within the thermosphere. There is also a significant variation of phase with latitude within the thermosphere. Associated with the above variations are significant changes in the latitude distribution of horizontal velocity within the thermosphere.