Diagnostic Relations between Pressure and Entropy Perturbations for Acoustic and Entropy Modes

Abstract

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered and applied to numerical modelling with the direct possibility to use in atmosphere monitoring especially in such strong events which follow magnetic storms and other large scale atmospheric phenomena. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on a vertical coordinate, which essentially complicates the diagnostics. The relations connecting perturbations for acoustic and entropy (stationary) modes are analytically established and led to the solvable diagnostic equations. These equations specify acoustic and entropy modes in an arbitrary stratified gas under the condition of stability. The diagnostic relations are independent of time and specify the acoustic and the entropy modes. They provide the ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts uniquely at any instant within the total accessible heights range. As a prospective model, we consider the diagnostics at the height interval 120–180 km, where the equilibrium temperature of a gas depends linearly on the vertical coordinate. For such a heights range it is possible to proceed with analytical expressions for pressure and entropy perturbations of gas variables. Individual profiles of acoustic and entropy parts for some data are illustrated by the plots for the pure numerical data against those obtained by the model. The total energy of a flow is determined for both approaches and its vertical profiles are compared.

Keywords

• acoustics of non-uniform media
• wave mode diagnostics
• entropy mode
• initialization of hydrodynamic field