Various approximations of mathematical models of planetary internal gravity waves in the f-plane approximation

Abstract

The paper proposes a mathematical model describing the propagation of internal inertial-gravity waves (IIGWs) in a stratified atmosphere. The necessity to propose a novel mathematical model stems from the fact that, as shown in the paper, the temperature disturbance field in the existing mathematical models depicting internal gravity waves (IGWs) in the incompressible fluid and anelastic gas approximations is not consistent with the temperature disturbance field derived from the heat conduction equation. In these models, the temperature field is obtained from the diagnostic Boussinesq relation, which states a direct proportionality between the density disturbance (or potential temperature disturbance) and the temperature disturbance. The temperature field in the compressible fluid approximation is consistent, yet it also describes the acoustic spectrum. In this paper, we propose a mathematical model describing the IIGWs in the compressible fluid approximation. In this model, the temperature field is consistent with the heat conduction equation, and the acoustic spectrum is absent. The paper also proposes a general mathematical model for the propagation of IIGWs in a baroclinic atmosphere. This model differs from the compressible fluid approximation in that the state of an air parcel is described not by the adiabatic equation, but by the Mendeleev–Clapeyron equation.