Equations of Hydro-and Thermodynamics of the Atmosphere when Inertial Forces Are Small in Comparison with Gravity

Abstract

Hydrodynamic and thermodynamic equations for the atmosphere are considered in the meteorological and climatic scales in which the inertial forces are negligibly small in comparison with gravity. In this case, the inertia of the horizontal velocity and temperature has an effect. For such a vertically quasi-static flow, an equation for the vertical velocity distribution asymptotically exact in density, temperature, and horizontal velocity is obtained. A closed system of hydro- and thermodynamic equations is presented in which the pressure at each point is determined by the weight of the air column above this point. It is this system of equations that should be used to calculate the climatic and meteorological processes in which the inertia of the horizontal velocity and the inertialess vertical velocity play an essential role.