Linear dynamics of hydrostatic adjustment to horizontally homogeneous heating

Abstract

The process of hydrostatic adjustment to horizontally homogeneous heating in a stably stratifiedatmosphere of arbitrary thermal structure is investigated in the limit of small perturbations. Alinear differential equation is derived for the vertical pressure distribution in the final balancedstate. Solutions of this equation are compared with the time dependent solution which is foundby numerically integrating the equations in time. During the process of hydrostatic adjustmentacoustic-buoyancy oscillations are generated. The amplitudes of these oscillations become sogreat that static instability is generated at heights above 100 km, depending on where and howabruptly the heat is added. As a crude representation of the unstable breakdown and dampingof these waves, Rayleigh damping is introduced. If the associated damping coefficient in theupper atmosphere is sufficiently large (greater than the Brunt Väisälä frequency), the oscillationsvanish. Below a height of about 50 km the steady state predicted by the above mentioneddifferential equation is reached approximately in 10 min.