Linear dynamics of hydrostatic adjustment to horizontally homogeneous heating

The process of hydrostatic adjustment to horizontally homogeneous heating in a stably stratified atmosphere of arbitrary thermal structure is investigated in the limit of small perturbations. A linear differential equation is derived for the vertical pressure distribution in the final balanced state. 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 adjustment acoustic-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 how abruptly the heat is added. As a crude representation of the unstable breakdown and damping of these waves, Rayleigh damping is introduced. If the associated damping coefficient in the upper atmosphere is sufficiently large (greater than the Brunt Väisälä frequency), the oscillations vanish. Below a height of about 50 km the steady state predicted by the above mentioned differential equation is reached approximately in 10 min.