Linear dynamics of hydrostatic adjustment to horizontally homogeneous heating

The process of hydrostatic adjustment to horizontally homogeneous heating i n a stably stratified atmosphere of arbitrary thermal structure is investig ated 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 found by numerically integrating the equations in time. During the process of hydrostatic adjustment acoustic-buoyancy oscillations are gener ated. The amplitudes of these oscillations become so great that static inst ability is generated at heights above 100 km, depending on where and how ab ruptly the heat is added. As a crude representation of the unstable breakdo wn and damping of these waves. Rayleigh damping is introduced. If the assoc iated damping coefficient in the upper atmosphere is sufficiently large (gr eater than the Brunt Vaisala frequency), the oscillations vanish. Below a h eight of about 50 km the steady state predicted by the above mentioned diff erential equation is reached approximately in 10 min.