The transient, linear response of a stably stratified atmosphere to thermal forcing in the presence of a critical level is investigated analytically using the Green's function method. The prescribed thermal forcing is located below or across a critical level. The target solution is for the finite-depth steady forcing, but intermediate solutions to the line-type pulse forcing, finite-depth pulse forcing, and line-type steady forcing are analyzed in some detail because these solutions give some insight into the basic dynamics of the response to the target forcing. The responses to the pulse forcings exhibit the moving mode whose center travels downstream with a speed of the basic-state wind. In the vicinity of the initial forcing, gravity waves are attenuated across the critical level. In response to the line-type pulse forcing, after some time the magnitude of the perturbation vertical velocity at the center of the moving mode remains almost unchanged with time. The transient critical level is a function of the horizontal location and time. In response to the finite-depth pulse forcing, after some time the magnitude of the perturbation vertical velocity at the line that connects the centers of the moving modes at the forcing top and bottom decreases with time due to the geometric expansion of the line. In responses to the steady forcings, the stationary mode as well as the moving mode appear. The origin of the stationary mode is very small-amplitude waves with zero or near-zero horizontal phase velocities in the pulse forcings. These waves work constructively to be perceptible in response to the steady forcings. The stationary mode is almost entirely absorbed at the critical level, and the dynamics of the moving modes in the pulse and steady forcing cases are similar to each other. It is shown that adding a widespread heating (cooling) term eventually yields a steady-state field in the stationary mode. Unlike the steady-state case, there is a gradual decrease of the momentum flux from the thermal forcing top to the critical level. The moving mode can transport a small amount of the momentum flux above the critical level.
|Number of pages
|Journal of the Atmospheric Sciences
|Published - 1999 Feb 15
All Science Journal Classification (ASJC) codes
- Atmospheric Science