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Transient, Linear Dynamics of a Stably Stratified Shear Flow with Thermal Forcing and a Critical Level

Abstract 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 f...