Enhanced Response of a Stably Stratified Two-Layer Atmosphere to Low-Level Heating

Abstract

Response of a stably stratified two-layer atmosphere to low-level heating is investigated by obtaining and analyzing analytic solution for the two-dimensional, steady-state, linear perturbation. The ambient wind is assumed to be constant and the Brunt-Vaisala frequency to be piecewise constant in each layer. The diabatic heating is specified from the surface to a certain height in the lower layer. In this study, discussion is made on only the case that the stability in the lower layer is larger than that in the upper layer. A steady-state solution is possible only when the upper layer is not neutrally stratified. If the upper layer is neutrally stratified, the incident wave is totally reflected from the layer interface and the wave resonance in the lower layer can result in a wave breaking eventually in the absence of dissipation. The lower layer depth to produce the maximum magnitude of the vertical velocity in the lower layer is presented in terms of the vertical wavelength of dominant gravity wave and the stability ratio between two layers. The magnitude of the maximum vertical velocity for this lower layer depth is larger than that for the uniform stability case and it increases as the stability ratio between two layer decreases. The vertical velocity in the upper layer is also amplified by the stability ratio between two layers. The reflection coefficient of waves at the layer interface and the transmission coefficient through it are obtained in terms of the stability ratio. It is shown that the transmission coefficient is larger than the reflection coefficient. The lower layer depth to produce the maximum magnitude of the horizontal velocity perturbation is the same as that for the ducting condition by Lindzen and Tung. In the upper layer, the magnitude of the horizontal velocity perturbation is the same as that for the uniform stability case regardless of the stability ratio. Position of the maximum positive horizontal velocity perturbation at the surface is shifted toward the heating center from the downstream side as the stability ratio decreases. The momentum flux for the two-layer case is much larger than that for the uniform stability case because both the horizontal and vertical velocity perturbations in the lower layer are amplified by the wave reflection from the layer interface.