Effects of Diabatic Cooling in a Shear Flow with a Critical Level

Abstract

The response of a two-dimensional, stably stratified shear flow to diabatic cooling, which represents the evaporative cooling of falling precipitation in the subcloud layer, is examined using both a linear analytical theory and a nonlinear numerical model. The ambient wind is allowed to reverse its direction at a certain height and the cooling is specified from the surface to a height below the wind reversal level. From a scale analysis of the governing equations a nonlinearity factor of the thermally induced finite-amplitude wave, gQ0l(cpT0U02N), is found. From a scale analysis of the linear system, it is shown that the wind shear can modify the condition in which the upstream propagation of the density current is opposed by the ambient wind. When the shear and the basic wind are of opposite sign, small basic wind is enough to prevent the upstream propagation of the density current. This is because part of the cooling is used to compensate the positive vorticity associated with the positive wind shear. Therefore, the effective cooling rate, or the speed of the density current, becomes smaller than that in the uniform wind case. In the nonlinear numerical simulations, it is found that the response of the atmosphere to a steady cooling in a shear flow may be categorized as either a stationary cold pool or a density current, depending upon the strength of the effective cooling. For a strong shear flow, the cold pool is stationary with respect to the upstream flow because most of the cooling is used to compensate the positive vorticity associated with the positive wind shear. In this case, the response is similar to the linear steady-state case. For a weak shear flow, the cold pool is able to propagate upstream because the effective cooling, which increases with time, is strong enough to push the outflow against the basic wind. From the comparison of linear and nonlinear numerical model simulations, it is found that the nonlinearity appears to reduce the wave disturbance below the critical height and above the cooling top, while it tends to strengthen the density current or cold pool near the surface.