Response of the atmosphere to a line-type heat sink, which represents a cold pool induced by evaporative cooling in falling precipitation, is investigated. Two-dimensional, steady-state, linear perturbations forced by the diabatic cooling in the presence of a critical level are solved analytically. The ambient flow is assumed to have a three-layer structure which is the same as that in Lindzen and Tung (1976, denoted as LT hereafter) except that an isolated diabatic cooling is specified in the lower layer. The shear layer with a critical level is assumed to be either dynamically stable or unstable. A steady-state solution is possible even for a dynamically unstable flow in the middle layer because the wave energy is allowed to propagate to infinity in the upper layer. Thermally induced wave response near the critical level depending on the stability and wind shear in terms of the Richardson number exhibits the same behavior as the eigen-value problem solved by Jones (1967) and LT because the source mechanism does not change the critical level behavior. That is, when the shear layer is dynamically stable, almost all of the wave energy is absorbed near the critical level, while for dynamically unstable case waves can be partially- or over-reflected from the critical level depending on the Richardson number. Waves can be over-reflected and over-transmitted simultaneously as they travel through the critical level in the process of the energy extraction from the unstable mean shear flow. Using the duct condition proposed by LT, it is found that the magnitude of the perturbation vertical velocity in the lower layer is 6 times larger than that for a nonducting case with the same cooling rate. This implies that under a proper choice of the critical level height and stability profile, the response of the atmosphere to a line-type heat sink can be significantly enhanced through the over-reflection process.
