Modes of linear stationary response of the atmospheric boundary layer to a cold surge in the Black Sea

To describe the phenomenon of cold surges in the Black Sea in winter, we study the problem of atmospheric response to a local heat source on the surface in two simple formulations. In the shallow-water model, the planetary boundary layer of the atmosphere is homogeneous with variable upper bound. In the second model, the boundary layer has a constant thickness and its stratification is homogeneous. In the one-dimensional problem, for a constant wind blowing perpendicularly to the sea coast, the atmospheric response is determined by a single dimensionless parameter called the Froude number. Depending on its value, there are two possible different modes of the response. The range Fr < 1 (subcritical mode) corresponds to gentle winds, strong stratifications, thick boundary layers, and high velocities of inertial gravitational waves. The range Fr > 1 (supercritical mode) corresponds to strong winds, weak stratifications, thin boundary layers, and low wave velocities. In the two-dimensional problem for a round sea, there are four qualitatively different types of response depending on the combination of two dimensionless parameters: the Froude number and the ratio of the radius of the sea to the radius of deformation. Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 3–22, September–October, 2008.