On perturbations of a horizontal stratified flow due to inhomogeneous volumetric heat release

Abstract

The linear stationary perturbations of horizontal stratified flows of an ideal medium caused by horizontally inhomogeneous volume sources of buoyancy have been studied analytically. Such problems have many applications including, in particular, geophysical ones. An example is the interaction of wind in the troposphere with the region of moist convection, in which heat release in phase transitions is significant. Unlike a number of other works, this study focuses on the perturbations trapped within the lower layer of the medium, which exist at rather small or at sufficiently large horizontal scales of inhomogeneities. To solve such problems, the representation of the non-periodic function as a Fourier integral (i.e., as a series expansion into harmonic components) is often used, and the superposition of horizontal harmonics is considered. The properties of such harmonics, depending on their horizontal scales are qualitatively different. Thus, the known interval of scales basically corresponds to the generation of internal gravitational waves, while other scales are associated with the occurrence of trapped perturbations. Since the superposition of such perturbations is very complex and its analytical study is unfeasible, it seems appropriate to analyze in detail the solution for an individual harmonic. This is the focus of the present work. The proposed approach made it possible to obtain and analyze the solutions in an explicit and transparent analytical form. In addition to the velocity, temperature, and pressure fields, the expressions for the vorticity and helicity of the resulting disturbances were obtained. The analysis of the results revealed the possibility of resonant amplification of the amplitudes of perturbations and the depth of their penetration into the medium, when the time of a horizontal flow past the source coincides with the characteristic period of buoyancy or inertial period.