Periodic Flows in a Viscous Stratified Fluid in a Homogeneous Gravitational Field

In natural, laboratory and industrial conditions, the density of a fluid or gas, depending on temperature, pressure, concentration of dissolved substances or suspended particles, changes under the influence of a large number of physical factors. We assume that undisturbed liquid is stratified. The analysis is based on a system of fundamental equations for the transfer of energy, momentum and matter in periodic flows of a viscous compressible fluid. The propagation of periodic flows in viscous uniformly stratified fluids is considered. Taking into account the compatibility condition, dispersion relations are constructed for two-dimensional internal, acoustic and surface linear disturbances with a positive definite frequency and complex wave number in a compressible viscous fluid exponentially stratified by density. The temperature conductivity and diffusion effects are neglected. The obtained regularly perturbed solutions to the equations describe weakly damped waves. Singular solutions characterize the thin ligaments that accompany each type of wave. In limiting cases, the constructed solutions transform into known expressions for a viscous homogeneous and ideal fluid or degenerate.