Analytic Properties of Solutions to the Equation of Internal Gravity Waves with Flows for Critical Modes of Wave Generation

Issues related to the statement of problems of describing the dynamics of linear internal gravity waves in stratified media with horizontal shear flows in critical modes of wave generation are considered. Model physical statements of problems in which critical levels may arise are discussed in the two-dimensional case. Analytic properties of the solutions near critical levels are studied. A system describing a flow of a stratified medium incident on an obstacle behind which outgoing waves may arise is discussed, in which case a singularity at the critical level is formed far away from the obstacle. Asymptotics of the solutions near the critical level are constructed and expressed in terms of the incomplete gamma function.