A problem of steady linear internal gravity wave generated by a thin rapidly moving solid body is considered. A linearized boundary no-flow condition and Boussinesq approximation are used. The solution of this problem is expressed in terms of the Green's function of the internal waves equation. The asymptotic representations of the solution in the far zone and the near zone are considered and its range of applicability is estimated. Numerical results are presented.

The problem of internal gravity waves fields in a stratified medium of finite depth is considered for model distributions of background shear currents. For the analytical solution of the problem, a constant distribution of the buoyancy frequency and various linear dependences of the background shear current on depth were used. The dispersion dependences are obtained, which are expressed in terms of the modified Bessel function of the imaginary index. Under the Miles–Howard stability condition and large Richardson numbers, the Debye asymptotics of the modified Bessel function of the imaginary index were used to construct analytical solutions. The dispersion equation is solved using the proposed analytical approximation. The properties of the dispersion equation are studied and the main analytical characteristics of the dispersion curves are investigated depending on the parameters of background shear flows.

The uniform asymptotic form of the internal gravity-wave field generated by a source moving above a smoothly varying bottom is constructed. The problem of reconstructing non-harmonic internal gravity-wave packets generated by a source moving in a stratified ocean is considered. The solution is proposed in terms of wave modes, propagating independently at the adiabatic approximation, and described as a non-integral-degree series of a small parameter characterizing the stratified medium. A specific form of the wave packets, which can be parameterized in terms of model functions (Airy functions), depends on the local behavior of the dispersion curves of the individual wave mode. A modified space-time ray method was proposed, which belongs to the class of geometrical-optics methods. The key point of the proposed technique is the possibility to derive the asymptotic representation of the solution in terms of a non-integral-degree series of the some small parameter.

We consider analytical solutions describing the generation of internal gravity waves far from a non-local source of disturbances. We suppose that the source moves on the surface of stratified medium of a finite depth. A model distribution of the non-local source shape with radial symmetry is used. This approximation correctly describes (qualitatively) the main spatiotemporal characteristics of natural sources of generation of internal gravity waves in the ocean. The resulting solution is the sum of wave modes. The solution is presented as a series of eigenfunctions of the spectral problem of internal gravity waves. The results of numerical calculations of internal gravity waves components at different depths are presented and discussed.

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