The paper considers a pulse point source in the lower layer of stratified fluid. An expression for the perturbation of its free surface is obtained. It is shown that two waves arise on the surface of the liquid, associated with the presence of a density jump in it. Examples of numerical calculations for real sea conditions are shown. The pulse point source is a model of elementary perturbation of the liquid medium depth, allowing a complete mathematical study in the framework of the approximation of small waves. This approximation is quite justified in cases of simulating real disturbance sources located at considerable depths, since these sources transmit a very weak signal to the sea surface. The main problem in such cases is the isolation of this signal from background noise, such as wind waves. The solution of the problem should be based on the results of mathematical modeling of sea surface disturbances by different sources in the depth of the marine environment. More complex models can be designed by considering real disturbances of the marine environment as some superpositions of model elementary disturbances from point pulse sources. Furthermore, a complete mathematical solution to the problem of a point pulse source gives an idea of the orders of the sea surface disturbance magnitudes, which creates the basis for obtaining various estimates of possible disturbances and therefore is of considerable interest in the development of requirements for sea surface remote sensing equipment.
Носов В.Н., Савин А.С. Численное моделирование возмущения свободной поверхности двухслойной жидкости точечным источником, локализованным в нижнем слое. Математическое моделирование и численные методы. 2019. № 3. с. 113–124.
The flow around a point source localized in the lower layer of a two-layer liquid with a free surface is considered. Expressions are obtained for the perturbation of the free surfaceof the liquid associated with the manifestation of an internal wave. The source operating in the liquid is represented as a superposition of point pulse sources. This approach made it possible to find the perturbation of the flow surface as a superposition of perturbations caused by point pulse sources. The approximation used is quite justified in cases of modeling real sources of disturbances located at considerable depths, since such sources cause small disturbances of the sea surface. It is established that the internal waves appearing on the flow surface form a wedge-shaped structure. The angle of the wedge solution of the internal waves coming to the surface decreases with increasing flow velocity. The dependence of the angle of the wave wedge solution on the Froude number determined by the flow velocity and thickness of the upper liquid layer is found. The considered problem is of theoretical and practical interest, since more complex models of real disturbances of the surface of the marine environment during the flow of various inhomogeneities can be constructed as superpositions of model elementary disturbances from point sources.
Носов В.Н., Савин А.С. Численное исследование воздействия внутренней волны на поверхность двухслойного потока, обтекающего точечный источник. Математическое моделирование и численные методы, 2023, № 3, с. 92–104.