Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Surface and Internal Waves: the Two-Dimensional Problem of a Two-Layer Flow About an Interface-Piercing Body

Author(s):

Nikolay Germanovich Kuznetsov

Laboratory for Mathematical Modelling of Wave Phenomena
Institute for Problems in Mechanical Engineering, Russian Academy of Sciences
V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russian Federation
Principal research scientist
Doctor of Science (Phys.-Math.)

kuzn-nikolay@yandex.ru

Oleg Valerievich Motygin

Laboratory for Mathematical Modelling of Wave Phenomena
Institute for Problems in Mechanical Engineering, Russian Academy of Sciences
V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russian Federation
Chief research scientist
Docent, Doctor of Science (Phys.-Math.)

o.v.motygin@gmail.com

Abstract:

The linear two-dimensional boundary value problem under consideration describes surface and internal waves due to the forward motion of a body in two superposed layers of fluid. The body is totally submerged and intersects the interface between layers having different densities. Two well-posed formulations of the problem are proposed; in these, along with the Laplace equation, boundary conditions, coupling conditions on the interface and conditions at infinity, a pair of supplementary conditions is imposed at the points, where the body contour intersects the interface. For one of the well-posed formulations of the problem (when the difference between horizontal components of momentum is given at each of these points) the existence of a unique solution is proved for all values of the parameters involved with the exception for a set (possibly empty) which is nowhere dense.

Keywords

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