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Ter-Krikorov, A. M.

Three-dimensional steady flows of stratified fluid and internal waves. (English. Russian original) Zbl 0589.76136

Fluid Dyn. 20, 445-449 (1985); translation from Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1985, No. 3, 127-132 (1985).
Summary: A study is made of three-dimensional steady flows of an ideal heavy incompressible fluid stratified in each layer over a flat or asymptotically flat base. Mixed Euler-Lagrange variables are chosen in which surfaces of constant density, including the layer division boundaries, become flat and parallel to the plane of the base. The original problem is reduced to a nonlinear boundary-value problem for a system of three quasilinear equations in a plane layer. This system of equations is used to construct an asymptotic theory of long waves in the three-dimensional case, which has particular solutions in the first approximation in the form of solitons and soliton systems.

MSC:

76V05 Reaction effects in flows
76B55 Internal waves for incompressible inviscid fluids
35B40 Asymptotic behavior of solutions to PDEs

Keywords:

steady-state equations; flat base; stratification of unperturbed; one- dimensional flow; stratification of three-dimensional flow; three- dimensional steady flows; ideal heavy incompressible fluid; asymptotically flat base; Mixed Euler-Lagrange variables; surfaces of constant density; layer division boundaries; nonlinear boundary-value problem; system of three quasilinear equations; plane layer; asymptotic theory of long waves; first approximation; soliton systems
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References:

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