Journal of Applied Mechanics and Technical Physics

, Volume 16, Issue 5, pp 734–738

# Motion of a vortex near the boundary between two heavy fluids

• V. V. Golovchenko
Article

## Abstract

The motion of a vortex beneath the surface of a heavy fluid has been discussed in both linear [1, 2] and nonlinear [3–5] formulation. The density of the upper medium is neglected, which makes it possible to replace the continuity of pressure during transition through the boundary between the media by constancy of the pressure at the boundary of the heavy fluid. In this paper, the problem is solved in a general nonlinear formulation, including the mutual effects of media motion, and the vortex can be in either the upper or lower medium. Steady-state motion of a vortex of given intensity near the boundary between two heavy fluids is discussed in terms of a model of an ideal and incompressible medium. Approximate expressions are obtained for the boundary.

### Keywords

Vortex Mathematical Modeling Mechanical Engineer Industrial Mathematic Mutual Effect

## Preview

### Literature cited

1. 1.
M. V. Keldysh, “Notes on certain motions of a heavy fluid,” Tekh. Zametki Tsentr. Aero-Gidrodinam. Inst., No. 52 (1935).Google Scholar
2. 2.
N. E. Kochin, “Wave resistance of bodies submerged in a fluid,” in: Collected Works [in Russian], Vol. 2, Izd. Akad. Nauk SSSR, Moscow (1949).Google Scholar
3. 3.
A. I. Nekrasov, “Point vortex beneath the surface of a heavy ideal fluid in plane-parallel flow,” in: Collected Works, [in Russian], Vol. 2, Izd. Akad. Nauk SSSR, Moscow (1962).Google Scholar
4. 4.
A. M. Ter-Krikorov, “Exact solution of the problem of motion of a vortex beneath the surface of a fluid,” Izv. Akad. Nauk SSSR, Ser. Mat.,22, No. 2 (1958).Google Scholar
5. 5.
I. G. Filippov, “Motion of a vortex beneath the surface of a fluid,” Prikl. Mat. Mekh.,25, No. 2 (1961).Google Scholar