On motions of an ideal fluid with a pressure discontinuity along the boundaries

• Published in: Journal of applied mathematics and mechanics 1962, Vol.26 (2), p.543-548
• Main Author: Chernous' ko, P.L
• Format: Article
• Language: English
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/0021-8928(62)90086-2

Pressure discontinuities occurring on the boundary of an ideal incompressible fluid occur, for example, in problems of the propagation of shock waves along the surface of a fluid. These problems are frequently solved in linearized form (the boundary perturbations are small because of the smallness of the ratio of the density of the air to the density of water) [1]. However, near the points where the discontinuity in pressure occurs (the front of the shock wave) the linearization is not valid, because the speed of the particles, as given by the linearized theory, increases indefinitely under these circumstances [1]. Below we shall consider the motion of an ideal fluid in the neighborhood of a pressure discontinuity, on its boundary without linearization of the problem. It is shown that the free boundary has a curved spiral form (it is assumed throughout that the fluid is ideal, incompressible, and not under the influence of gravity).