A class of exact, time-dependent, free-surface flows
- 10 October 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 55 (03), 529-543
- https://doi.org/10.1017/s0022112072001995
Abstract
Attention is drawn to a class of inviscid irrotational flows which satisfy the conditions at a time-dependent free surface exactly. The flows are related to the ellipsoids of Dirichlet (1860).Depending on a parameter P, the cross-section may take the form of a variable ellipse (P < 0), a hyperbola (P > 0) or a pair of parallel lines (P = 0). The elliptical case was investigated both theoretically and experimentally by Taylor (1960). The hyperbolic case (P > 0) is remarkable in that the flow develops a singularity when the angle between the asymptotes approaches a right-angle. It is suggested that this solution represents a possible instability near the crest of a standing gravity wave of large amplitude.In the intermediate case (P = 0) the solution describes an open-channel flow in which the fluid filaments are stretched uniformly in a horizontal direction. The latter flow is demonstrated experimentally.Keywords
This publication has 3 references indexed in Scilit:
- Standing waves on a contracting or expanding currentJournal of Fluid Mechanics, 1962
- The changes in amplitude of short gravity waves on steady non-uniform currentsJournal of Fluid Mechanics, 1961
- Part II. finite periodic stationary gravity waves in a perfect liquidPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1952