Uniqueness of free-boundary flows under gravity
Abstract
A class of steady potential flows of an ideal fluid is considered in which the fluid flows between fixed boundaries and then emerges as a jet with one free boundary. Gravity acts on the fluid perpendicularly to the direction of the jet at infinity downstream. An inverse Froude number α is defined in terms of the flux Q and the depth d of the fluid at the separation point. It is proved that for each α>0 there is at most one flow which reaches to a supercritical uniform stream depth at infinity downstream. Monotonicity properties are proved for various flow parameters, and the behaviour of the flow as α → 0 is described.
- Publication:
-
Archive for Rational Mechanics and Analysis
- Pub Date:
- July 1982
- DOI:
- 10.1007/BF00249586
- Bibcode:
- 1982ArRMA..78..361B
- Keywords:
-
- Free Boundaries;
- Gravitational Effects;
- Ideal Fluids;
- Potential Flow;
- Steady Flow;
- Uniqueness Theorem;
- Flow Theory;
- Froude Number;
- Incompressible Flow;
- Inviscid Flow;
- Supercritical Flow;
- Uniform Flow;
- Fluid Mechanics and Heat Transfer