Uniqueness of freeboundary 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