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Separated inviscid sheet flows

Published online by Cambridge University Press:  03 May 2011

BUM-SANG YOON  and
YURIY A. SEMENOV
BUM-SANG YOON
Affiliation:
School of Naval Architecture and Ocean Engineering University of Ulsan, 102 Daehakro, Ulsan 680-749, Republic of Korea WCU team, University of Ulsan, 102 Daehakro, Ulsan 680-749, Republic of Korea
YURIY A. SEMENOV*
Affiliation:
School of Naval Architecture and Ocean Engineering University of Ulsan, 102 Daehakro, Ulsan 680-749, Republic of Korea
*
†Email address for correspondence: [email protected]
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Abstract

A steady sheet flow of an inviscid incompressible fluid along a curvilinear surface ending with a rounded trailing edge is considered in the presence of gravity. The effect of surface tension is ignored. The formulation of the problem is applicable to the study of free-surface flows over obstacles in channels, weirs and spillways, and pouring flows. An advanced hodograph method is employed for solving the problem, which is reduced to a system of two integro-differential equations in the velocity modulus on the free surface and in the slope of the bottom surface. These equations are derived from the dynamic and kinematic boundary conditions. The Brillouin–Villat criterion is applied to determine the location of the point of flow separation from the rounded trailing edge. Results showing the effect of gravity on the flow detachment and the geometry of the free boundaries are presented over a wide range of Froude numbers including both subcritical and supercritical flows. For supercritical flows two families of solutions for an arbitrary bottom shape are reproduced. It is shown that the additional condition requiring the free surface to be flat at a finite distance from the end of the channel selects a unique solution for a given bottom height and geometry for supercritical flows. This solution is continuous in going from the subcritical to the supercritical flow regime.

JFM classification

Waves/Free-surface Flows: Channel flow Waves/Free-surface Flows: Critical layers Waves/Free-surface Flows: Solitary waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 511 - 534
Copyright
Copyright © Cambridge University Press 2011

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References

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