Hydraulic Jumps in Two-Layer Flow with a Free Surface
S. L. Gavrilyuk1, M. Yu. Kazakova2,3
1Institute of Industrial Thermal Systems University of Aix-Marseille, Marseille, 13453 France
2Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
3Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: two-layer shallow water equations, conservation laws, Rankine-Hugoniot relations, conservative equations
Abstract
This paper presents a closure relation which describes hydraulic jumps in two-layer flows with a free surface over a flat bottom. This relation is derived from the momentum equations for each layer, which, subject to the condition of conservation of the total momentum and mass of each layer, become conservative in a sense. It is shown that use of this relation provides a reduction in the total energy at the jump.
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