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Structure of the hydraulic jump in convergent radial flows

Published online by Cambridge University Press:  07 December 2018

K. A. Ivanova Open the ORCID record for K. A. Ivanova [Opens in a new window]  and
S. L. Gavrilyuk Open the ORCID record for S. L. Gavrilyuk [Opens in a new window]
K. A. Ivanova
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille cedex 13, France
S. L. Gavrilyuk*
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille cedex 13, France
*
†Email address for correspondence: sergey.gavrilyuk@univ-amu.fr
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Abstract

We are interested in the modelling of multi-dimensional turbulent hydraulic jumps in convergent radial flow. To describe the formation of intensive eddies (rollers) at the front of the hydraulic jump, a new model of shear shallow water flows is used. The governing equations form a non-conservative hyperbolic system with dissipative source terms. The structure of equations is reminiscent of generic Reynolds-averaged Euler equations for barotropic compressible turbulent flows. Two types of dissipative term are studied. The first one corresponds to a Chézy-like dissipation rate, and the second one to a standard energy dissipation rate commonly used in compressible turbulence. Both of them guarantee the positive definiteness of the Reynolds stress tensor. The equations are rewritten in polar coordinates and numerically solved by using an original splitting procedure. Numerical results for both types of dissipation are presented and qualitatively compared with the experimental works. The results show both experimentally observed phenomena (cusp formation at the front of the hydraulic jump) as well as new flow patterns (the shape of the hydraulic jump becomes a rotating square).

JFM classification

Nonlinear Dynamical Systems: Pattern formation Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Shear waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 441 - 464
Copyright
© 2018 Cambridge University Press 

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