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Harmonic solutions for polygonal hydraulic jumps in thin fluid films

Published online by Cambridge University Press:  03 September 2015

N. Rojas  and
E. Tirapegui
N. Rojas*
Affiliation:
Manchester Centre for Nonlinear Dynamics, and School of Mathematics, The University of Manchester, Manchester M13 9PL, UK
E. Tirapegui
Affiliation:
Departamento de Física, Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Avenida Blanco Encalada 2008, Santiago, Chile
*
†Email address for correspondence: nicolas.rojas@email.com
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Abstract

This article contains numerical and theoretical results on the circular and polygonal hydraulic jumps in the framework of inertial lubrication theory. The free surface and velocity fields are computed along with cross-sections of the vorticity and pressure, in agreement with experimental data. The forces that drive and resist the instability are identified with the radial shear force, the azimuthal surface tension and the hydrostatic azimuthal force, in addition to a nonlinear term in the radial coordinate. Periodic solutions are obtained from the first orders of a perturbation theory by considering azimuthal symmetries. The thresholds of the instability are defined at closed jumps for discontinuous solutions and at one-sided hydraulic jumps for continuous curves that conserve fluid mass density.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 780 , 10 October 2015 , pp. 99 - 119
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Copyright
© 2015 Cambridge University Press 

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