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A multiple‐scales solution of the undular hydraulic jump problem
Author(s) -
Jurisits Richard,
Schneider Wilhelm,
Bae Yee Seok
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700755
Subject(s) - hydraulic jump , ode , jump , flow (mathematics) , mechanics , mathematics , motion (physics) , free surface , thermodynamics , classical mechanics , physics , quantum mechanics
A non‐linear third‐order ODE governing the free surface of an undular hydraulic jump is solved by means of a multiple‐scales analysis. The resulting solutions are compared with direct numerical solutions of the ODE, and good agreement is found. Furthermore, new flow features, which are not evident in the numerical solutions, are revealed by the multiple‐scales solutions. The results of the analysis are also compared with numerical solutions of the full equations of motion and with experimental data, and satisfactory agreement is obtained. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)