Abstract
The objective of this paper is to study the solutions of a model equation for steady surface waves on an ideal fluid over a semicircular or semielliptical bump. For upstream Froude number F>1, we show that the numerical solution of the equation has two branches and there is a cut-off value of F below which no solution exists. For F<1, the problem is reformulated to overcome the so-called infinite-mass dilemma. A branch of solutions and a cut-off value of F, above which no solution exists, are found. Furthermore, we also obtain a branch of hydraulic-fall solutions which decrease monotonically from upstream to downstream.
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Shen, S.P., Shen, M.C. & Sun, S.M. A model equation for steady surface waves over a bump. J Eng Math 23, 315–323 (1989). https://doi.org/10.1007/BF00128905
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DOI: https://doi.org/10.1007/BF00128905