A model equation for steady surface waves over a bump

✍ Scribed by S. P. Shen; M. C. Shen; S. M. Sun

• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 313 KB
• Volume: 23
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00128905

✦ Synopsis

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.