Abstract
A uniform ow disturbed by a bump is studied. The eect of the disturbance is presented at the surface, generating wave. The wave propagation is modeled into a couple of equations, in terms of the surface elevation and the depth average velocity. The numerical solution of the equations is simulated to observe the propagation, especially for long run time, using a predictor-corrector method. A steady solitary surface prole is obtained for supercritical upstream ow, similarly for subcritical ow but for negative amplitude. In the transient process, more waves are generated but some of them propagates to the left or right, and only one wave remains above the bump. Mathematics Subject Classication: 35C20, 76B07, 76B25
Highlights
A 2-D flow is considered over a bump on the bottom of a channel
In case the forcing term is a secant-hyperbolic bump, corresponding to the solution of the KdV, Chardar et al [6] as well as Camassa and Wu [7, 8] obtained one solution of secant-hyperbolic-type, only for a certain Froude number depending on the height and width of the bump. The difference between these two and one solution is observed by Wiryanto [9]. They derived the model in a form of the forced Korteweg de Vries (fKdV) equation, based on the perturbation of the potential function from the uniform flow, and observes the effect of the bump width
We have derived a Bousinesq-type model for surface wave, generated by flow disturbed by a bump
Summary
Department of Mathematics, Bandung Institute of Technology Jalan Ganesha 10, Bandung 40132, Indonesia Department of Mathematics, Sanata Dharma University Mrican, Tromol Pos 29, Yogyakarta 55002, Indonesia Copyright c 2014 L. H. Wiryanto and Sudi Mungkasi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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