Propagation of discontinuouswaves along a dry bed. (English. Russian original) Zbl 1200.76032
Fluid Dyn. 41, No. 4, 606-618 (2006); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2006, No. 4, 135-148 (2006).
Summary: The possibility of simulating the process of propagation of discontinuous waves along a dry bed on the basis of the equations of the first approximation of shallow water theory is studied. It is shown that the consistent losses of the free-stream total momentum and energy can be found from the mass conservation law within the framework of the shallow water equations. As an example, solutions of the problem of dam break with a dry bed in the lower pool and the problem of impingement of a discontinuous wave on a coastal shelf are constructed. These exact solutions are compared with the results of laboratory experiments.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
shallow water theory; discontinuous waves; dry bed; self-similar solutions; laboratory experimentReferences:
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