2006
DOI: 10.1007/s10808-006-0038-8
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Flows Resulting from the Incidence of a Discontinuous Wave on a Bottom Step

Abstract: The solvability of the problem of the flows resulting from the incidence of a discontinuous wave on a bottom step is studied using a single-layer shallow water model. Solutions in which the total energy of the flow is conserved at the step and those in which it is lost at the step are considered. Regions of double and triple hystereses in the obtained self-similar solutions are found. An analogy is drawn with the problem of single-layer flow over a bottom obstacle.

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Cited by 2 publications
(2 citation statements)
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“…The solution of the generalized discontinuity-decay problem (2.12)-(2.14) based on the modified system of the basic conservation laws (2.1), (2.2) is constructed by the generalized method of adiabats [13]. This is done using the results of a study [27], in which a similar problem for the case z 0 δ (the step is under water at the initial time) is solved using the classical system of the basic conservation laws (2.1), (2.3). In view of these results, it can be shown that only two flow regimes of type A and B (the solid and dashed curves in Fig.…”
Section: Formulation Of the Problem Based On Shallow-water Theorymentioning
confidence: 99%
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“…The solution of the generalized discontinuity-decay problem (2.12)-(2.14) based on the modified system of the basic conservation laws (2.1), (2.2) is constructed by the generalized method of adiabats [13]. This is done using the results of a study [27], in which a similar problem for the case z 0 δ (the step is under water at the initial time) is solved using the classical system of the basic conservation laws (2.1), (2.3). In view of these results, it can be shown that only two flow regimes of type A and B (the solid and dashed curves in Fig.…”
Section: Formulation Of the Problem Based On Shallow-water Theorymentioning
confidence: 99%
“…For a uniform theoretical description of the results of these experiments, we used the modified system of the basic conservation laws of shallow-water theory proposed in [20,26], which, on the one hand, admits discontinuous-wave propagation in a dry channel and, on the other hand, correctly reproduces the parameters of these waves for channels of finite depth. Exact solutions are constructed using the methods proposed in [14,15] and the results of a study [27], in which the unique solvability of the problem for the step under water at the initial time was studied using the classical system of the basic conservation laws of shallow-water theory. A comparison with results of laboratory experiments was performed.…”
mentioning
confidence: 99%