Geodesic
Numerical analysis of a linearized one-dimensional hydraulic jump model
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 4, pp. 74-87

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In this paper, a one-dimensional linear hydraulic jump problem is numerically analyzed. The stability of the solution is investigated, the investigation is based on the known formulas for the linear problem's solution, which express it in the terms of the model parameters. A system of calculations, that allows to separate the regions of stability and instability and calculate their common boundary – the surface of neutral stability, is constructed. For the cases of stability and neutral stability, the principal asymptotic characteristics of the hydraulic jump are calculated: the front asymptotics and, accordingly, the first oscillation frequency. The results are compared with the available numerical results for the solution of the general (nonlinear) problem.
Keywords: hydraulic jump, shallow water theory, shear shallow water theory, shock wave, shock wave front. 
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     author = {E. V. Semenko and T. I. Semenko},
     title = {Numerical analysis of a linearized one-dimensional hydraulic jump model},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
     volume = {14},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2021_14_4_a5/}
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E. V. Semenko; T. I. Semenko. Numerical analysis of a linearized one-dimensional hydraulic jump model. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 4, pp. 74-87. http://geodesic.mathdoc.fr/item/VYURU_2021_14_4_a5/