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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Imprimer: 2152-5102
ISSN En ligne: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v33.i1.70
pages 106-118

Tsunami Wave Runup on Coasts of Narrow Bays

V. Golinko
Department of Applied Mathematics, Nizhny Novgorod Technical University, 24 Minin Str., Nizhny Novgorod, 603950, Russia
N. Osipenko
Department of Applied Mathematics, Nizhny Novgorod Technical University, 24 Minin Str., Nizhny Novgorod, 603950, Russia
E. N. Pelinovsky
Departement de Physique, Universite des Antilles et de la Guyane, UFR Sciences, Campus de Fouillole, 97159 Pointe a Pitre Cedex, Guadeloupe, France; Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia
N. Zahibo
Departement de Physique, Universite des Antilles et de la Guyane, UFR Sciences, Campus de Fouillole, 97159 Pointe a Pitre Cedex, Guadeloupe, France

RÉSUMÉ

The runup of tsunami waves on the coasts of the narrow bays, channels and straits is studied in the framework of the nonlinear shallow water theory. Using the narrowness of the water channel, the one-dimensional equations are applied; they include the variable cross-section of the channel. It is shown that the analytical solutions can be obtained with the use of the hodograph (Legendre) transformation similar to the wave runup on the plane beach. As a result, the linear wave equation is derived and all physical variables (water displacement, fluid velocity, coordinate and time) can be determined. The dynamics of the moving shoreline (boundary of the flooding zone) is investigated in details. It is shown that all analytical formulas for the moving shoreline can be obtained explicitly. Two examples of the incident wave shapes are analyzed: sine wave and parabolic pulse. The last example demonstrates that even for approaching of the crest only, the flooding can appear very quickly; then water will recede relatively slowly, and then again quickly return to the initial state.


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