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Waves over Curved Bottom: The Method of Composite Conformal Mapping

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
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Abstract

A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal variables are used. In addition to the previously known applications for shear flows with constant (including zero) vorticity, here a generalization is made to the case of potential flows in uniformly rotating coordinate systems, where centrifugal and Coriolis forces are added to the gravity force. A brief review is given of previous results obtained by this method in a number of physically interesting problems such as modeling of tsunami waves caused by the movement of nonuniform bottom, the dynamics of Bragg (gap) solitons over a spatially periodic bottom profile, the Fermi–Pasta–Ulam (FPU) recurrence phenomenon for waves in a finite pool, the formation of anomalous waves in an opposing nonuniform curent, and the propagation of a solitary wave in a shear current and its runup on a depth difference. In addition, a number of new numerical results are presented concerning the nonlinear dynamics of a free boundary in closed rotating containers partially filled with a fluid—centrifuges of complex shape. In this case, the equations of motion differ in some essential details from those of x-periodic systems.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow oblast, Russia

    V. P. Ruban

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  1. V. P. Ruban
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Correspondence to V. P. Ruban.

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Translated by I. Nikitin

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Ruban, V.P. Waves over Curved Bottom: The Method of Composite Conformal Mapping. J. Exp. Theor. Phys. 130, 797–808 (2020). https://doi.org/10.1134/S1063776120040081

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  • DOI: https://doi.org/10.1134/S1063776120040081

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