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Application of Green−Naghdi Equations for Modeling Wave Flows with Undular Bores

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Abstract

The basic conservation laws in the Green–Naghdi model of shallow-water theory are derived from the two-dimensional integral conservation laws of mass and the total momentum describing the plane-parallel flow in an ideal incompressible fluid above a horizontal bottom. This conclusion is based on the concept of a local hydrostatic approximation, which generalizes the concept of the long-wavelength approximation and is used for analyzing the applicability of the Green–Naghdi equations in modeling the wave flows of a fluid with undular bores.

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Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    V. V. Ostapenko

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    V. V. Ostapenko

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  1. V. V. Ostapenko
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Correspondence to V. V. Ostapenko.

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Translated by V. Bukhanov

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Ostapenko, V.V. Application of Green−Naghdi Equations for Modeling Wave Flows with Undular Bores. Dokl. Phys. 64, 66–69 (2019). https://doi.org/10.1134/S1028335819020046

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