Open AccessOn the application of the Green‒Nagdi equations for the simulation of wave flows with undular bores
Author(s) -
В. В. Остапенко,
В. В. Остапенко
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524844426-430
Subject(s) - conservation law , momentum (technical analysis) , hydrostatic equilibrium , conservation of mass , compressibility , flow (mathematics) , mechanics , plane (geometry) , physics , geology , classical mechanics , mathematics , geometry , mathematical analysis , finance , quantum mechanics , economics
The basic conservation laws in the Green–Nagdi 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–Nagdi equations in modeling the wave flows with undular bores.