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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