This paper focuses on the temporal and spatial evolutions of critical flow under unsteady rapidly varied conditions, which is defined based different viewpoints steady gradually conditions in classical fluid mechanics theory. So far, fundamental theory largely unknown for conditions. Taking a Gauss-type weir as an example, this work investigates comprehensively comparatively influences unsteadi...

A wide variety of hydraulic and coastal flows can be modeled using shallow water theories, where the so-called Serre-Green-Naghdi (SGN) equations constitute a fully nonlinear weakly dispersive wave theory that has been successfully applied in fluvial maritime contexts. In present contribution, we show SGN models with wave-breaking parameterizations reproduce challenging processes surf swash zon...

The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for...

Head-on collision of two solitary waves in the presence linear shear currents is studied by use High-Level Green–Naghdi (HLGN) theory. The finite difference method used to solve HLGN model time-domain simulation. initial values are obtained steady solution currents. Shear with different velocities considered assess their effect on solitary-wave collision. Three aspects head-on process current s...

We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike well-known (nonlinear) Saint-Venant equations, takes into account effects of pressure term as well dispersive phenomena. Two numerical schemes are designed, based on finite volume - difference type splitting scheme and iterative co...

The present paper is concerned with  the investigation of disturbances in a homogeneous  transversely isotropic thermoelastic rotating  medium with two temperatures, in the presence of the combined effects of   Hall currents and magnetic field due to thermomechanical sources. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi Theories of Type-II and Type-III. ...

SM1. Introduction. This supplement contains details that were omitted from the main paper [SM2] because of page limitations. SM2. The Model for the Shell Structure Acoustic Interaction. To avoid switching between the main paper and this supplement, we have included the entire expanded version of Section 2, not only the details and proofs missing from Section 2 of the main paper. SM2.1. Naghdi S...

This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green-Naghdi type model in the Camassa-Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent, well-pose...

This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre–Green–Naghdi equations with surface tension, because it provides a tractable model that, in the same time, is not...