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...

We consider a bilinear reduced-strain nite element formulation for a shallow shell model of Reissner-Naghdi type. The formulation is closely related to the facet models used in engineering practice. We estimate the error of this scheme when approximating an inextensional displacement eld. We make the strong assumptions that the domain and the nite element mesh are rectangular and that the bound...

We study the relevance of various scalar equations, such as inviscid Burgers’, Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptotic models for the propagation of internal waves in a two-fluid system. These scalar evolution equations may be justified with two approaches. The first method consists in approximating the flow with two decoupled, cou...

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. ...

In this work we prove that the solution of Serre-Green-Naghdi equation cannot be globally defined when interface reaches impervious bottom tangentially. As a consequence, our result complements paper Camassa, R., Falqui, G., Ortenzi, Pedroni, M., & Thomson, C. Hydrodynamic models and confinement effects by horizontal boundaries. Journal Nonlinear Science, 29(4), 1445-1498, 2019. Furthermore, al...