Abstract “Green — Naghdi Theory, Part A: Green (GN) Equations for Shallow Water Waves” have investigated the linear dispersion relations of high-level GN equations in shallow water. In this study, deep water waves are investigated. traditional waves, velocity distribution assumption involves only one representative wave number. Herein, a new shape function with multiple numbers is employed. Fur...

In this paper we propose some thermodynamic theories of materials with internal variables. In concrete, we extend the arguments of the theories of the thermoelasticity of type I, II and III proposed by Green and Naghdi to the case of materials with internal variables. We state the system of equations in the linear case when the material is centrosymmetric. We end with an existence and uniquenes...

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic...

The present paper is aimed at studying the effect of gravity on the general model of the equations of the generalized thermomicrostretch for a homogeneous isotropic elastic half-space solid whose surface is subjected to a Mode-I crack problem. The problem is in the context of the Green and Naghdi theory (GN). The normal mode analysis is used to obtain the exact expressions for the displacement ...

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. ...

The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as fully non-linear Boussinesq equations) with full topography effects introduced in Green, A.E. and Naghdi, P.M. (J. Fluid Mech., 78, 237-246, 1976) Seabra-Santos el al Mec.h, 176, 117-134, 1997). This done by revisiting similar Guermond Comput. Phys., 399, 10...

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. ...

We study the behavior in time of solutions to several systems equations for porous-thermo-elastic problems when one variables is considered be quasi-static or, other words, whose second derivative can neglected. analyze three different situations using classical Fourier law and also type II or III Green–Naghdi heat conduction models.

The fully nonlinear and weakly dispersive Green-Naghdi equations for shallow water waves of large amplitude is studied. An hybrid finite volume and finite difference splitting approach is proposed. Numerical validations are then performed in one horizontal dimension.