Abstract We derive the Whitham equations from water waves in shallow regime using two different methods, thus obtaining a direct and rigorous link between these models. The first one is based on construction of approximate Riemann invariants for Whitham–Boussinesq system adapted to unidirectional waves. second generalisation Birkhoff’s normal form algorithm almost smooth Hamiltonians bidirectio...

A boundary value problem is formulated for a stationary model of mass transfer, which generalizes the Boussinesq approximation in case when coefficients equations can depend on concentration substance or spatial variables. The global existence weak solution this proved. Some fundamental properties its solutions are established. In particular, validity maximum principle substance’s has been Suff...

This paper deals with a mathematical and numerical investigation of double-diffusive natural convective heat mass transfer in cavity filled Newtonian fluid significant density diffusivity changes. In such situation, the assumption Boussinesq approximation is not justified, an appropriate model based on set Low Mach Number equations used. The active parts two vertical walls are maintained at fix...

We aim to improve the techniques to predict tsunami wave heights along the coast. The modeling of tsunamis with the shallow water equations has been very successful, but often shortcomings arise, for example because wave dispersion is neglected. To bypass the latter shortcoming, we use the (linearized) variational Boussinesq model derived by Klopman et al. [12]. Another shortcoming is that comp...

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

A grid of numerical simulations of double-diffusive convection is presented for the astrophysical case where viscosity (Prandtl number Pr) and solute diffusivity (Lewis number Le) are much smaller than the thermal diffusivity. As in laboratory and geophysical cases convection takes place in a layered form. The proper translation between subsonic flows in a stellar interior and an incompressible...

This paper presents a parametric finite-difference scheme concerning the numerical solution of theone-dimensional Boussinesq-type set of equations, as they were introduced byPeregrine, in the case of wavesrelatively long with small amplitudes in water of constant depth. The method which is used can be considered asa generalization of the Crank-Nickolson method and it has been ap...

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-B enard convection at large Prandtl number. In particular, we show that the global attractors to the Boussinesq system for Rayleigh-B enard convection converge to that of the in nite Prandtl number model for convection as the Prandtl number approaches in nity. This o ers partial justi cation of the in ni...