Abstract Boussinesq theory can model quite accurately viscous flows that involve multiple fluids with interfaces between them, so long as there is not much difference the densities of various fluids. However, approximation generally poor when density ratio large. Here, we propose an Extended approximate equation, allows for large ratios, while still remaining straightforward to implement. Examp...

Standard perturbation methods are applied to Euler’s equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α = a/h0, and long-wavelength parameter, β = (h0/l), where a and l are the actual amplitude and wavelength of the surface wave, and h0 is the height of the undisturbed water surf...

The system is called a Benjamin-Ono-Boussinesq system because it can be reduced to a pair of equations whose linearization uncouples to a pair of linear Benjamin-Ono equations. Equations of type (1.1) are a class of essential model equations appearing in physics and fluid mechanics. To describe two-dimensional irrotational flows of an inviscid liquid in a uniform rectangular channel, Boussinesq...

In this paper we consider a three-parameter system of Boussinesq/Boussinesq type, modeling the propagation internal waves. Some theoretical and numerical properties systems were previously analyzed by authors. As second part study, present is concerned with analysis existence simulation some issues dynamics solitary-wave solutions. Standard theories are used to derive several results classical ...

The resolvent framework for the Navier-Stokes equations with Boussinesq approximation was applied to a stratified turbulent boundary layer. results show that despite using only very limited range of representative scales, model able reproduce relative magnitude turbulence intensities and balance energy budget as well provide meaningful analysis structures in flow. response modes were predict va...

This is the third in a series of our study of Rayleigh-Bénard convection at large Prandtl number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number are related to those of the infinite Prandtl number model for convection that is formally derived from the Boussinesq system via setting the Prandtl number t...

In this paper, we are concerned with the generalized Boussinesq equation including the singularly sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By the means of two proper ansatzs, we obtain explicit traveling solitary wave solutio...

We establish the eventual regularity of suitably defined weak solutions to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. The existence of a global attractor of the Boussinesq system at large Prandtl number is also presented.