We prove the existence of a large family of two-dimensional travelling wave patterns for a Boussinesq system which describes three-dimensional water waves. This model equation results from full Euler equations in assuming that the depth of the fluid layer is small with respect to the horizontal wave length, and that the flow is potential, with a free surface without surface tension. Our proof u...

Turbulent convection in the solar photosphere can act as a small-scale dynamo, maintaining a disordered magnetic field that is locally intense. On the other hand, convection is inhibited in the presence of a strong, externally imposed magnetic field, as for instance, in a sunspot. Large-scale, three-dimensional, numerical experiments on highly nonlinear magnetoconvection in a Boussinesq fluid s...

Abstract We consider a general compressible viscous and heat conducting fluid confined between two parallel plates heated from the bottom. The time evolution of is described by Navier–Stokes–Fourier system considered in regime low Mach Froude numbers suitably interrelated. Surprisingly differently to case Neumann boundary conditions for temperature, asymptotic limit identified as Oberbeck–Bouss...

We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenb...

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For threedimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition...

In inviscid fluid flows instability arises generically due to a resonance between two wave modes. Here, it is shown that the structure of the weakly nonlinear régime depends crucially on whether the modal structure coincides, or remains distinct, at the resonance point where the wave phase speeds coincide. Then in the weakly nonlinear, long-wave limit the generic model consists either of a Bous...

Here e2 = (0, 1) T , v is the velocity vector, p is the pressure, θ is a scalar function. The Boussinesq equations arises from many geophysical flows, such as atmospheric fronts and ocean circulations (see, for example, [25],[27]). To understand the turbulence phenomena in fluid mechanics, one needs to go beyond classical solutions. The pair (v, p, θ) on R2×R is called a weak solution of (1.1) ...

A simple exact solution of the Boussinesq equations of motion, thermal energy, and mass conservation is obtained for an oscillatory flow regime in a stably stratified rotating fluid. The flow is unbounded and characterized by velocity gradients that vary with time but are spatially uniform—the basic state of Craik-Criminale flows. The solution describes an oscillatory convergent-divergent flow ...

We derive block preconditioners for a finite element discretization of incompressible flow coupled to heat transport by the Boussinesq approximation. Our techniques rely on effectively approximating the Schur complement obtained by eliminating the fluid variables to obtain an equation for temperature alone. Additionally, the method utilizes existing block-structured preconditioners and multilev...

The present work investigates the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal layer of a binary fluid mixture saturating a porous medium. We assume that the fluid component of the mixture is viscous and incompressible, the porous medium is homogeneous and isotropic, and the boundaries are rigid and impermeable, with slip allowed. A constant tempera...