We investigate the asymptotic limit of solutions to Navier-Stokes-Fourier system with Mach number proportional a small parameter $\rightarrow 0$, Froude $\sqrt{}$ and when fluid occupies large domain spatial obstacle rough surface varying 0$. The velocity field is solenoidal satisfies incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak approach in order pass convecti...

We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction, which arises in Ocean dynamics. This work improves the global well-posedness results established recently by R. Danchin and M. Paicu for the Boussinesq system with anisotropic viscosity and zero diffusion. Although we follow some of their...

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...

This is the first paper in a two-part series in which we analyze two model systems to study pinchoff and reconnection in binary fluid flow in a Hele-Shaw cell with arbitrary density and viscosity contrast between the components. The systems stem from a simplification of a general system of equations governing the motion of a binary fluid ~NSCH model @Lowengrub and Truskinovsky, Proc. R. Soc. Lo...

We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time ...

Considered here are Boussinesq systems of equations of surface water wave theory over a variable bottom. A simplified such Boussinesq system is derived and solved numerically by the standard Galerkin-finite element method. We study by numerical means the generation of tsunami waves due to bottom deformation and we compare the results with analytical solutions of the linearized Euler equations. ...

We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show that the solitary–wave of the Boussinesq equation can be written as a solitary–wave satisfying simultaneously all equations of the KdV hierarchy, each one in a...

We investigate the linear stability of unstably strati ed Poiseuille ow between two horizontal parallel plates under non-Boussinesq conditions. It is shown, that Squire's transformation can be used to reduce the three-dimensional stability problem to an equivalent two-dimensional one. The eigenvalue problem, consisting of the generalized Orr-Sommerfeld equations, is solved numerically using an ...

Layek and Pati (Phys. Lett. A, 2017) studied a nonlinear system of five coupled equations, which describe thermal relaxation in Rayleigh-Benard convection Boussinesq fluid layer, heated from below. Here we return to that paper use techniques dynamical systems theory analyse the codimension-one Hopf bifurcation codimension-two double-zero Bogdanov-Takens bifurcation....

1 We present a numerical study of a model of pattern formation following a con-vective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on CO 2 gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls and spirals is studied, as well as the transitions...