The linear stability problem for a fluid in a classic Benard configuration is considered. The applied temperature gradient is the sum of a steady component and a time-dependent periodic component. Only infinitesimal disturbances are considered. The time-dependent perturbation is expressed in Fourier series. The shift in critical Rayleigh number is calculated and the modulating effect of the osc...

Thermal radiation from finite-conductivity boundaries can strongly affect the stability of horizontally unbounded, plane fluid layers heated from below. The role of thermal radiation in plane layer instabilities is studied under the assumption that the fluid medium is transparent, as a model of infrared transfer through gas layers. The solution procedure modifies a previous formulation of the c...

We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard setup). We consider a 1-dimensional stationary solution, which is close for small Knudsen number to the laminar purely conductive stationary solution ...

In this paper, we study a phase field model for a two-layer fluid where the temperature dependence of both the density (buoyancy forces) and the surface tension (Marangoni effects) is considered. The phase model consisting of a modified N-S equation, a Cahn-Hilliard phase field equation and an energy transport equation is derived through an energetic variational procedure. An appropriate variat...

Abstract The Kuramoto–Velarde equation describes slow space-time variations of disturbances at interfaces, diffusion–reaction fronts and plasma instability fronts. It also Benard–Marangoni cells that occur when there is large surface tension on the interface in a microgravity environment. Under appropriate assumption initial data, time T , coefficients such equation, we prove well-posedness cla...

This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of C vector fields equivariant with respect to a symmetry group. In the space X(M) of C vector fields on a manifold M, there is a residual set of vector fields having no trajectories joining saddle points with stable m...

Modulationor Amplitude-Equations are a universal tool to approximate solutions of complicated systems given by partial or stochastic partial differential equations (SPDEs) near a change of stability, when there is no center manifold theory available. Relying on the natural separation of time-scales at the bifurcation the solution of the original equation is well approximated by the bifurcating ...