Homoclinic snaking of localized states in doubly diffusive convection

Homoclinic snaking of localized states in doubly diffusive convection

Spatially localized states in natural doubly diffusive convection

Numerical continuation is used to compute a multiplicity of stable spatially localized steady states in doubly diffusive convection in a vertical slot driven by imposed horizontal temperature and concentration gradients. The calculations focus on the so-called opposing case, in which the imposed horizontal thermal and solutal gradients are in balance. No-slip boundary conditions are used at the...

Localized pinning states in closed containers: Homoclinic snaking without bistability.

Binary mixtures with a negative separation ratio are known to exhibit time-independent spatially localized convection when heated from below. Numerical continuation of such states in a closed two-dimensional container with experimental boundary conditions and parameter values reveals the presence of a pinning region in Rayleigh number with multiple stable localized states but no bistability bet...

Homoclinic snaking in bounded domains.

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. On the real line this process continues forever. In finite domains snaking terminates once the domain is filled but the details of ho...

Eckhaus instability and homoclinic snaking.

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. This behavior is simplest to understand within the subcritical Swift-Hohenberg equation, but is also present in the subcritical regi...