Near-onset dynamics in natural 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...

Natural doubly diffusive convection in three-dimensional enclosures

Numerical continuation is used to study bifurcations in doubly diffusive convection in three-dimensional enclosures driven by opposing horizontal temperature and concentration gradients, and the results are compared with the two-dimensional case. Direct numerical simulation is used to show that in certain regimes the first stable nontrivial state of the three-dimensional system is a finite ampl...

Oscillatory doubly diffusive convection in a finite container.

Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying t...

Homoclinic snaking of localized states in doubly diffusive convection

Dynamics of zero-Prandtl number convection near onset.

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Bénard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (...