Non-Boussinesq Convection at Low Prandtl Numbers: Hexagons and Spiral Defect Chaos

We study the stability and dynamics of non-Boussinesq convection in pure gases (CO$_2$ and SF$_6$) with Prandtl numbers near $Pr\simeq 1$ and in a H$_2$-Xe mixture with $Pr=0.17$. Focusing on the strongly nonlinear regime we employ Galerkin stability analyses and direct numerical simulations of the Navier-Stokes equations. For $Pr \simeq 1$ and intermediate non-Boussinesq effects we find reentrance of stable hexagons as the Rayleigh number is increased. For stronger non-Boussinesq effects the hexagons do not exhibit any amplitude instability to rolls. Seemingly, this result contradicts the experimentally observed transition from hexagons to rolls. We resolve this discrepancy by including the effect of the lateral walls. Non-Boussinesq effects modify the spiral defect chaos observed for larger Rayleigh numbers. For convection in SF$_6$ we find that non-Boussinesq effects strongly increase the number of small, compact convection cells and with it enhance the cellular character of the patterns. In H$_2$-Xe, closer to threshold, we find instead an enhanced tendency toward roll-like structures. In both cases the number of spirals and of target-like components is reduced. We quantify these effects using recently developed diagnostics of the geometric properties of the patterns.