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We perform a bifurcation analysis of the steady state solutions of Rayleigh--Benard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an initialisation strategy based on the eigenmodes of the conducting state, we are able to discover multiple solutions to this non-linear problem, including disconnected branches of the bifurcation diagram, without the need of any prior knowledge of the dynamics. One of the disconnected branches we find contains a s-shape bifurcation with hysteresis, which is the origin of the flow pattern that may be related to the dynamics of flow reversals in the turbulent regime. Linear stability analysis is also performed to analyse the steady and unsteady regimes of the solutions in the parameter space and to characterise the type of instabilities.
We analyse the nonlinear dynamics of the large scale flow in Rayleigh-Benard convection in a two-dimensional, rectangular geometry of aspect ratio $Gamma$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions
We study the stability of steady convection rolls in 2D Rayleigh--Benard convection with free-slip boundaries and horizontal periodicity over twelve orders of magnitude in the Prandtl number $(10^{-6} leq Pr leq 10^6)$ and five orders of magnitude in
We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number (Ra)
In this numerical study on two-dimensional Rayleigh-Benard convection we consider $10^7 leq Ra leq 10^{12}$ in aspect ratio $0.23 leq Gamma leq 13$ samples. We focus on several cases. First we consider small aspect ratio cells, where at high Ra numbe
Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Benard convection with no-slip horizontal walls for a variety of Prandtl numbers $Pr$ and Rayleigh number up to $Rasim 10^9$. Power law scalings of $Nusim Ra^{gamma}$