Flow states in two-dimensional Rayleigh-Bénard convection as a function of aspect-ratio and Rayleigh number

In this numerical study on two-dimensional Rayleigh-Bénard convection we consider 107 ⩽ Ra ⩽ 1012 in aspect-ratio 0.23 ⩽ Γ ⩽ 13 samples. We focus on several cases. First, we consider small aspect-ratio cells, where at high Ra number we find a sharp transition from a low Ra number branch towards a high Ra number branch, due to changes in the flow structure. Subsequently, we show that the influence of the aspect-ratio on the heat transport decreases with increasing aspect-ratio, although even at very large aspect-ratio of Γ ≈ 10 variations up to 2.5% in the heat transport as a function of Γ are observed. Finally, we observe long-lived transients up to at least Ra = 109, as in certain aspect-ratio cells we observe different flow states that are stable for thousands of turnover times.