Flow states in two-dimensional Rayleigh-B\'enard convection as a function of aspect-ratio and Rayleigh number

In this numerical study on two-dimensional Rayleigh-B'enard convection we consider ${10}^7\le Ra\le {10}^{12}$ in aspect ratio $0.23\le \mathrm{\Gamma }\le 13$ 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 $\mathrm{\Gamma }\approx 10$ variations up to 2.5% in the heat transport as a function of \Gamma are observed. Finally, we observe long-lived transients up to at least $Ra={10}^9$, as in certain aspect ratio cells we observe different flow states that are stable for thousands of turnover times.