The effects of aspect ratio on flow states and heat transport in vertical convection

We present direct numerical simulations of two-dimensional vertical convection (VC) to investigate how the aspect ratio upper A A $A$ influences the evolution of flow states and heat transport. The study covers a Rayleigh number range of 10 Superscript 7 Baseline less than or equals italic Ra Subscript upper H Baseline less than or equals 10 Superscript 11 10 7 ≤ Ra H ≤ 10 11 $10^{7}\le \textit{Ra}_H \le 10^{11}$ at a fixed Prandtl number of italic probability equals 1 Pr = 1 $\textit{Pr}=1$ with upper A A $A$ varying in the range of 1 divided by 50 less than or equals upper A less than or equals 8 1 / 50 ≤ A ≤ 8 $1/50\le A \le 8$ . It is found that, for a fixed value of upper A A $A$ , the flow evolves from steady convection to periodic oscillations, chaotic flows and finally turbulence as italic Ra Subscript upper H Ra H $\textit{Ra}_H$ increases. At fixed italic Ra Subscript upper H