Transition of the flow dynamics in two-dimensional Rayleigh-Bénard convection

We investigate the flow dynamics in two-dimensional Rayleigh-Bénard convection through high resolution direct numerical simulation, with the Rayleigh number Ra range being 10$^{\mathrm{7}}$\textasciitilde 10$^{\mathrm{12}}$ and the Prandtl number Pr fixed at 4.3. It is found that there exists a transitional Rayleigh number Ra$_{\mathrm{c}}$ at which the flow pattern changes significantly and the large-scale circulation (LSC) evolves from an elliptical shape into a circular one. Detailed Fourier mode analysis reveals that, while the single-roll mode becomes weaker and other modes become stronger during the transition, all the flow modes experience violent fluctuations. This is also manifested by the sharp change of the local turbulent fluctuations near Ra$_{\mathrm{c}}$, in both magnitude and Ra-dependent scaling. We understand this transition by stability analysis.