Coherent solutions and transition to turbulence in two-dimensional Rayleigh-Bénard convection

For two-dimensional Rayleigh-B\'{e}nard convection, classes of unstable, steady solutions were previously computed using numerical continuation (Waleffe, 2015; Sondak, 2015). The `primary' solution bifurcates from the conduction state at $Ra \approx 1708$, and has a characteristic aspect ratio (length/height) approximately $2$. primary corresponds to one pair counterclockwise-clockwise convection rolls with temperature updraft in between an adjacent downdraft on sides. By adjusting horizontal length domain, 2015) also found steady, maximal heat transport solutions, less than $2$ decreasing increasing $Ra$. Compared optimal have modifications boundary layer thickness, scale plume, structure downdrafts. current study establishes direct link these (unstable) transition turbulence for $Pr = 7$ 100$. transitional values $Ra$, both appear prominently appropriately-sized sub-fields time-evolving fields. $Ra$ beyond transitional, our data analysis shows persistence 7$, while are more easily detectable In cases 100$, relative prevalence is consistent $Nu$ vs. scalings solutions.