Elliptical Instability and Multi-Roll Flow Modes of the Large-scale Circulation in Confined Turbulent Rayleigh-B\'enard Convection

Turbulent Rayleigh-B'enard convection in slender cylindrical cells exhibits rich dynamics of the large-scale circulation (LSC), with several rolls stacked on top of each other. We propose that the elliptical instability is the mechanism which causes the twisting and breaking of the LSC into multiple rolls and that the volume-averaged heat and momentum transport, represented by the Nusselt number and Reynolds number, is generally weaker for larger number $n$ of the LSC rolls. This is supported by direct numerical simulations for $Ra=5\times {10}^5$, $Pr=0.1$, $H=5D$ and $1\le n\le 4$.