Elliptical Instability and Multiple-Roll Flow Modes of the Large-Scale Circulation in Confined Turbulent Rayleigh-Bénard Convection

The large-scale circulation (LSC) of fluid is one of the main concepts in turbulent thermal convection as it is known to be important in global heat and mass transport in the system. In turbulent Rayleigh-Bénard convection (RBC) in slender containers, the LSC is formed of several dynamically changing convective rolls that are stacked on top of each other. The present study reveals the following two important facts: (i) the mechanism which causes the twisting and breaking of a single-roll LSC into multiple rolls is the elliptical instability and (ii) the heat and momentum transport in RBC, represented by the Nusselt (Nu) and Reynolds (Re) numbers, is always stronger (weaker) for smaller (larger) number n of the rolls in the LSC structure. Direct numerical simulations support the findings for n=1, …, 4 and the diameter-to-height aspect ratio of the cylindrical container Γ=1/5, the Prandtl number Pr=0. 1 and Rayleigh number Ra=5×10^5. Thus, Nu and Re are, respectively, 2. 5 and 1. 5 times larger for a single-roll LSC (n=1) than for a LSC with n=4 rolls.