On the dynamics of the large scale circulation in turbulent convection with a free-slip upper boundary

Abstract

In this paper we present a numerical study of the dynamics of the Large-Scale Circulation (LSC) in turbulent convection with a free surface. Our study is based on Large-Eddy Simulations of thermal convection in a cube with a heated bottom wall and a cooled free-slip upper boundary which approximates the free surface. With water as the working fluid, simulations are performed at two different Rayleigh numbers, Ra=2×107 and Ra=1×108. The LSC is the principal convective structure and is driven by plume formation at the top and bottom boundaries. In cuboidal domains, the LSC orientates itself along one of the diagonal planes. However, neither the orientation plane nor the direction of circulation remain fixed with time and reorientation events occur. Herein we first present the basic features of the LSC and then examine the frequency of reorientations and their role in turbulence statistics. According to our simulations, the most frequent event is the change of orientation plane, whereas changes in the direction of circulation are scarce. Also, the frequency of reorientations reduces significantly as the Rayleigh number increases. Finally, our analysis shows that reorientation events have an impact on the root-mean-square of the fluctuating component of the horizontal velocity. Therefore, statistics should be taken over long time periods so as to account for a sufficiently large number of events.