Anisotropy in turbulent Rayleigh–Bénard convection with and without rotation

Abstract

We present results of direct numerical simulations on anisotropy in the velocity and the convective temperature fields of turbulent Rayleigh–Bénard convection in low-Prandtl-number fluids with and without uniform rotation about the vertical direction. Our results are in the intermediate range of Rayleigh number ([Math Processing Error]) and high Rossby number ([Math Processing Error]). The probability distribution for the fluctuating velocity field [Math Processing Error] shows exponential tails. The distribution function for the vertical velocity is significantly different from those for the horizontal velocity components, which we take as a mark of anisotropy. The probability distribution function for the fluctuating temperature field θ is also quite different from that of any component of the velocity field and is proportional to [Math Processing Error], where θ0 is a constant. To study the anisotropy in Fourier space, we look at the Fourier modes of the velocity fields and compare our numerical results with a calculation based on an effective linear model.