Lagrangian analysis of turbulent convection

Abstract

Turbulent convection is one of the best studied flows in experimental and numerical fluid dynamics [1]. One reason is the existence of a wide range of natural phenomena and industrial applications in which turbulent motion is initiated and sustained by heating a fluid from below and cooling from above. In this paper, we present direct numerical simulations of three-dimensional turbulent convection with the focus on the Lagrangian properties of the flow. Two different systems are studied for this purpose. The first one is a Cartesian slab with an aspect ratio of four, bounded by free-slip planes at the top and bottom and periodic side walls [2, 3]. The second configuration is a closed cylindrical cell with an adiabatic side wall and isothermal top and bottom plates with an aspect ratio of one [4]. Turbulent Rayleigh-Bénard convection is discussed in the Boussinesq approximation in both cases. We apply a pseudospectral method for the Cartesian case and a second-order finite difference method for the cylindrical one. The Prandtl number is Pr = 0.7 for all cases. The Rayleigh numbers Ra vary between 10⁷ and 10⁹. Figure 1 shows a snapshot of the temperature field in the Cartesian cell. Clearly visible skeleton-like structures of thermal plumes close to the top and bottom planes are present in the contour plots of temperature.