Filtering Analysis of a Direct Numerical Simulation of the Turbulent Rayleigh-Benard Problem

摘要

A filtering analysis of a turbulent flow has been developed which providesdetails of the path of the kinetic energy of the flow from its creation via thermal production to its dissipation. A low-pass spatial filter is used to split the velocity and the temperature field into a filtered component (composed mainly of scales larger than a specific size, nominally the filter width) and a fluctuation component (scales smaller than a specific size). Variables derived from these fields can fall into one of the above two ranges or be composed of a mixture of scales dominated by scales near the specific size. The filter is used to split the kinetic energy equation into three equations corresponding to the three scale ranges described above. The data from a direct simulation of the Rayleigh-Benard problem for conditions where the flow is turbulent is used to calculate the individual terms in the three kinetic energy equations. This is done for a range of filter widths. These results are used to study the spatial location and the scale range of the thermal energy production, the cascading of kinetic energy, the diffusion of kinetic energy and the energy dissipation. These results are used also to evaluate two subgrid models typically used in large eddy simulations of turbulence. Subgrid models attempt to model the energy below the filter width that is removed by a low-pass filter.