Study On Multi-scale Energy Transfer In Wall Turbulence

The SGS model in Large Eddy Simulation must be able to describe the energy transfer between grid scale and sub-grid scale. The multi-scale energy transfer between different scales in wall turbulence is very complex, especially in the near-wall region which greatly hindered the development and application of LES modeling in wall turbulence. It is very important to have a clear concept about the multi-scale energy transfer in wall turbulence. In present study the multi-scale energy transfer is analyzed using orthogonal wavelets and Fourier method. The relationship between energy transfer and flow structure is investigated.By multi-scale decomposition of flow field in streamwise and spanwise directions, the energy transfer in these two directions is investigated. It is found that in the streamwise direction there is only a little backward transfer in the near-wall region and other regions are dominated by forward scatters. But in the spanwise direction there is obvious backward transfer in near-wall region, and backscatter is only found in regions that are faraway from the wall. In the spanwise direction, at first, the energy transfer becomes larger with the increasing of the cut-off scales, and then the energy transfer decreases as the cut-off scale further increases. In the spanwise direction, the peak of the energy transfer appears much nearer to the wall compared with that in the streamwise direction.The SGS energy transfer has been studied in detail by using Fourier analysis. It is found that energy transfer is dominated by energy cascade in which the kinetic energy is transported from grid scale to sub-grid scale and dissipates in the viscous scale ultimately. But there is obvious backscatter. The energy transfer is not always local in scale, but varies with the cut-off scale. This property must be well considered in the construction of SGS models. It is found that the SGS diffusion plays an important role in the process of energy transfer in wall turbulence.The relationship between energy transfer and flow structure is investigated. According to the critical point theory, the flow structures can be classified as: steady focus, unsteady focus, steady node/saddle and unsteady node/saddle. It is found that the forward transfer is highly related to unsteady node/saddle. But there is no obvious relationship between backward transfer and some kind of flow structures.