Study On The Relationship Between Multi-scale Energy Transfer And Flow Structure In Wall Turbulence

The SGS model in Large Eddy Simulation (LES) must be able to describe the energy transfer between grid scale and sub-grid scale. The multi-scale energy transfer between different scales in near-wall region is very complex, which greatly hindered the development and application of LES modeling in wall turbulence. The complexity is correlated with the coherent structure; hence the investigation into the relationship between the multi-scale energy transfer and near-wall coherent structures is helpful for both the understanding of the physics of wall turbulence and further development of the modeling of wall turbulence. In present the relationship between energy transfer and flow structure is investigated by the identification of flow patterns according to the critical point theory using the data from a direct numerical simulation of a turbulent channel flow.According to the critical point theory, the flow structures can be classified as: steady focus, unsteady focus, steady node/saddle and unsteady node/saddle. Taking the classification of flow pattern as condition to do statistics, it is found that in logarithmic region the forward transfer of sub-grid dissipating energy transfer of is highly related to unsteady node/saddle,and the steady focus take the maximal ratio in backward scatter events. Analyzing further, we found the forward scatter occurs between the heads of spanwise vortices, where the node-saddle structures exist,the backward scatter events mostly occur at foci (vortex).For sub-grid diffusing energy transfer, there is no a kind of flow pattern related specifically with it.The distribution in invariant space of flow pattern represents the characteristic of flow structure, in present we analyze the distribution of multi-scale energy transfer in invariant space of flow pattern and found that, in logarithmic region,the distribution for forward scatter events converges to small but negative, which represents unstable node-saddle structure, and the distribution for backward scatter events lies in the region of Q > 0which means the vortex structure, as is consistent with the conclusion previous. Filtering the velocity using Fourier method, we found that the large scale motions distribute round the origin in invariant space of flow pattern, and the fine scale motions lie far from the origin which conforms to the DNS result more. For a further research of the joint Probability Density Function (PDF) in (R,Q)-plane, the PDF deceases as the distance to origin becomes long and the scale in ( k_M / 8, k_M/ 4) is sensitive, so it can be neglected in LES. The distribution of energy transfer events do not lie far from the origin, that is to say, the large scale motions is important to multi-scale energy transfer.