Statistics of transfer fluxes of the kinetic energy and scalar variance

Statistics of transfer fluxes of kinetic energy and scalar variance are studied theoretically and numerically. The degree of localness in wavenumber space for the mean transfer fluxes is computed as a function of scale disparity parameter using a Lagrangian spectral theory and is compared to direct numerical simulation data at high Reynolds number. It is found that although most of the transfer flux is local, due to the interactions among wavenumber components of nearly equal size, the degree of localness in the scalar transfer flux is weaker than that of the energy, especially for interactions with large scale disparity. The difference is due to the absence of a pressure term in the scalar equation. High order statistics of the transfer fluxes are also studied in terms of structure functions and probability density functions in physical space. The scaling exponents of the scalar transfer flux are smaller than those of the kinetic energy flux. The probability density functions near the peak are examined and it is found that scale similarity holds approximately. Implications for subgrid scale modeling are discussed.

Acknowledgements

The authors thank Dr Rubinstein for helpful discussions and comments. The Nagoya University Computation Center, the Computer Center of the National Fusion Science of Japan and the Earth Simulator Center are also acknowledged for providing computational resources. T. G. thanks the Tatematsu fundation and JSPS (Grant-in-Aid for Scientific Research No. 14654073) for their partial support.