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Abstract
Small-scale statistics of wavelet-based quantities of turbulence are examined, with particular attention to t α,β[ ι ], which is the wavelet-based transfer of the wavelet-based energy e α[ ι ] at location ι and scale r α to all scales smaller than r β (⩽r α). A divergence-free orthonormal wavelet decomposition method is applied to direct numerical simulation data of three-dimensional incompressible homogeneous isotropic turbulence with grid points and Taylor microscale Reynolds numbers up to 20483 and 732, respectively. We propose a new statistical measure for the degree of scale locality of wavelet-based energy flux to scales smaller than r β constructed from t α,β[ ι ]. At R λ = 732, the measure retains a constant value in the inertial subrange, a value about two-thirds as large as that in the dissipation range, though the flux is local in scale throughout the range, from the inertial subrange to the dissipation range. We confirm that the influence of energy transfer from the large-scale flow on the flux becomes smaller with decreasing scales and negligible in the dissipation range. Scale-dependent spatial correlation between t α,β[ ι ] and e α[ ι ] is discussed. We find that, when r β is in the inertial range, the conditional correlation between forward transfer, which is t α,β[ ι ] at the positions satisfying t α,β[ ι ]>0, and e α[ ι ] becomes stronger as scale r α increases from r β, while this behavior is reversed when r β is in the dissipation range.
Acknowledgements
This work was financially supported by a Grant-in-Aid for the 21st Century COE “Frontiers of Computational Science” and by a Grant-in-Aid for Young Scientists(B) 20760055 of the Ministry of Education, Culture, Sports, Science and Technology of Japan. N.O. acknowledges financial support in the form of a Grant-in-Aid for JSPS Fellows. The computations were carried out on HPC2500 system at the Information Technology Center of Nagoya University. The authors would like to express their thanks to Y. Kaneda, T. Ishihara, M. Yokokawa, K. Itakura and A. Uno for providing us with the DNS data. The authors thank Y. Kaneda for fruitful discussions on turbulence and T. Ishihara for support of the data handling. They are grateful to M. Farge and K. Schneider for valuable discussions on wavelets and their applications to turbulence and for providing us with their wavelet decomposition code based on the Coiflet 12 for single processor. The authors are also grateful to a referee for useful comments regarding the presentation of the paper.