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Extraction of the hierarchical energy spectrum in forced turbulence

Horiuti, K (Tokyo Institute of Technology)
Tuesday 30 September 2008, 17:10-17:40

Seminar Room 1, Newton Institute


Properties of the energy spectrum in turbulent flows are studied using the DNS data for forced homogeneous isotropic and shear turbulence. The perturbation expansion about the Kolmogorov -5/3 energy spectrum yields the hierarchical spectrum, in which the -7/3 spectrum induced by the fluctuation of the dissipation rate is added. Averaging conditioned on the temporal variations of dissipation rate is applied to the ensemble of the energy spectra. The base steady spectrum fits -5/3 power, but its deviatoric part exhibits a fitting with -7/3 power. The role of the -7/3 power spectrum in generation of energy cascade is elucidated by examining the temporal variations of the energy spectrum and transfer function. The cascade process is divided into two phases. The energy contained in the low-wavenumber range in Phase 1 is transferred to the high wavenumbers in Phase 2 with switchover of the sign in the -7/3 power component. In Phase 1, a very large gain in the energy transfer function occurs at the scale corresponding to the integral length. The vortex sheet whose lateral length is comparable to the scale of this input is created, and many Mode 3 or 2 spiral vortices (LSV) (Horiuti & Fujisawa 2008) are detected in Phase 1. These LSVs are converted to Mode 1 in Phase 2. The statistics are compared in Phases 1 and 2. The turbulent energy is larger in Phase 1 than in Phase 2. The moderately large dissipation rate dominates in Phase 2, but the dissipation field is more intermittent in Phase 1. Averaging conditioned on the dissipation and enstrophy indicates that the regions of extreme dissipation and enstrophy possess a significant degree of overlap in space in Phase 1. These extreme events occur along the spiral sheet of Mode 3 LSV which is strained and stretched by the tube in the core.


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