Comprehensive interscale energy transfer in homogeneous isotropic turbulence.

Abstract

This study examines interscale energy transfer, conventionally denoted as the "energy cascade," in forced homogeneous isotropic turbulence. By employing spatial filtering techniques, the turbulent kinetic energy is decomposed into distinct large- and small-scale components, as well as local- and subfilter-scale constituents-specifically encompassing large-scale, small-scale, subfilter-large-scale, and subfilter-small-scale terms. Transport equations for each component are derived to establish an analytical framework elucidating the mechanisms governing cross-scale energy transfer. Within this framework, energy is primarily transferred scale-by-scale from the large-scale and subfilter-small-scale components to the small-scale and subfilter-large-scale portions of the turbulent kinetic energy. Building upon this framework, the following results and discussions are presented. First, the scaling laws governing interscale energy transfer and viscous dissipation rates are elucidated across both the dissipative and inertial subranges. Second, via Leonard decomposition, the subfilter-large-scale and subfilter-small-scale stress tensors are partitioned into Leonard, cross, and Reynolds components. In the dissipative range, interscale energy transfer is predominantly governed by the Leonard and cross-stress terms, whereas all three components contribute significantly in the inertial subrange, with their respective contributions quantitatively assessed. Third, the accuracy of several classical models in predicting interscale energy transfer rates-both from large to subfilter-large scales and from subfilter-small to small scales-is validated. Finally, investigation of extreme dissipation events reveals substantial amplification at small scales and marked alterations in scaling behavior near the inertial subrange, which are closely associated with turbulent intermittency, as evidenced by probability density distributions.