Energy Transfer from Large to Small Scales in Turbulence by Multiscale Nonlinear Strain and Vorticity Interactions

An intrinsic feature of turbulent flows is an enhanced rate of mixing and kinetic energy dissipation due to the rapid generation of small-scale motions from large-scale excitation. The transfer of kinetic energy from large to small scales is commonly attributed to the stretching of vorticity by the strain-rate, but strain self-amplification also plays a role. Previous treatments of this connection are phenomenological or inexact, or cannot distinguish the contribution of vorticity stretching from that of strain self-amplification. In this paper, an exact relationship is derived which quantitatively establishes how intuitive multi-scale mechanisms such as vorticity stretching and strain self-amplification together actuate the inter-scale transfer of energy in turbulence. Numerical evidence validates this result and uses it to demonstrate that the contribution of strain self-amplification to energy transfer is higher than that of vorticity stretching, but not overwhelmingly so.