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An intrinsic feature of turbulent flows is an enhanced rate of mixing andkinetic energy dissipation due to the rapid generation of small-scale motionsfrom large-scale excitation. The transfer of kinetic energy from large to smallscales is commonly attributed to the stretching of vorticity by thestrain-rate, but strain self-amplification also plays a role. Previoustreatments of this connection are phenomenological or inexact, or cannotdistinguish the contribution of vorticity stretching from that of strainself-amplification. In this paper, an exact relationship is derived whichquantitatively establishes how intuitive multi-scale mechanisms such asvorticity stretching and strain self-amplification together actuate theinter-scale transfer of energy in turbulence. Numerical evidence validates thisresult and uses it to demonstrate that the contribution of strainself-amplification to energy transfer is higher than that of vorticitystretching, but not overwhelmingly so.

Energy transfer from large to small scales in turbulence by multi-scale nonlinear strain and vorticity interactions