  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.
