  Three-dimensional turbulent flows enhance velocity gradients via strong
non-linear interactions of the rate-of-strain tensor with the vorticity vector,
and with itself. For statistically homogeneous flows, their total contributions
to gradient production are related to each other by conservation of mass, and
so are the total enstrophy and total dissipation. However, locally they do not
obey this relation and have different (often extreme) values, and for this
reason both production mechanisms have been subject to numerous studies, often
decomposed in multiscale interactions. In general lines, their dynamics and
contributions to the cascade processes and turbulent kinetic dissipation are
different, which posses a difficulty for turbulence modelling. In this paper,
we explore the consequence of the 'Betchov' relations locally, and show that
they implicitly define a length scale. This length scale is found to be about
three times the size of the turbulent structures and their interactions. It is
also found that while the non-locality of the dissipation and enstrophy at a
given scale comes mostly from larger scales that do not cancel, the non-local
production of strain and vorticity comes from multiscale interactions. An
important consequence of this work is that isotropic cascade models need not
distinguish between vortex stretching and strain self-amplification, but can
instead consider both entities part of a more complex transfer mechanism,
provided that their detailed point-value is not required and a local average of
reasonable size is sufficient.
