  We develop an expansion of the turbulent stress tensor into a double series
of contributions from different scales of motion and different orders of
space-derivatives of velocity, a Multi-Scale Gradient (MSG) expansion. The
expansion is proved to converge to the exact stress, as a consequence of the
locality of cascade both in scale and in space. Simple estimates show, however,
that the convergence rate may be slow for the expansion in spatial gradients of
very small scales. Therefore, we develop an approximate expansion, based upon
an assumption that similar or `coherent' contributions to turbulent stress are
obtained from disjoint subgrid regions. This Coherent-Subregions Approximation
(CSA) yields an MSG expansion that can be proved to converge rapidly at all
scales and is hopefully still reasonably accurate. As an application, we
consider the cascades of energy and helicity in three-dimensional turbulence.
To first order in velocity-gradients, the stress has three contributions: a
tensile stress along principal directions of strain, a contractile stress along
vortex lines, and a shear stress proportional to `skew-strain.' While
vortex-stretching plays the major role in energy cascade, there is a second,
less scale-local contribution from `skew-strain'. For helicity cascade the
situation is reversed, and it arises scale-locally from `skew-strain' while the
stress along vortex-lines gives a secondary, less scale-local contribution.
These conclusions are illustrated with simple exact solutions of 3D Euler
equations. In the first, energy cascade occurs by Taylor's mechanism of
stretching and spin-up of small-scale vortices due to large-scale strain. In
the second, helicity cascade occurs by `twisting' of small-scale vortex
filaments due to a large-scale screw.
