  The Desnyanski-Novikov shell model is a deterministic dynamical model for
scalar velocities $v_t(n)$ defined on the one-dimensional-lattice $n=0,1,2,..$
labelling the length-scales $l_n=l_0 2^{-n}$, in order to describe the cascade
of energy from the biggest scale where it is injected by some external forcing
towards the smaller scales where it is dissipated by viscosity. We describe the
generalization of this model in two directions : (i) the
one-dimensional-lattice $n=0,1,2,..$ labelling the length-scales $l_n=l_0
2^{-n}$ is replaced by a scale-spatial tree structure of nested cells in order
to allow spatial heterogeneities between different coherent structures that are
localized in different regions of the whole volume ; (ii) the scalar velocities
$v_t(n)$ are replaced by 3D-vector velocities in order to take into account the
vorticity in the dynamical equations and to include vortex-stretching effects.

Statistical Mechanics;Chaotic Dynamics