  This note studies the mechanism of turbulent energy cascade through an
opportune bifurcations analysis of the Navier--Stokes equations, and furnishes
explanations on the more significant characteristics of the turbulence. A
statistical bifurcations property of the Navier--Stokes equations in fully
developed turbulence is proposed, and a spatial representation of the
bifurcations is presented, which is based on a proper definition of the fixed
points of the velocity field. The analysis first shows that the local
deformation can be much more rapid than the fluid state variables, then
explains the mechanism of energy cascade through the aforementioned property of
the bifurcations, and gives reasonable argumentation of the fact that the
bifurcations cascade can be expressed in terms of length scales. Furthermore,
the study analyzes the characteristic length scales at the transition through
global properties of the bifurcations, and estimates the order of magnitude of
the critical Taylor--scale Reynolds number and the number of bifurcations at
the onset of turbulence.
