Turbulence revisited

A new approach to turbulence based upon the Stabilization Principle is introduced. Onset of turbulence is interpreted as loss of stability of solutions to the Navier-Stokes equations in the class of differentiable functions. Developed turbulence is considered as postinstability motion in the class of non-differentiable functions. A non-linear version of the Liouville equation is proposed for describing postinstability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, velocities are represented by a set of stochastic invariants found from the Stabilization Principle.