Turbulence revisited

Abstract

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.

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