Intermittency in Fully Developed Turbulence as a Consequence of the Navier-Stokes Equations

Abstract

Fully developed hydrodynamic turbulence is considered in terms of a steady-state solution to the exact Fokker-Planck equation for the probability functional of the velocity field. The nested intermittency argument of Yaglom is restated in this formulation. A divergent buildup of fluctuations during the energy cascade modifies the $k^{\frac{-5\mathrm{}}{3}}$ inertial subrange spectrum. A physical analogy of the critical exponent $\eta$ to the Yaglom intermittency parameter ($\frac{\mu }{9}$) is proposed.