On the rapid increase of intermittency in the near-dissipation range of fully developed turbulence

Intermittency, measured as <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\log \left({F(r)}/{3}\right)$</EquationSource> </InlineEquation>, where F(r) is the flatness of velocity increments at scale r, is found to rapidly increase as viscous effects intensify, and eventually saturate at very small scales. This feature defines a finite intermediate range of scales between the inertial and dissipation ranges, that we shall call near-dissipation range. It is argued that intermittency is multiplied by a universal factor, independent of the Reynolds number Re, throughout the near-dissipation range. The (logarithmic) extension of the near-dissipation range varies as <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\sqrt{\log Re}$</EquationSource> </InlineEquation>. As a consequence, scaling properties of velocity increments in the near-dissipation range strongly depend on the Reynolds number. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005