Electronic edition ISSN 1574-0579

"Internal" scale and large scale vortex formation

S. N. Gordienko¹ - S. S. Moiseev²

¹ Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
² Space Research Institute, Russian Academy of Sciences, 117810 Moscow, Russia

Abstract
Experimental evidence for intermittency - the extremely alternating inhomogeneous distribution of small-scale turbulence - proves that this phenomenon is related to spontaneous generation of new non-trivial internal scales in a turbulent flow. The new characteristic (internal) scales differ parametrically from the scale of an external force driving turbulence. This parametrical difference has allowed us to develop a new approach to the problem of intermittency. The discrete set of all possible non-trivial characteristic scales has been found, L_int=r₀/γ^1/(n+1), n=1,2,... and the spectra corresponding to turbulent fluctuations at these scales have been established, E_k ∼ 1/k^1−2∆(n), where ∆(n) = −(n + 1)/(n + 2), γ = f₀τ₀²/r₀ is the dimensionless parameter of the theory, f₀, τ₀ and r₀ are the amplitude, the correlation time and the correlation length of a force driving turbulence. The generation of new scales in some points of a turbulent flow implies spontaneous development of vortexes at these points. For γ << 1 it is shown that the largest scale vortexes are associated with the 7/3- spectrum (or n=1) and governed by the flux of helicity through the spectrum. Refs 4.