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Dynamical interpretation of multifractal velocity statistics

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Multiscaling statistics of velocity increments in hydrodynamical turbulence, i.e. nonlinear dependence of their moments, is derived using a simple one-dimensional stochastic equation modeling the flow inside a vortex filament. The main idea is that random oscillations of large-scale velocity result in systematical stretching of a filament. Stretching produces power-law structure functions. Different filaments contribute to scaling exponents of different orders. In the model, scaling relations are not produced by singular velocity distribution: there is no singularity at any finite time.

Author(s):

Valeria Sirota    
P.N. Lebedev Physical Institute, Theory Department
Russian Federation

Kirill Zybin    
P.N. Lebedev Physical Institute, Theory Department
Russian Federation