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Small-scale vorticity filaments and structure functions of the developed turbulence. (English) Zbl 1457.76079

Summary: We develop a theory of turbulence based on the Navier - Stokes equation, without using dimensional or phenomenological considerations. A small scale vortex filament is the main element of the theory. The theory allows to obtain the scaling law and to calculate the scaling exponents of Lagrangian and Eulerian velocity structure functions in the inertial range. The obtained results are shown to be in very good agreement with numerical simulations and experimental data. The introduction of stochasticity into the equations and derivation of scaling exponents are discussed in details. A weak dependence on statistical propositions is demonstrated. The relation of the theory to the multifractal model is discussed.

MSC:

76F02 Fundamentals of turbulence
35Q30 Navier-Stokes equations
76M35 Stochastic analysis applied to problems in fluid mechanics
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