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Vortex filament model and multifractal conjecture.

K P Zybin¹, V A Sirota

¹P. N. Lebedev Physical Institute of RAS, Leninskij Prospekt, Moscow, Russia. zybin@lpi.ru

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This summary is machine-generated.

We present a new theory of turbulence using the inviscid Navier-Stokes equation, yielding an exact stochastic solution. This approach accurately predicts turbulence scaling laws, aligning with experimental and simulation data.

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Area of Science:

Fluid Dynamics
Statistical Physics
Turbulence Theory

Background:

Understanding turbulence is a fundamental challenge in physics.
The Navier-Stokes equation describes fluid motion but is difficult to solve analytically for turbulent flows.

Purpose of the Study:

To develop an exact stochastic solution for the inviscid Navier-Stokes equation.
To derive turbulence scaling laws in the inertial range.
To validate the model against numerical and experimental results.

Main Methods:

Developing a vortex filament model as an exact stochastic solution.
Applying the multifractal conjecture to calculate scaling exponents.
Comparing results with existing numerical simulations and experimental data.

Main Results:

An exact power law for velocity structure functions in the inertial range was obtained.
Scaling exponents were calculated without relying on extended self-similarity.
The model demonstrated excellent agreement with numerical and experimental findings.

Conclusions:

The proposed vortex filament model offers a powerful tool for turbulence research.
The study validates the combination of stochastic solutions and multifractal analysis for turbulence.
Further exploration of general stochastic solutions is warranted.