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Summary

This study explores the transition to strong turbulence, identifying anomalous scaling in velocity derivatives. Rare, intermittent events are described using multiple Reynolds numbers, with the transition disappearing below a critical threshold.

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Area of Science:

Fluid dynamics
Turbulence theory
Statistical physics

Background:

Investigating the transition from low-Reynolds-number flow to strong turbulence.
Understanding anomalous scaling in normalized moments of velocity derivatives (dissipation rates).

Purpose of the Study:

To define and analyze the transition to strong turbulence in a fluid driven by a Gaussian random force.
To explain the emergence of anomalous scaling and multiscaling behavior.

Main Methods:

Theoretical analysis of fluid dynamics under random forcing.
Application of multiscaling concepts to describe intermittent events.
Comparison with large-scale numerical simulations.

Main Results:

Anomalous scaling of dissipation rates appears with the onset of strong turbulence.
Multiscaling provides a framework to describe rare, intermittent events using infinite Reynolds numbers.
The theoretically predicted transition vanishes for Reynolds numbers (R_λ) below 3.

Conclusions:

The transition to strong turbulence is characterized by multiscaling and anomalous scaling exponents.
The developed theory quantitatively aligns with numerical simulation results.
Understanding these phenomena is crucial for advanced fluid dynamics research.