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Spontaneous Stochasticity in the Presence of Intermittency.
André Luís Peixoto Considera1,2, Simon Thalabard3
1Instituto de Matemática Pura e Aplicada-IMPA, 22460-320 Rio de Janeiro, Brazil.
Physical Review Letters
|August 25, 2023
Summary
Spontaneous stochasticity in turbulent transport surprisingly transitions to deterministic behavior with increased spatial intermittency. Roughness, usually favoring stochasticity, hinders it in these multifractal random flows.
Area of Science:
- Turbulence and Complex Systems
- Statistical Physics
- Fluid Dynamics
Background:
- Spontaneous stochasticity explains turbulent transport at infinite Reynolds numbers.
- It posits that tracer particles in rough turbulent flows remain non-deterministic even without thermal noise.
- Spatial intermittency, characterized by multifractal scaling, is common in turbulence.
Purpose of the Study:
- To investigate the effect of spatial intermittency on spontaneous stochasticity in turbulent transport.
- To analyze Lagrangian transport in unidimensional multifractal random flows.
- To understand the interplay between spontaneous stochasticity and spatial intermittency.
Main Methods:
- Utilized systematic Monte Carlo simulations.
- Employed formal stochastic calculations.
- Studied Lagrangian transport in unidimensional multifractal random flows generated via Gaussian multiplicative chaos.
Main Results:
- A transition from spontaneously stochastic to deterministic behavior was observed as intermittency increased.
- Contrary to expectations, increased roughness due to multifractality hindered spontaneous stochasticity.
- The study revealed a non-intuitive relationship between spatial intermittency and spontaneous stochasticity.
Conclusions:
- Spatial intermittency can suppress spontaneous stochasticity in turbulent transport.
- The findings challenge the intuitive notion that increased roughness always promotes stochasticity.
- This work highlights a complex interplay between multifractality and non-deterministic particle dynamics in random flows.
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