Instanton-based importance sampling for extreme fluctuations in a shell model for turbulent energy cascade

Area of Science:

• Turbulence modeling
• Computational fluid dynamics
• Statistical physics

Background:

• Out-of-equilibrium flows exhibit non-Gaussian fluctuations in observables like energy dissipation rate.
• Extreme fluctuations, though rare, possess significant phenomenology in physical systems.
• Path integral methods from quantum field theory are increasingly applied to fluid dynamics.

Purpose of the Study:

• To explore the applicability of instanton-based importance sampling to a shell model of turbulence.
• To assess the method's performance across varying degrees of nonlinearity.
• To evaluate the efficiency of sampling extreme events in turbulent energy cascades.

Main Methods:

• Utilized a shell model, a dynamical system for turbulent energy cascade.
• Employed instanton-based importance sampling, a path integral method.
• Validated the methodology against the heat equation limit.
• Investigated performance with increasing nonlinear coefficients.

Main Results:

• The instanton method showed good qualitative agreement for weak nonlinearities.
• Accuracy in estimating distribution flatness degraded as nonlinear intensities increased.
• The shell model allowed efficient numerical sampling of extreme events.

Conclusions:

• Instanton-based importance sampling is a promising technique for studying extreme events in turbulent systems.
• The method's accuracy is sensitive to the strength of nonlinear interactions.
• Further research is needed to refine the approach for strongly nonlinear regimes.