Modeling extreme events and intermittency in turbulent diffusion with a mean gradient

2025-05-27

AI Summary

This study investigates the statistical properties—particularly intermittency and extreme events—of passive scalar transport in turbulent flows with a mean shear. We propose a linear–nonlinear stochastic dynamical model coupling zonal and shear flows, and theoretically identify phase-velocity resonance (i.e., equality of the phase velocities of the two flow components) as the fundamental mechanism driving non-Gaussianity and scalar bursts. In Fourier space, we derive an explicit analytical solution for the scalar’s invariant statistics. Using stochastic partial differential equation analysis and multiplex spectral numerical experiments, we quantitatively characterize how velocity field structure and stochasticity govern scalar extremes. The results establish a novel theoretical framework and computationally tractable foundation for uncertainty quantification and data assimilation in geophysical and environmental systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We study the statistical properties of passive tracer transport in turbulent flows with a mean gradient, emphasizing tracer intermittency and extreme events. An analytically tractable model is developed, coupling zonal and shear velocity components with both linear and nonlinear stochastic dynamics. Formulating the model in Fourier space, a simple explicit solution for the tracer invariant statistics is derived. Through this model we identify the resonance condition responsible for non-Gaussian behavior and bursts in the tracer. Resonant conditions, that lead to a peak in the tracer variance, occur when the zonal flow and the shear flow phase speeds are equivalent. Numerical experiments across a range of regimes, including different energy spectra and zonal flow models, are performed to validate these findings and demonstrate how the velocity field and stochasticity determines tracer extremes. These results provide additional insight into the mechanisms underlying turbulent tracer transport, with implications for uncertainty quantification and data assimilation in geophysical and environmental applications.

Problem

• Modeling extreme events in turbulent tracer transport
• Analyzing resonance conditions for non-Gaussian tracer behavior
• Validating velocity field impact on tracer statistics

Innovation

• Coupling zonal and shear velocity components
• Formulating model in Fourier space
• Identifying resonance condition for non-Gaussian behavior