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This study investigates the connection between stochastic Lorenz equations and wind reversals observed in Rayleigh-Bénard convection experiments. Through long-time numerical simulations, researchers found that the probability distribution of timing between flow reversals exhibits non-Gaussian, multifractal behavior, despite showing Brownian statistics in certain frequency ranges. The work demonstrates that a simplified stochastic Lorenz system can accurately model the complex turbulent statistics of large-scale flow reversals in thermal convection.
Why it matters
This research provides a low-dimensional mathematical model that can predict the behavior of turbulent convection systems without requiring computationally expensive full-scale simulations. The findings have implications for understanding atmospheric and oceanic circulation patterns, as well as industrial processes involving heat transfer and fluid dynamics.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: The Lorenz equations [1] are a severe Galerkin-truncation of the Oberbeck-Boussinesq (OB) equations describing Rayleigh-B’enard convection (RBC). Here we examine the mathematical connections between the chaotic lobe-switching behavior of a stochastic form of the Lorenz equations, that model the interaction between the thermal boundary layers and the core circulation, and the mean wind reversals in the experiments of Sreenivasan et al. [2]. Long-time numerical simulations of these stochastic equations, not easily accessible with the OB equations, yield a probability distribution for lobe inter-switch timings that exhibits non-Gaussian, multifractal behavior. In the Gaussian frequency range the simulations mirror the laboratory measurements and the classical Hurst exponent and quadratic variation show Brownian second-moment statistics. Further scrutiny reveals a non-linear cumulant generating function, or moment-exponent function, and thus multifractality. A simple generalized two-scale Cantor-cascade analysis reproduces these properties, showing that multiplicative intermittency, characteristic of turbulence, strongly influences the statistics. This demonstrates that this stochastic Lorenz system is a faithful, low-dimensional surrogate for mean-wind reversals in RBC.
Source: Stochastic Lorenz dynamics and wind reversals in Rayleigh-B'enard Convection