From simulating rotating Rayleigh-Bénard convection at very low Rossby numbers to stochastic dynamics of 3D modes in quasi-2D turbulence
- Adrian van Kan (University of California at Berkeley)
Abstract
Geophysical and astrophysical fluid flows are typically driven by buoyancy and strongly constrained by planetary rotation at large scales. Rapidly rotating Rayleigh-Bénard convection (RRRBC) provides a paradigm for direct numerical simulations (DNS) and laboratory studies of such flows, but the accessible parameter space remains restricted to moderately fast rotation (Ekman numbers
Beyond the specific example of rotating convection, turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres, oceans and stars, its manifestations can vary considerably between different physical systems. For instance, three-dimensional (3D) turbulent flows display a forward energy cascade from large to small scales, while in two-dimensional (2D) turbulence, energy cascades from small to large scales. In various physical systems, a transition between such disparate regimes of turbulence can occur when a control parameter reaches a critical value. Specifically for turbulent flow confined in a thin fluid layer, there is a critical layer height where the fluid flow becomes two-dimensional under suitable conditions. Close to this threshold, 3D variations in the velocity are highly intermittent, and display jumps in the linear growth rate. Modeling of this problem motivates the study of stochastic ODE driven by Lévy noise, representing the dynamics of the amplitude of 3D modes. The probability density function (PDF) of the amplitude is then governed by a fractional Fokker-Planck equation containing a nonlocal, linear fractional diffusion operator. I describe certain results which I derived on this problem, including the asymptotic behavior of the PDF which lead to heuristic estimates of the moments that agree favorably with numerical solutions and outline some remaining questions.
References:
[1] AvK et al., Bridging the Rossby number gap in rapidly rotating thermal convection. (in prep.)
[2] AvK, Alexakis, A., Brachet, M.E., 2021. Lévy on-off intermittency. Phys. Rev. E, 103(5), p.052115.
[3] AvK, Pétrélis, F., 2023. 1/f noise and anomalous scaling in Lévy noise-driven on–off intermittency. J. Stat. Mech., 2023(1), p.013204.