A low-dimensional model predicting geometry-dependent dynamics of large-scale coherent structures in turbulence

TL;DR

This paper evaluates a low-dimensional stochastic model derived from Navier-Stokes equations for predicting how large-scale coherent structures in turbulence, like convection rolls, depend on boundary geometry, with successful experimental validation.

Contribution

The paper demonstrates that a geometry-dependent low-dimensional model can accurately predict and reproduce complex turbulence dynamics observed in experiments.

Findings

Model predicts a new mode of convection roll alignment switching.

Predicted switching rate matches experimental measurements within 30%.

Model effectively captures geometry-dependent turbulence behavior.

Abstract

We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations, which are derived as a function of boundary geometry from the Navier-Stokes equations (Brown and Ahlers 2008). We test the model using Rayleigh-B\'enard convection experiments in a cubic container. The model predicts a new mode in which the alignment of a convection roll switches between diagonals. We observe this mode with a measured switching rate within 30% of the prediction.