A Low-Dimensional Stochastic Model for Large-Scale Coherent Structures

Abstract:

We demonstrate a methodology to predict the dynamics of the large-scale coherent structures in turbulence, such as convection rolls in the atmosphere, using a simple low dimensional stochastic model proposed by Brown and Ahlers (Phys. Fluids, 2008). The model terms are derived from the Navier-Stokes equations, including a potential term that can be predicted for arbitrary topography of the system. The model has previously described several dynamical modes of a convection roll, such as cessation, meandering, and internal oscillations, in turbulent Rayleigh-Benard convection, i.e. a fluid heated from below. Here we test a model prediction for the existence of a new mode where the convection roll stochastically changes direction to align with different diagonals of a cubic container. The model successfully predicts the switching rate of the convection roll under various conditions. The success of the prediction of the switching mode demonstrates that a low-dimensional turbulent model can quantitatively predict the existence and properties of different dynamical states that result from boundary geometry. Since this methodology can in principle be applied to other turbulent flows, it has potential for the development of general, predictive, low-dimensional models for turbulence, and for various geophysical flows in different topography.