Deep learning in turbulent convection networks

Abstract

Significance Turbulent convection in horizontally extended systems comprises vortices and plumes on many time and length scales. These structures interact nonlinearly to self-organize into slowly evolving turbulent superstructures, which are horizontally more extended than in height. We use a U-shaped deep-learning algorithm to generate a time-varying planar network, resulting in a drastic reduction of degrees of freedom, and use it to detect the 3D superstructures and estimate their effectiveness in transporting heat. We thus demonstrate the likely utility of deep learning for parameterizing convection in global models of atmospheric and stellar convection whenever mesoscale structures are conspicuous. We explore heat transport properties of turbulent Rayleigh–Bénard convection in horizontally extended systems by using deep-learning algorithms that greatly reduce the number of degrees of freedom. Particular attention is paid to the slowly evolving turbulent superstructures—so called because they are larger in extent than the height of the convection layer—which appear as temporal patterns of ridges of hot upwelling and cold downwelling fluid, including defects where the ridges merge or end. The machine-learning algorithm trains a deep convolutional neural network (CNN) with U-shaped architecture, consisting of a contraction and a subsequent expansion branch, to reduce the complex 3D turbulent superstructure to a temporal planar network in the midplane of the layer. This results in a data compression by more than five orders of magnitude at the highest Rayleigh number, and its application yields a discrete transport network with dynamically varying defect points, including points of locally enhanced heat flux or “hot spots.” One conclusion is that the fraction of heat transport by the superstructure decreases as the Rayleigh number increases (although they might remain individually strong), correspondingly implying the increased importance of small-scale background turbulence.