Describing the Heat Transport of Turbulent Rayleigh--B\'enard Convection by POD methods

TL;DR

This paper introduces a novel POD-based method optimized for identifying modes that most significantly contribute to heat transport in turbulent Rayleigh-Bénard convection, outperforming standard modes in lower-dimensional representations.

Contribution

The authors develop a new POD approach focused on heat transport, enabling better identification of coherent structures influencing heat transfer in convection.

Findings

New POD modes outperform standard modes in heat transport analysis.

Method effectively identifies dominant heat-carrying structures.

Applicable to both 2D and 3D convection data.

Abstract

Rayleigh--B\'enard convection, which is the buoyancy-induced motion of a fluid enclosed between two horizontal plates, is an idealised setup to study thermal convection. We analyse the modes that transport the most heat between the plates by computing the proper orthogonal decomposition (POD) of numerical data. Instead of the usual POD ansatz of finding modes that describe the energy best, we propose a method that is optimal in describing the heat transport. Thereby, we can determine the modes with the major influence on the heat transport and the coherent structures in the convection cell. We also show that in lower-dimensional projections of numerical convection data, the newly developed modes perform consistently better than the standard modes. We then use this method to analyse the main modes of three-dimensional convection in a cylindrical vessel as well as two-dimensional convection with varying Rayleigh number and varying aspect ratio.