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Rayleigh--B\'enard convection, which is the buoyancy-induced motion of afluid enclosed between two horizontal plates, is an idealised setup to studythermal convection. We analyse the modes that transport the most heat betweenthe plates by computing the proper orthogonal decomposition (POD) of numericaldata. Instead of the usual POD ansatz of finding modes that describe the energybest, we propose a method that is optimal in describing the heat transport.Thereby, we can determine the modes with the major influence on the heattransport and the coherent structures in the convection cell. We also show thatin lower-dimensional projections of numerical convection data, the newlydeveloped modes perform consistently better than the standard modes. We thenuse this method to analyse the main modes of three-dimensional convection in acylindrical vessel as well as two-dimensional convection with varying Rayleighnumber and varying aspect ratio.

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