Proper orthogonal decomposition vs. Fourier analysis for extraction of large-scale structures of thermal convection

TL;DR

This study compares proper orthogonal decomposition and Fourier analysis for extracting large-scale flow structures in thermal convection, highlighting their respective strengths and suggesting Fourier analysis as a viable alternative.

Contribution

The paper demonstrates that Fourier analysis can effectively capture large-scale flow structures, offering an alternative to POD in thermal convection studies.

Findings

POD modes capture more energy than Fourier modes.

Fourier modes better detect flow reversals.

Flow profiles of dominant modes are similar.

Abstract

We performed a comparative study of extraction of large-scale flow structures in Rayleigh B\'enard convection using proper orthogonal decomposition (POD) and {\em Fourier analysis}. We show that the free-slip basis functions capture the flow profiles successfully for the no-slip boundary conditions. We observe that the large-scale POD modes capture a larger fraction of total energy than the Fourier modes. However, the Fourier modes capture the rarer flow structures like flow reversals better. The flow profiles of the dominant POD and Fourier modes are quite similar. Our results show that the Fourier analysis provides an attractive alternative to POD analysis for capturing large-scale flow structures.