Title: Proper orthogonal decomposition vs. Fourier analysis for extraction of large-scale structures of thermal convection,
Abstract: We performed a comparative study of extraction of large-scale flow structures
in Rayleigh Bénard 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.