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

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.