POD-based analysis of time-resolved tornado-like vortices

In this study, three representative configurations of tornado-like vortices, i.e., single vortex, vortex breakdown and multi-vortex, are numerically simulated using large-eddy simulation (LES). Proper orthogonal decomposition (POD) is firstly employed to decompose flow-field snapshots into a series of orthogonal flow patterns (POD modes) and time-dependent coefficients. Then, a conditional-average analysis is conducted to obtain the four kinds of conditionally-averaged flow fields, which are then compared with instantaneous and ensemble-averaged flow fields. Next, a quadruple POD analysis is performed to decompose the instantaneous flow field into mean, coherent, transition and noise components. Finally, a qualitative analysis is implemented for unsteady vortex motions in horizontal and vertical planes. Results show that the conditional average shows larger-scale coherent structures than the classical ensemble average, while it loses the small-scale turbulent fluctuations present in instantaneous flow. The tornado vortex structure is controlled by the mean component in the single-vortex stage. With increase in swirl ratio, the tornado vortex evolves from single-vortex, to vortex-breakdown to multi-vortex, companied by kinetic energy transference to coherent and transition components. The horizontal and vertical vortex motions are essentially the results of horizontal and vertical velocity perturbations.