Coherent structures detection using the DMD and OPD methods: Differences between the methods and sensitivity to the adjustable parameters

¹ Institute of Thermomechanics, Czech Academy of Sciences, Department of Fluid Dynamics, Dolejškova 1402/5, 18200, Praha 8, Czech Republic
² Charles University, Faculty of Mathematics and Physics, Department of Atmospheric Physics, Ke Karlovu 3, 12116, Praha 2, Czech Republic

^* Corresponding author: klukovaz@it.cas.cz

Published online: 4 July 2024

Abstract

The turbulent part of the flow within the Atmospheric boundary layer is not necessarily totally random, but it usually reports some structures with inner coherence. These so called coherent structures can be decomposed from measured or modelled spatio-temporal data using mathematical methods as for instance dynamic mode decomposition (DMD) or oscillating pattern decomposition (OPD). These two methods produce complex eigenvectors and eigenvalues revealing cyclic propagation of the structures in space accompaigned with the information about the frequency of the structure’s excitation and decay time of the amplitude’s oscillation. This contribution will show that despite some differences in the DMD and OPD calculation, these methods produce very similar results. In contrary, the results are very sensitive to some parametrs occurring in the algorithm, mainly the number of the POD modes included to the calculation. The fewer POD modes are taken, the smoother topology of the DMD or OPD modes containing fewer but bigger whirls is produced, usually going hand by hand with lower frequencies.