Implications of the selection of a particular modal decomposition technique for the analysis of shallow flows

Abstract

This work deals with the capabilities of two synoptic modal decomposition techniques for the identification of the spatial patterns and temporal dynamics of coherent structures in shallow flows. Using two different experimental datasets it is shown that due to the linear behaviour of large-scale, quasi-two-dimensional flow structures, there are almost no differences in the identification of dominant modes between the results obtained from a traditional proper orthogonal decomposition and the more recently developed dynamic mode decomposition. However, it is also shown that nonlinear dynamics can arise in the transition of these structures to a quasi-two-dimensional behaviour, which can result in the proper orthogonal decomposition identifying structures composed of multi-frequencies, a sign of a convoluted dynamics. Thus dynamic mode decomposition is recommended instead for the analysis of such phenomena. In addition, this paper introduces a simple ranking methodology for the use of the dynamic mode decomposition technique in shallow flows, which is based on the results of the proper orthogonal decomposition.