Multiresolution Optimized Dynamic Mode Decomposition

The performance of exact-DMD, optimized-DMD, and Multiresolution optimized-DMD are examined for an intricate flow around a vertical retaining wall structure embedded in a gravel bed. The experimental configuration is of paramount interests for the practitioners dealing with sediment erosion around the base of instream structures. The measurements were obtained employing a stereo particle image velocimetry (SPIV) in a plane perpendicular to the approach flow direction at the leading edge of the protrusion. The results indicate that optimized-DMD outperforms exact-DMD as it pulls out the stable modes. However, the flow under consideration is too complex, consist of multi-temporal and spatial scales, that it requires a large number of modes to approximate the coherent structures present in the flow. Thus, multiresolution optimized-DMD capable of separating slow and fast moving modes in a recursive manner is employed. Two criteria are considered for the selection of modes at each level: 1) a frequency cut-off, and 2) energy content. This is a robust approach to separate complex systems into a hierarchy of important multiresolution time-scale components.