Mori–Zwanzig Mode Decomposition: Transient Flows and Laminar-Turbulent Boundary Layer Transition

In this work, we apply and analyze the data-driven Mori-Zwanzig Mode Decomposition (MZMD), a novel technique used for extracting large-scale spatio-temporal coherent structures representing an efficient generalization of Dynamic Mode Decomposition (DMD). We first demonstrate that by adding memory terms, MZMD is able to reconstruct a 2D transient flow over a cylinder; where the flow transitions from an unstable equilibrium point to a heteroclinic orbit representing the von Kármán vortex street. For this flow regime, DMD is not able to reconstruct the flow, which we demonstrate. We next show that MZMD significantly improves upon DMD for reconstructing and performing future state predictions of a high-dimensional flow with strong nonlinearities, namely the laminar-turbulent transition in a hypersonic boundary layer of a tangent ogive with a blunted nose tip at Mach 5. For this flow, we demonstrate the diagnostic ability of MZMD for predicting and extracting the dominant mechanisms relevant to the transition to turbulence. The results improve as more memory terms are added, however the improvement saturates after a certain number of memory terms are considered, suggesting a finite memory effect. The transition to turbulence is further analyzed using the MZMD modal structures and spectrum.