Mori-Zwanzig Mode Decomposition: Transient Flows

Many flows in nature contain transient dynamics, where the fluid system moves from one equilibrium state to another. Flows of this type represent significant challenges for current modal decomposition techniques, such as Dynamic Mode Decomposition. We investigate the data-driven Mori- Zwanzig Mode Decomposition (MZMD) to reconstruct and perform future state prediction of transient dynamics. We first consider a 2D transient flow over a cylinder; where the flow transitions from an unstable equilibrium point to a heteroclinic orbit representing the von Karman vortex street. We then perform MZMD analysis of a more complex multiphase flow in 3D, simulating the growth and departure of vapor bubbles from a heated orifice in a quiescent liquid. We show that MZMD significantly improves upon DMD for reconstructing and performing future state predictions by extracting transient modes that improve the ability to resolve such transient dynamics, by increasing the spectral complexity at a similar computational cost. This is achieved by the introduction of Mori-Zwanzig memory terms, which account for the effects the unresolved dynamics have on the resolved variables (observables). The improvement saturates after a certain number of memory terms are considered, with a finite decaying memory effect.