  We introduce the Mori-Zwanzig (MZ) Modal Decomposition (MZMD), a novel
technique for performing modal analysis of large scale spatio-temporal
structures in complex dynamical systems, and show that it represents an
efficient generalization of Dynamic Mode Decomposition (DMD). The MZ formalism
provides a mathematical framework for constructing non-Markovian reduced-order
models of resolved variables from high-dimensional dynamical systems,
incorporating the effects of unresolved dynamics through the memory kernel and
orthogonal dynamics. We present a formulation and analysis of the modes and
spectrum from MZMD and compare it to DMD when applied to a complex flow: a
Direct Numerical Simulation (DNS) data-set of laminar-turbulent boundary-layer
transition flow over a flared cone at Mach 6. We show that the addition of
memory terms by MZMD improves the resolution of spatio-temporal structures
within the transitional/turbulent regime, which contains features that arise
due to nonlinear mechanisms, such as the generation of the so-called "hot"
streaks on the surface of the flared cone. As a result, compared to DMD, MZMD
improves future state prediction accuracy, while requiring nearly the same
computational cost.
