Conditional Space-Time Pod Extensions for Stability and Prediction Analysis

The correlation and extraction of coherent structures from a turbulent flow is a principal objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into transient dynamics, revealing the causation of specific flow phenomena - or events, in a customizable manner. This work targets the temporal evolution of CPOD modes in a reduced subspace, resulting in new extensions and adaptations that exceed the capabilities of other decomposition methods. First, the properties of CPOD and its relation to the ensemble average is instantiated with a simple Lorenz system. Other CPOD properties are examined with new applications to supersonic boundary layer transition and Schlieren video processing of unstarted inlet buzz. These examples explore the pragmatic concerns of oversampling and offer theoretical connection to the sampling of a larger Hankel space. Capitalizing on these insights, it is demonstrated that the subsequent application of dynamic mode decomposition (DMD) to CPOD modes, provides a flexible tool to investigate targeted flow instabilities, both absolute (tonal) and convective in nature. By extending the CPOD time-horizon to educe tones, it is shown that CPOD-DMD can exactly reproduce Spectral POD modes of a resonating jet. Regarding convective instabilities, a multi-resolution framework (CPOD-mrDMD) yields a refined "cause and effect" stability analysis, capable of diagnosing the natural forcing mechanisms within the jet, and the resulting unstable shear-layer mode. In a separate utilization, the potential for real-time flow prediction of extreme events is derived from an active sensor correlated to a CPOD mode using the example of bluff-body wake structures impinging on a channel wall.