A phase-based proper orthogonal decomposition that accounts for intrinsic large scale motion

A number of important fluid flows are driven by an intrinsic large scale within the flow, whose dynamics modulate the behavior of other flow scales via nonlinear mechanisms. Traditional modal analysis approaches, such as snapshot proper orthogonal decomposition (POD), represent this behavior inefficiently, using a cascade of modes even when representing a small number of physical scales interacting. To address this issue, we present a new space-phase POD method that extracts modes informed by this nonlinear interplay, within a formal POD framework. The modes utilize a transformation between time and phase of the large scale motion to create modes that coherently evolve along the large scale’s dynamics. We demonstrate the method’s utility using two examples: a low-Reynolds-number bluff-body flow and a more complex turbulent shock problem, using data from Duvvuri et al (“Large- and small-amplitude shock-wave oscillations over axisymmetric bodies in high-speed flow”, Journal of Fluid Mechanics, 913 (2021)). The proposed approach distills the large-scale behavior in the former example, and in the latter example yields modes that represent both the shock motion that drives large scale dynamics as well as the smaller scale turbulence occurring about the shock. In both cases, the space-phase POD technique is able to capture additional information about the dynamic structures within the flow as compared to classical data-driven techniques.