Modes, Manifolds and Clusters—Different flavours of reduced-order models

Since over a century, reduced-order models (ROM) are at the heart of theoretical fluid dynamics thanks to their paramount importance for physical understanding, data compression, estimation, control and optimization. In this talk, we exemplify different ROM approaches for the fluidic pinball [1,2,3] , the wake flow behind a cluster of three parallel cylinders on an equilateral triangle pointing upstream. The flow may be actuated by rotating cylinders. First, the transition scenario of the unforced fluidic pinball is modeled with a five-mode sparse Galerkin model. This model comprises successive Hopf and pitch-fork bifucations, which are typical for a number of wake flows. Second, a feature-based manifold-fold model [4] is identified describing transient and post-transient flow dynamics more accurate and more low-dimensional than the Galerkin model. Third, a cluster-based network model (CNM) [5] is presented describing the fluidic pinball wake with actuation as free input, employing thousand differently actuated pinball simulations. CNM yields a robust dynamics from a fully automatable procedure. Finally, other applications and a broader perspective of ROM is provided.