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The Finite-time Lyapunov Exponent (FTLE) is a measure for the rate of separation of particles in time-dependent flow fields. It provides a valuable tool for the analysis of unsteady flows. Commonly it is defined based on the flow map, analyzing the separation of trajectories of nearby particles over a finite-time span. This paper proposes a localized… (More)

This paper proposes a Galilean invariant generalization of critical points of vector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extracts long-living features, like saddles and centers, and filters out short-living local structures. This is well suited for analysis of… (More)

We generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the… (More)

- Laurent Cordier, Bernd R. Noack, +5 authors Robert K. Niven
- 2013

A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To… (More)

— A representation of actuation effects is developed for low-order empirical Galerkin models of incompressible fluid flows. These actuation models fill a missing link and, indeed, provide a key enabler towards feedback design in flow control utilizing empirical Galerkin models. A flow control strategy is proposed based on the extended flow models and on the… (More)

— Reduced Galerkin models of fluid flows are traditionally obtained by the Galerkin projection of a low-dimensional flow expansion onto the the Navier-Stokes equation. A new approach in this application domain is the a posteriori model parameter estimation to correct for distortions due to the low dimensional compression. Preserving model structure, this… (More)

- Bernd R. Noack, Robert K. Niven
- Computers & Mathematics with Applications
- 2013

We propose a maximum-entropy closure strategy for dissipative dynamical systems building on and generalizing earlier examples (Noack & Niven (2012) [11]). Focus is placed on Galerkin systems arising from a projection of the incompressible Navier–Stokes equation onto orthonormal expansionmodes. Themaximum-entropy closure is motivated by a simple analytical… (More)

- OLIVER LEHMANN, MARK LUCHTENBURG, BERND R. NOACK, RUDIBERT KING, MAREK MORZYŃSKI, GILEAD TADMOR
- 2005

A principal challenge in the use of empirical proper orthogonal decomposition (POD) Galerkin models for feedback control design in fluid flow systems is their typical fragility and poor dynamic envelope. Closed loop performance and optimized sensor(s) location are significantly improved by use of interpolated POD modes from a succession of low dimensional… (More)

- Gilead Tadmor, Oliver Lehmann, +4 authors Marek Morzyński
- Philosophical transactions. Series A…
- 2011

We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and… (More)

- Michael Schlegel, Bernd R. Noack, +7 authors Gilead Tadmor
- 2012

We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed 'observable inferred decomposition' (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a… (More)