Focus and expertize

Our model-based turbulence control employs reduced-order models (ROMs) which are accurate enough to capture the main unactuated and actuated coherent structures but low-dimensional enough to be on-line capable for the experiment. In the past 25 years we have developed numerous enablers for such control-oriented ROMs.

Introductory reading

Noack, B.R., Morzynski, M. & Tadmor, G.(eds.) (2011) "Reduced-Order Modelling for Flow Control." CISM Courses and Lectures 528, Springer-Verlag, Vienna. (html)	Brunton, S. L. & Noack, B. R. (2015) "Closed-loop turbulence control: Progress and challenges". Applied Mechanics Reviews (online) (html).

Part of the 2011 Springer book are illustrated by following introductory slides.

• Motivation for ROM (PDF)
• Standard POD Galerkin method (PDF)
• POD models for natural flows (PDF)
• Mean-field models for transient dynamics (PDF)
• Finite-time thermodynamics as unifying discipline for stability analysis, turbulence theory and control theory (PDF)

Closed-loop wake stabilization using ROM

• Gerhard, J., Pastoor, M., King, R., Noack, B.R., Dillmann, A., Morzynski, M. & Tadmor, G. (2003) "Model-based control of vortex shedding using low-dimensional Galerkin models", AIAA Paper 2003-4262 (PDF) (BibTeX)
• Pastoor, M., Henning, L., Noack, B.R., King, R. & Tadmor, G. (2008) "Feedback shear layer control for bluff body drag reduction." J. Fluid Mech. 608, 161-196. (html) (pdf) (BibTeX)

Enablers of POD models

• Noack, B.R., Afanasiev, K., Morzynski, M., Tadmor, G. & Thiele, F. (2003) "A hierarchy of low-dimensional models of the transient and post-transient cylinder wake". J. Fluid Mech. 497, 335-363. (html) (pdf) (BibTeX)
• Noack, B.R., Papas, P. & Monkewitz, P.A. (2005) "The need for a pressure-term representation in empirical Galerkin models of incompressible shear flow", J. Fluid Mech. 523, 339-365. (html) (pdf) (BibTeX)
• Luchtenburg, D.M., Günther, B., Noack, B.R., King, R. & Tadmor, G. (2009) "Generalized mean-field model of natural and actuated flows over a high-lift configuration." J. Fluid Mech. 623, 283-316. (html) (pdf) (BibTeX)

Subscale turbulence closures of POD models

• Protas, B., Noack, B. R. & Östh, J. (2015) "Optimal nonlinear eddy viscosity in Galerkin models of turbulent flows". Journal of Fluid Mechanics 766, 337-367.
• Östh, J., Noack, B. R., Krajnovic, S., Barros, D. & Borée, J. (2014) "On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body". J. Fluid Mech. 747, 518-544. (html) (pdf)
• Balajewicz, M., Dowell, E.H. & Noack, B.R. (2013) "Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier-Stokes equation". J. Fluid Mech. 729, 285-308. (html) (pdf) (BibTeX)

Generalized modal expansions

• Noack, B. R., Stankiewicz, W., Morzynski & Schmid, P. J. (2016) "Recursive dynamic mode decomposition of a transient cylinder wake." Journal of Fluid Mechanics 809, 843--872. (html)
• Stankiewicz, W., Morzynski, M., Kotecki, K. & Noack, B.R. (2016) "On the need of mode interpolation for data-driven Galerkin models of a transient floow around a sphere". Theoretical and Computational Fluid Mechanics (in print).
• Schlegel, M., Noack, B.R., Jordan, P., Gröschel, E., Schröder, W. Wei, M., Freund, J.B., Lehmann, O., & Tadmor, G. (2012) "On least-order representations for aerodynamics and aeroacoustics". J. Fluid Mech. 697, 387-398. (html) (pdf) (BibTeX)

Statistical closures of Galerkin models

• Kaiser, E. Noack, B.R., Cordier, L., Spohn, A., Segond, M., Abel. M., Daviller, G., Östh, J., Krajnovic, S., & Niven, R.K. (2014) "Cluster-based reduced-order modelling of a mixing layer". J. Fluid Mech. 754, 365-414. (html) (pdf)
• Noack, B.R. & Niven, R.K. (2012) "A maximum entropy closure for a Galerkin system of an incompressible periodic wake". J. Fluid Mech. 700, 187-213 (html) (pdf) (BibTeX)
• Noack, B.R., Schlegel, M., Ahlborn, B., Mutschke, G., Morzynski, M., Comte, P. & Tadmor, G. (2008) "A finite-time thermodynamics formalism for unsteady flows". J. Non-Equilib. Thermodyn. 33 (2), p. 103-148. (html) (PDF) (BibTeX)

Time-resolving 3D POD models of PIV data

• Bourgeois, J., Noack, B.R & Martinuzzi, R. (2013) "Generalised phase average with applications to sensor-based flow estimation of the wall-mounted square cylinder wake". J. Fluid Mech. 736, 316--350. (html) (pdf) (BibTeX)
• Oberleithner, K., Sieber, M., Nayeri, C.N., Paschereit, C.O., Petz, C., Hege, H.-C., Noack, B.R. & Wygnanski, I. (2011) "Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: Stability analysis and empirical mode construction". J. Fluid Mech. 679, 383-414. (html) (pdf) (BibTeX)

Mathematical Galerkin models

• Noack, B.R. & Eckelmann, H. (1994) "A global stability analysis of the steady and periodic cylinder wake". J. Fluid Mech. 270 , 297-330. (html) (pdf) (BibTeX)

Pioneers in Reduced-Order Modeling

• Ludwig BOLTZMANN (1844-1906): Introduction of entropy, attractor (equilibrium) model for complete chaos. (html)
• Lev Davidovich LANDAU (1908-1968): Dynamic models for order parameters during transitions (Landau model, Ginzburg-Landau equation, phase transition). (html)
• Norbert WIENER (1894-1964): Cybernetics as framework for modern control design. From linear models, stochastic processes to Maxwellian demons (information theory). (html)