Bernd Noack

Focus of Noack's work are physical theories and mathematical methods for turbulence control. One direction is the development of control-oriented nonlinear models and associated control design building on the Galerkin method, originally proposed by Boris Galerkin. He proposed the first mathematical Galerkin model for the two- and three-dimensional cylinder wake from Hilbert space considerations. Subsequent works employ the proper orthogonal decomposition and propose numerous enablers accounting for the pressure term, subscale turbulence and departures from the training set.

He has distilled three major facets of nonlinearity in dynamical least-order models:

• The role of the base flow in saturation of fluctuation level building on J. T. Stuart's mean field theory and generalizing the Landau model for a supercritical Hopf bifurcation.^[3]
• The interaction of two coherent structures at different frequencies via the base flow leading to coupled Landau oscillators.^[4]
• A statistical closure for the energy cascade of broadband dynamics via a finite time non-equilibrium thermodynamics (FTT) framework.^[5]

The associated control laws can be derived from energy considerations and have been applied to streamlined and bluff bodies.

Recently, Noack works on implementing the powerful methods of machine learning in turbulence control. Major breakthroughs are learning the control law in real-world experiments with Machine learning control (MLC) and an automated learning the control-oriented dynamical gray-box model from experimental data.

Supplementary projects include data visualization, phenomenological models, vortex models and entropy-based optimization in addition to a spectrum of model-free and model-based control approaches. The breadth of this research builds on a network of cross disciplinary collaborations with leading teams.

• Bernd R. Noack; Marek Morzynski; Gilead Tadmor, eds. (2011). Reduced-Order Modelling for Flow Control. Springer-Verlag. ISBN 978-3-7091-0758-4.
• Thomas Duriez; Steven L. Brunton; Bernd R. Noack (2016). Machine Learning Control - Taming Nonlinear Dynamics and Turbulence. Springer-Verlag. ISBN 978-3-319-40624-4.
• Steven L. Brunton; Bernd R. Noack (2015). "Closed-loop turbulence control: Progress and challenges". Applied Mechanics Reviews. 67 (5): 050801. Bibcode:2015ApMRv..67e0801B. doi:10.1115/1.4031175. S2CID 120783766.
• Steven L. Brunton; Bernd R. Noack; Petros Koumoutsakos (2020). "Machine learning for fluid mechanics". Annu. Rev. Fluid Mech. 52: 477–508. arXiv:1905.11075. Bibcode:2020AnRFM..52..477B. doi:10.1146/annurev-fluid-010719-060214. S2CID 166227999.