Oberseminar Numerische Mathematik / Scientific Computing
Bernd R. Noack
Berlin Institute of Technology
Finite-time thermodynamics for shear flows - a unifying framework for stability analysis, statistical mechanics and control theory
Abstract:
Turbulent fluid has often been conceptualized as transient thermodynamic phase. A description of turbulence in terms of statistical physics has been a long-term endeavour since the 20th century (e.g. by L. Onsager and R. Kraichnan). Here, a finite-time thermodynamics (FTT) formalism is proposed to compute the mean flow and fluctuation levels of unsteady, incompressible, shear flows [J. Non.-Equilib. Thermodyn. 33 (2), 2008]. This formalism yields a definition of a thermodynamic degree of freedom of the velocity fluctuation, conditions for thermal equilibrium (TE), as well as a Fickian law of energy re-distribution under non-equilibrium conditions. In general, the dynamics of unsteady flow is shown to be in partial TE, a state governed by finite time scales of energy transfer. Mathematically, this partial TE arises from a continuous interpolation between a linear instability of a few degrees of freedom and TE of the whole system.
The FTT model has been successfully applied to shear flows with simple to complex dynamics. The focus of this talk is placed on vortex shedding behind a cylinder. Further examples presented include the 1D Burgers' equation and 3D homogenous shear turbulence. In addition to the statistical physics embedding, the FTT formalism opens the first path to a fully nonlinear, infinite-horizon control theory, a unified description of the normal and inverse turbulence cascade, and an alternative to the eddy viscosity concept. The study was performed in collaboration with Boye Ahlborn, Marek Morzynski, Gerd Mutschke, Michael Schlegel, Gilead Tadmor, the Collaborative Research Center (Sfb 557) "Control of Complex Turbulent Shear Flows" at TU Berlin and the Laboratoire d'Etudes Aerodynamiques (Poitiers).
BIOGRAPHY:
Prof. Dr.-Ing. habil. Dr. rer.nat. Bernd R. Noack
heads the research group ''Reduced-order modelling
for flow control'' at the Berlin Institute of Technology.
He has 20 years of research and teaching expertise in low-order modelling
for flow analysis and robust control design.
His group focusses on
for feedback flow control solutions associated with transport vehicles
in a close interdisciplinary and international collaboration.
His past affiliations include the Max-Planck-Institut für Strömungsforschung,
the German Aerospace Center, the Georg-August-Universität Göttingen
and the United Technologies Corporation (E. Hartford, CT, USA).
His contributions were honoured by
the 2005 Richard von Mises award of the International Association of
Applied Mathematics and Mechanics (GAMM) and
other prizes from German and US institutions.
| Datum: | 30.06.08 | Zeit: | 16:15 Uhr | Ort: | FU Berlin, Institut für Mathematik II, Arnimallee 6, 14195 Berlin. | Raum: | 032 im Erdgeschoss |