Fake turbulence

Abstract: Turbulence is a high-dimensional dynamical system with known equations of motion. It can be numerically integrated, but the simulation results are also high-dimensional and hard to interpret. Lower-dimensional models are not dynamical systems, because some dynamics is discarded in the projection, and a stochastic Perron-Frobenius operator substitutes the equations of motion. Using as example turbulent flows at moderate but non-trivial Reynolds number, we show that particularly deterministic projections can be identified by either Monte-Carlo or exhaustive testing, and can be interpreted as coherent structures. We also show that they can be used to construct data-driven ‘fake’ models that retain many of the statistical characteristics of the real flow.

Bio: Aeronautical Engineer (1969) by the School of Aeronautical Engineering at Madrid. Master in
Aeronautics (1970) and Ph.D. in Applied Mathematics (1973) by the California Institute of
Technology, Pasadena, Ca.
Currently Emeritus research professor of Fluid Mechanics at the School of Aeronautics of the Universidad Politécnica de Madrid. He has been professor of Mechanics at the Ecole Polytechnique, Palaiseau, France and senior research fellow and visiting professor at the Centre for Turbulence Research, Stanford University and NASA Ames Res. Centre, Ca. USA. Research scientist at the IBM Madrid Scientific Centre (1975-1990).
His research interests include: the physics of turbulence and hydrodynamic transition, numerical simulation and data-driven analysis of turbulence and combustion, vortex dynamics, computer graphics for the analysis of experimental results, flow at low Reynolds numbers, numerical simulation of transonic flows, turbulent mixing, digital image processing and its applications, and theory of nonlinear waves and resonance.
He has been principal investigator of numerous research contracts, both institutional and industrial, including three consecutive Advanced Grants of the European Research Council. He has coauthored over a hundred publications in international refereed journals, 10 books, 85 book chapters and invited conferences, 13 invited courses, 21 technical reports and numerous other publications, resulting in about 25000 citations. He has directed 19 doctoral theses.
He is member of the Spanish Royal Academy of Sciences and of the Spanish Royal Academy of Engineering. Elected fellow of the American Physical Society, of the Institute of Physics of London and of the European Mechanics Society (Euromech). He received the research prize of the Spanish Royal Academy of Sciences in 1998, and the Fluid Mechanics prize of Euromech in 2018.