Journal
JOURNAL OF FLUID MECHANICS
Volume 812, Issue -, Pages 636-680Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2016.682
Keywords
control theory; turbulence modelling; turbulent flows
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Funding
- National Science Foundation [CMMI 1363266]
- Air Force Office of Scientific Research [FA9550-16-1-0009]
- University of Minnesota Informatics Institute Transdisciplinary Faculty Fellowship
- University of Minnesota Doctoral Dissertation Fellowship
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1739243] Funding Source: National Science Foundation
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In this paper, We address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of velocity correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for coloured-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that coloured-in-time excitation of the Navicr Stokes equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics Our method provides a data-driven refinement of models that originate from first principles and captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization and control design.
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