Colour of turbulence
By Armin Zare, M. Jovanovi'c, Tryphon T. Georgiou. Journal of Fluid Mechanics, 2016
151 citations recorded by the source corpus.
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 Navier–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.
Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/9b2df62639fd9a1b3a03345d45927236d53c8261
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In Computational Mechanics
- Oliver T. Schmidt
- Aaron Towne
- Tim Colonius
- G. Brès
- Georgios Rigas
- Javier Jiménez
- Sergio Pirozzoli
- P. Jordan
In Statistical and Nonlinear Physics
In Statistics and Probability
Citations in the corpus
- Coherent structures in wall-bounded turbulence (2017, background): “A partial answer is due to Zare et al. (2017), who look at the theoretical question of which are the requirements on the forcing noise to reproduce the second-order statistics of the flow.”
- Spectral analysis of jet turbulence (2017, methodology): “t is conceptually intuitive{when there is no bias in the forcing, the modes with highest gain are also the most energetic. The nonlinear forcing terms in real turbulent ows are, of course, not white. Zare et al. (2017) showed that it is necessary to account for correlated forcing in order to reconst”