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Resolvent-based estimation of space–time flow statistics

Published online by Cambridge University Press:  25 November 2019

Aaron Towne Open the ORCID record for Aaron Towne [Opens in a new window] ,
Adrián Lozano-Durán Open the ORCID record for Adrián Lozano-Durán [Opens in a new window]  and
Xiang Yang Open the ORCID record for Xiang Yang [Opens in a new window]
Aaron Towne*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI48109, USA
Adrián Lozano-Durán
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
Xiang Yang
Affiliation:
Department of Mechanical and Nuclear Engineering, Penn State University, State College, PA16802, USA
*
†Email address for correspondence: towne@umich.edu
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Abstract

We develop a method to estimate space–time flow statistics from a limited set of known data. While previous work has focused on modelling spatial or temporal statistics independently, space–time statistics carry fundamental information about the physics and coherent motions of the flow and provide a starting point for low-order modelling and flow control efforts. The method is derived using a statistical interpretation of resolvent analysis. The central idea of our approach is to use known data to infer the statistics of the nonlinear terms that constitute a forcing on the linearized Navier–Stokes equations, which in turn imply values for the remaining unknown flow statistics through application of the resolvent operator. Rather than making an a priori assumption that the flow is dominated by the leading singular mode of the resolvent operator, as in some previous approaches, our method allows the known input data to select the most relevant portions of the resolvent operator for describing the data, making it well suited for high-rank turbulent flows. We demonstrate the predictive capabilities of the method, which we call resolvent-based estimation, using two examples: the Ginzburg–Landau equation, which serves as a convenient model for a convectively unstable flow, and a turbulent channel flow at low Reynolds number.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A17
Copyright
© 2019 Cambridge University Press

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