Completion of partially known turbulent flow statistics

Armin Zare, Mihailo R. Jovanović, Tryphon T. Georgiou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


Second-order statistics of turbulent flows can be obtained either experimentally or via high fidelity numerical simulations. The statistics are relevant in understanding fundamental flow physics and for the development of low-complexity models. For example, such models can be used for control design in order to suppress or promote turbulence. Due to experimental or numerical limitations it is often the case that only partial flow statistics are known. In other words, only certain correlations between a limited number of flow field components are available. Thus, it is of interest to complete the statistical signature of the flow field in a way that is consistent with the known dynamics. Our approach to this inverse problem relies on a model governed by stochastically forced linearized Navier-Stokes equations. In this, the statistics of forcing are unknown and sought to explain the given correlations. Identifying suitable stochastic forcing allows us to complete the correlation data of the velocity field. While the system dynamics impose a linear constraint on the admissible correlations, such an inverse problem admits many solutions for the forcing correlations. We use nuclear norm minimization to obtain correlation structures of low complexity. This complexity translates into dimensionality of spatio-temporal filters that can be used to generate the identified forcing statistics.

Original languageEnglish (US)
Title of host publication2014 American Control Conference, ACC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781479932726
StatePublished - Jan 1 2014
Event2014 American Control Conference, ACC 2014 - Portland, OR, United States
Duration: Jun 4 2014Jun 6 2014

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2014 American Control Conference, ACC 2014
Country/TerritoryUnited States
CityPortland, OR


  • Convex optimization
  • flow control
  • low-rank approximation
  • stochastically forced Navier-Stokes equations
  • structured matrix completion problems
  • turbulence modeling


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