TY - GEN

T1 - Completion of partially known turbulent flow statistics

AU - Zare, Armin

AU - Jovanović, Mihailo R.

AU - Georgiou, Tryphon T.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Convex optimization

KW - flow control

KW - low-rank approximation

KW - stochastically forced Navier-Stokes equations

KW - structured matrix completion problems

KW - turbulence modeling

UR - http://www.scopus.com/inward/record.url?scp=84905714746&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905714746&partnerID=8YFLogxK

U2 - 10.1109/ACC.2014.6859504

DO - 10.1109/ACC.2014.6859504

M3 - Conference contribution

AN - SCOPUS:84905714746

SN - 9781479932726

T3 - Proceedings of the American Control Conference

SP - 1674

EP - 1679

BT - 2014 American Control Conference, ACC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 American Control Conference, ACC 2014

Y2 - 4 June 2014 through 6 June 2014

ER -