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Protas, B., Noack, B. och Östh, J. (2015) *Optimal nonlinear eddy viscosity in Galerkin models of turbulent flow*.

** BibTeX **

@article{

Protas2015,

author={Protas, Bartosz and Noack, Bernd R. and Östh, Jan},

title={Optimal nonlinear eddy viscosity in Galerkin models of turbulent flow},

journal={Journal of Fluid Mechanics},

issn={0022-1120},

volume={766},

pages={337-367},

abstract={We propose a variational approach to the identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for proper orthogonal decomposition (POD) models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved fluctuation energy. This function is found as a minimizer of a cost functional measuring the difference between the target data coming from a resolved direct or large-eddy simulation of the flow and its reconstruction based on the POD model. The optimization is performed with a data-assimilation approach generalizing the 4D-VAR method. POD models with optimal eddy viscosities are presented for a 2D incompressible mixing layer at Re=500 (based on the initial vorticity thickness and the velocity of the high-speed stream) and a 3D Ahmed body wake at Re=300000 (based on the body height and the free-stream velocity). The variational optimization formulation elucidates a number of interesting physical insights concerning the eddy-viscosity ansatz used. The 20-dimensional model of the mixing-layer reveals a negative eddy-viscosity regime at low fluctuation levels which improves the transient times towards the attractor. The 100-dimensional wake model yields more accurate energy distributions as compared to the nonlinear modal eddy-viscosity benchmark proposed recently by Östh et al. (J. Fluid Mech., vol. 747, 2014, pp. 518–544). Our methodology can be applied to construct quite arbitrary closure relations and, more generally, constitutive relations optimizing statistical properties of a broad class of reduced-order models.},

year={2015},

keywords={low-dimensional models; turbulent flows; variational methods},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 212218

A1 Protas, Bartosz

A1 Noack, Bernd R.

A1 Östh, Jan

T1 Optimal nonlinear eddy viscosity in Galerkin models of turbulent flow

YR 2015

JF Journal of Fluid Mechanics

SN 0022-1120

VO 766

SP 337

OP 367

AB We propose a variational approach to the identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for proper orthogonal decomposition (POD) models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved fluctuation energy. This function is found as a minimizer of a cost functional measuring the difference between the target data coming from a resolved direct or large-eddy simulation of the flow and its reconstruction based on the POD model. The optimization is performed with a data-assimilation approach generalizing the 4D-VAR method. POD models with optimal eddy viscosities are presented for a 2D incompressible mixing layer at Re=500 (based on the initial vorticity thickness and the velocity of the high-speed stream) and a 3D Ahmed body wake at Re=300000 (based on the body height and the free-stream velocity). The variational optimization formulation elucidates a number of interesting physical insights concerning the eddy-viscosity ansatz used. The 20-dimensional model of the mixing-layer reveals a negative eddy-viscosity regime at low fluctuation levels which improves the transient times towards the attractor. The 100-dimensional wake model yields more accurate energy distributions as compared to the nonlinear modal eddy-viscosity benchmark proposed recently by Östh et al. (J. Fluid Mech., vol. 747, 2014, pp. 518–544). Our methodology can be applied to construct quite arbitrary closure relations and, more generally, constitutive relations optimizing statistical properties of a broad class of reduced-order models.

LA eng

DO 10.1017/jfm.2015.14

LK http://dx.doi.org/10.1017/jfm.2015.14

OL 30