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A fractional PDE model for turbulent velocity fields near solid walls

Published online by Cambridge University Press:  12 April 2021

Brendan Keith Open the ORCID record for Brendan Keith [Opens in a new window] ,
Ustim Khristenko Open the ORCID record for Ustim Khristenko [Opens in a new window]  and
Barbara Wohlmuth Open the ORCID record for Barbara Wohlmuth [Opens in a new window]
Brendan Keith*
Affiliation:
Chair for Numerical Mathematics, Technical University of Munich, Garching85748, Germany
Ustim Khristenko
Affiliation:
Chair for Numerical Mathematics, Technical University of Munich, Garching85748, Germany
Barbara Wohlmuth
Affiliation:
Chair for Numerical Mathematics, Technical University of Munich, Garching85748, Germany
*
†Email address for correspondence: keith@ma.tum.de
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Abstract

This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of solutions is Gaussian. Interaction of the turbulence with solid walls is incorporated through the enforcement of various boundary conditions. The various boundary conditions deliver extensive flexibility in the near-wall statistics that can be modelled. Reproduction of both fully developed shear-free and uniform shear boundary layer turbulence are highlighted as two simple physical applications; the first of which is also directly validated with experimental data. The rendering of inhomogeneous synthetic turbulence inlet boundary conditions is an additional application, motivated by contemporary numerical wind tunnel simulations. Calibration of model parameters and efficient numerical methods are also conferred upon.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulence simulation Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A21
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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