Revised Prandtl mixing length model applied to the two-dimensional turbulent classical wake

Previous applications of Prandtl׳s mixing length model to turbulent wake flows, which neglect the kinematic viscosity of the fluid, have underestimated the width of the boundary layer. In this paper, we present a revised Prandtl mixing length model by including the kinematic viscosity of the fluid....

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Bibliographic Details
Published in:International journal of non-linear mechanics 2015-12, Vol.77, p.162-171
Main Authors: Hutchinson, A.J., Mason, D.P.
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Conservation law
Eddy viscosity
Fluid flow
Fluids
Kinematics
Mathematical models
Prandtl׳s mixing length
Turbulence
Turbulent classical wake
Turbulent flow
Wakes
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Summary:Previous applications of Prandtl׳s mixing length model to turbulent wake flows, which neglect the kinematic viscosity of the fluid, have underestimated the width of the boundary layer. In this paper, we present a revised Prandtl mixing length model by including the kinematic viscosity of the fluid. We show that this model predicts a boundary that lies outside the one predicted by Prandtl. We also prove that the results for the two models converge for very large Reynolds number wake flows. •The turbulent classical described by Prandtl׳s mixing length model is studied.•A revised Prandtl mixing length model is introduced.•Lie symmetry methods are used to generate the invariant solution.•The revised model is shown to be more accurate in predicting the width of the wake.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2015.08.006