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arXiv:1507.06951 [physics.flu-dyn]AbstractReferencesReviewsResources

A Cautionary Note on the Zagarola and Smits Similarity Parameter for the Turbulent Boundary Layer

David Weyburne

Published 2015-07-23Version 1

Zagarola and Smits developed an empirical velocity parameter for scaling the outer region of the turbulent boundary layer velocity profile that has been widely applied and has resulted in similarity in many of those datasets. In all the cases studied thus far claims for similarity involving the Zagarola and Smits scaling parameter have been based on examining plots of the defect profile. In the work herein it is shown that the common practice of finding similarity behavior using the defect profile has often been incomplete in the sense that not all of the criteria for similarity have been checked for compliance. When full compliance is checked it is found that some datasets displaying defect similarity do not satisfy all the criteria for similarity. The nature of this contradiction and noncompliance is described in detail. It is shown that the original datasets used by Zagarola and Smits display this flawed similarity behavior. Hence, a careful reassessment of any claims in the literature is required for those groups that attempted to use the defect profile and the Zagarola and Smits type of velocity scaling parameter to assert similarity of the velocity profile.

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