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The persistence of logarithmic solutions in turbulent boundary layer systems

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Abstract

The present work studies the prevalence of logarithmic solutions in the near wall region of turbulent boundary layers. Local solutions for flows subject to such diverse effects as compressibility, wall transpiration, heat transfer, roughness, separation, shock waves, unsteadiness, non-Newtonian fluids or a combination of these factors are discussed. The work also analyzes eleven different propositions by several authors for the near wall description of the mean velocity profile for the incompressible zero-pressure-gradient turbulent boundary layer. The asymptotic structure of the flow is discussed from the point of view of double limit processes. Cases of interest include attached and separated flows for the velocity and temperature fields.

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Acknowledgments

Many people have contributed to the results discussed in the present work. Their relative importance is easily recognized through a casual inspection of the list of references. To these people—most of them my former students—I owe my gratitude. Specifically, most of the figures shown in this review have been prepared by Dr. J.B.R. Loureiro. Thank you for this particular effort. APSF is grateful to the Brazilian National Research Council (CNPq) for the award of a Research Fellowship (Grant No. 305338/2014-5). The work was financially supported by CNPq through Grants No. 477293/2011-5 and by the Rio de Janeiro Research Foundation (FAPERJ) through Grant E-26/102.937/2011.

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  1. Programa de Engenharia Mecanica (COPPE/UFRJ), Universidade Federal do Rio de Janeiro, C.P. 68503, Rio de Janeiro, 21945-970, Brazil

    Atila P. Silva Freire

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Correspondence to Atila P. Silva Freire.

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Technical Editor: Francisco Ricardo Cunha.

The work is dedicated to Dr. Sergio Luis Villares Coelho, who would have had a brilliant professional carrier, had not departed the planet Earth in October 1989 at the very early age of 32 after a long struggle against cancer. The longer the elapsed time, the more his absence is felt.

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Silva Freire, A.P. The persistence of logarithmic solutions in turbulent boundary layer systems. J Braz. Soc. Mech. Sci. Eng. 38, 1359–1399 (2016). https://doi.org/10.1007/s40430-015-0433-2

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