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Supersonic turbulent boundary layer on a plate. Universal velocity and temperature defect laws and skin-friction law at moderate free-stream Mach numbers

Published online by Cambridge University Press:  01 October 2025

Igor Vigdorovich Open the ORCID record for Igor Vigdorovich [Opens in a new window]
Igor Vigdorovich*
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Michurinsky ave 1, 119192 Moscow, Russia
*
Corresponding author: Igor Vigdorovich, vigdorovich.igor@gmail.com
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Abstract

We develop an asymptotic theory of a compressible turbulent boundary layer on a flat plate, in which the mean velocity and temperature profiles can be obtained as exact asymptotic solutions of the boundary-layer equations, which are closed using functional relations of a general form connecting the turbulent shear stress and turbulent enthalpy flux to the mean velocity and enthalpy gradients. The outer region of the boundary layer is considered at moderate supersonic free-stream Mach numbers, when the relative temperature difference across the layer is of order one. A special change of variables allows us to construct the solution in the outer region in the form of asymptotic expansions at large values of the logarithm of the Reynolds number based on the boundary-layer thickness. As a result of asymptotic matching of the solutions for the outer region and logarithmic sublayer, the velocity and temperature defect laws are obtained, which allow us to describe the profiles of these quantities in the outer and logarithmic regions by universal curves known for the boundary layer of an incompressible fluid. Similarity rules for the Reynolds-tensor components and root-mean-square enthalpy fluctuation are given. The recovery and Reynolds-analogy factors are calculated. A friction law is established that is valid under arbitrary wall-heat-transfer conditions.

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulent boundary layers

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JFM Papers
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Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A17
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© The Author(s), 2025. Published by Cambridge University Press

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