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The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers

Published online by Cambridge University Press:  19 June 2015

Guillermo Araya ,
Luciano Castillo  and
Fazle Hussain
Guillermo Araya*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Luciano Castillo
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Fazle Hussain
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
*
†Email address for correspondence: araya@mailaps.org
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Abstract

Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, $\overline{u^{\prime }v^{\prime }}^{+}$ , monotonically decreases downstream and exhibits a logarithmic behaviour (e.g.  $-\overline{u^{\prime }v^{\prime }}^{+}=-(1/A_{uv})\ln y^{+}+B_{uv}$ ) in the mesolayer region (e.g.  $50\leqslant y^{+}\leqslant 170$ ). The thickness of the log layer of $\overline{u^{\prime }v^{\prime }}^{+}$ increases with the streamwise distance and with the pressure gradient strength, extending over a large portion of the TBL thickness (up to 55 %). Simulations reveal that $V^{+}\,\partial U^{+}/\partial y^{+}\sim 1/y^{+}\sim \partial \overline{u^{\prime }v^{\prime }}^{+}/\partial y^{+}$ , resulting in a logarithmic $\overline{u^{\prime }v^{\prime }}^{+}$ profile. Also, $V^{+}\sim -y^{+}$ is no longer negligible as in zero-pressure-gradient (ZPG) flows. Other experimental/numerical data at similar favourable-pressure-gradient (FPG) strengths also show the presence of a log region in $\overline{u^{\prime }v^{\prime }}^{+}$ . This log region in $\overline{u^{\prime }v^{\prime }}^{+}$ is larger in sink flows than in other spatially developing FPG flows. The latter flows exhibit the presence of a small power-law region in $\overline{u^{\prime }v^{\prime }}^{+}$ , which is non-existent in sink flows.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulence simulation

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Papers
Information
Journal of Fluid Mechanics , Volume 775 , 25 July 2015 , pp. 189 - 200
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© 2015 Cambridge University Press 

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