TY - JOUR

T1 - The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers

AU - Araya, Guillermo

AU - Castillo, Luciano

AU - Hussain, Fazle

N1 - Publisher Copyright:
© 2015 Cambridge University Press.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015/6/19

Y1 - 2015/6/19

N2 - Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, u′ v′+, monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. -u′ v′+ = -(1/Auv) ln y+ + Buv) in the mesolayer region (e.g. 50 ≤ y+ ≤ 170). The thickness of the log layer of u′ v′+ 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+ ∂ U+/∂y+ ∼ 1/y+ ∼ ∂u′ v′+/∂y+, resulting in a logarithmic u′ v′+ profile. Also, V+ ∼ -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 u′ v′+. This log region in u′ v′+ 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 u′ v′+, which is non-existent in sink flows.

AB - Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress, u′ v′+, monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. -u′ v′+ = -(1/Auv) ln y+ + Buv) in the mesolayer region (e.g. 50 ≤ y+ ≤ 170). The thickness of the log layer of u′ v′+ 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+ ∂ U+/∂y+ ∼ 1/y+ ∼ ∂u′ v′+/∂y+, resulting in a logarithmic u′ v′+ profile. Also, V+ ∼ -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 u′ v′+. This log region in u′ v′+ 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 u′ v′+, which is non-existent in sink flows.

KW - turbulence simulation

KW - turbulent boundary layers

KW - turbulent flows

UR - http://www.scopus.com/inward/record.url?scp=84934905914&partnerID=8YFLogxK

U2 - 10.1017/jfm.2015.296

DO - 10.1017/jfm.2015.296

M3 - Article

AN - SCOPUS:84934905914

VL - 775

SP - 189

EP - 200

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -