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The effect of stable thermal stratification on turbulent boundary layer statistics

Published online by Cambridge University Press:  11 January 2017

Owen Williams Open the ORCID record for Owen Williams [Opens in a new window] ,
Tristen Hohman ,
Tyler Van Buren ,
Elie Bou-Zeid  and
Alexander J. Smits
Owen Williams*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, WA 98195, USA
Tristen Hohman
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Tyler Van Buren
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Elie Bou-Zeid
Affiliation:
Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA
Alexander J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

The effects of stable thermal stratification on turbulent boundary layers are experimentally investigated for smooth and rough walls. For weak to moderate stability, the turbulent stresses are seen to scale with the wall shear stress, compensating for changes in fluid density in the same manner as done for compressible flows. This suggests little change in turbulent structure within this regime. At higher levels of stratification turbulence no longer scales with the wall shear stress and turbulent production by mean shear collapses, but without the preferential damping of near-wall motions observed in previous studies. We suggest that the weakly stable and strongly stable (collapsed) regimes are delineated by the point where the turbulence no longer scales with the local wall shear stress, a significant departure from previous definitions. The critical stratification separating these two regimes closely follows the linear stability analysis of Schlichting (Z. Angew. Math. Mech., vol. 15 (6), 1935, pp. 313–338) for both smooth and rough surfaces, indicating that a good predictor of critical stratification is the gradient Richardson number evaluated at the wall. Wall-normal and shear stresses follow atmospheric trends in the local gradient Richardson number scaling of Sorbjan (Q. J. R. Meteorol. Soc., vol. 136, 2010, pp. 1243–1254), suggesting that much can be learned about stratified atmospheric flows from the study of laboratory scale boundary layers at relatively low Reynolds numbers.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 1039 - 1075
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© 2017 Cambridge University Press 

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