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The K-type and H-type transitions of natural convection boundary layers

Published online by Cambridge University Press:  05 July 2017

Yongling Zhao Open the ORCID record for Yongling Zhao [Opens in a new window] ,
Chengwang Lei  and
John C. Patterson
Yongling Zhao*
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Chengwang Lei
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
John C. Patterson
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
*
†Email address for correspondence: yongling.zhao@sydney.edu.au
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Abstract

The K-type and H-type transitions of a natural convection boundary layer of a fluid of Prandtl number 7 adjacent to an isothermally heated vertical surface are investigated by means of three-dimensional direct numerical simulation (DNS). These two types of transitions refer to different flow features at the transitional stage from laminar to turbulence caused by two different types of perturbations. To excite the K-type transition, superimposed Tollmien–Schlichting (TS) and oblique waves of the same frequency are introduced into the boundary layer. It is found that a three-layer longitudinal vortex structure is present in the boundary layer undergoing the K-type transition. The typical aligned $\wedge$-shaped vortices characterizing the K-type transition are observed for the first time in pure natural convection boundary layers. For exciting the H-type transition, superimposed TS and oblique waves of different frequencies, with the frequency of the oblique waves being half of the frequency of the TS waves, are introduced into the boundary layer. Unlike the three-layer longitudinal vortex structure observed in the K-type transition, a double-layer longitudinal vortex structure is observed in the boundary layer undergoing the H-type transition. The successively staggered $\wedge$-shaped vortices characterizing the H-type transition are also observed in the downstream boundary layer. The staggered pattern of $\wedge$-shaped vortices is considered to be caused by temporal modulation of the TS and oblique waves. Interestingly the flow structures of both the K-type and H-type transitions observed in the natural convection boundary layer are qualitatively similar to those observed in Blasius boundary layers. However, an analysis of turbulence energy production suggests that the turbulence energy production by buoyancy rather than Reynolds stresses dominates the K-type and H-type transitions. In contrast, the turbulence energy production by Reynolds stresses is the only factor contributing to the transition in Blasius boundary layers.

JFM classification

Boundary Layers: Boundary layer structure Convection: Buoyancy-driven instability Convection: Buoyant boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 352 - 387
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Copyright
© 2017 Cambridge University Press 

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