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Role of coherent structures in multiple self-similar states of turbulent planar wakes

Published online by Cambridge University Press:  22 August 2013

Jean-Pierre Hickey ,
Fazle Hussain  and
Xiaohua Wu
Jean-Pierre Hickey*
Affiliation:
Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario K7K 7B4, Canada
Fazle Hussain
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Xiaohua Wu
Affiliation:
Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario K7K 7B4, Canada
*
†Present address: Center for Turbulence Research, Stanford University, CA 94305, USA. Email address for correspondence: jphickey@stanford.edu
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Abstract

We study the nature of archetypal, incompressible, planar splitter-plate wakes, specifically the effects of the exit boundary layer state on multiple approximate self-similarity. Temporally developing direct numerical simulations, at a Reynolds number of 1500 based on the volume-flux defect, are performed to investigate three distinct wake evolution scenarios: Kelvin–Helmholtz transition, bypass transition in an asymmetric wake, and an initially fully turbulent wake. The differences in the evolution and far-wake statistics are analysed in detail. The individual approximately self-similar states exhibit a relative variation of up to 48 % in the spread rate, in second-order statistics, and in peak values of the energy budget terms. The multiplicity of self-similar states is tied to the non-universality of the large-scale coherent structures. These structures maintain the memory of the initial conditions. In the far wake, two distinct spanwise-coherent motions are identified: (i) staggered, segregated spanwise rollers on either side of the centreplane, dominant in wakes transitioning via anti-symmetric instability modes; and, (ii) larger spanwise rollers spanning across the centreplane, emerging in the absence of a near-wake characteristic length scale. The latter structure is characterized by strong spanwise coherence, cross-wake velocity correlations and a larger entrainment rate caused by deep pockets of irrotational fluid within the folds of the turbulent/non-turbulent interface. The mid-sized structures, primarily vortical rods, are generic for all initial conditions and are inclined at ∼$\pm 3{3}^{\circ } $ to the downstream, shallower than the preferential $\pm 4{5}^{\circ } $ inclination of the vorticity vector. The spread rate is driven by the inner-wake dynamics, more specifically the advective flux of spanwise vorticity across the centreplane, which depends on the large-scale coherent structures.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , pp. 312 - 363
Copyright
©2013 Cambridge University Press 

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