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Scale interactions in a mixing layer – the role of the large-scale gradients

Published online by Cambridge University Press:  15 February 2016

D. Fiscaletti ,
A. Attili ,
F. Bisetti  and
G. E. Elsinga
D. Fiscaletti*
Affiliation:
Laboratory for Aero and Hydrodynamics, Department of Mechanical, Maritime, and Materials Engineering, Delft University of Technology, Leeghwaterstraat 21, 2628 CA, Delft, The Netherlands
A. Attili
Affiliation:
Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
F. Bisetti
Affiliation:
Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
G. E. Elsinga
Affiliation:
Laboratory for Aero and Hydrodynamics, Department of Mechanical, Maritime, and Materials Engineering, Delft University of Technology, Leeghwaterstraat 21, 2628 CA, Delft, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The interaction between the large and the small scales of turbulence is investigated in a mixing layer, at a Reynolds number based on the Taylor microscale ($Re_{{\it\lambda}}$) of $250$, via direct numerical simulations. The analysis is performed in physical space, and the local vorticity root-mean-square (r.m.s.) is taken as a measure of the small-scale activity. It is found that positive large-scale velocity fluctuations correspond to large vorticity r.m.s. on the low-speed side of the mixing layer, whereas, they correspond to low vorticity r.m.s. on the high-speed side. The relationship between large and small scales thus depends on position if the vorticity r.m.s. is correlated with the large-scale velocity fluctuations. On the contrary, the correlation coefficient is nearly constant throughout the mixing layer and close to unity if the vorticity r.m.s. is correlated with the large-scale velocity gradients. Therefore, the small-scale activity appears closely related to large-scale gradients, while the correlation between the small-scale activity and the large-scale velocity fluctuations is shown to reflect a property of the large scales. Furthermore, the vorticity from unfiltered (small scales) and from low pass filtered (large scales) velocity fields tend to be aligned when examined within vortical tubes. These results provide evidence for the so-called ‘scale invariance’ (Meneveau & Katz, Annu. Rev. Fluid Mech., vol. 32, 2000, pp. 1–32), and suggest that some of the large-scale characteristics are not lost at the small scales, at least at the Reynolds number achieved in the present simulation.

JFM classification

Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , pp. 154 - 173
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Copyright
© 2016 Cambridge University Press 

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