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Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

Published online by Cambridge University Press:  01 June 2009

ROMAIN MATHIS ,
NICHOLAS HUTCHINS  and
IVAN MARUSIC
ROMAIN MATHIS
Affiliation:
Walter Bassett Aerodynamics Laboratory, Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
NICHOLAS HUTCHINS
Affiliation:
Walter Bassett Aerodynamics Laboratory, Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
IVAN MARUSIC*
Affiliation:
Walter Bassett Aerodynamics Laboratory, Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: [email protected]
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Abstract

In this paper we investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 628 , 10 June 2009 , pp. 311 - 337
Copyright
Copyright © Cambridge University Press 2009

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