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Amplitude and frequency modulation in wall turbulence

Published online by Cambridge University Press:  27 September 2012

B. Ganapathisubramani ,
N. Hutchins ,
J. P. Monty ,
D. Chung  and
I. Marusic
B. Ganapathisubramani*
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University of Southampton, Southampton SO17 1BJ, UK
N. Hutchins
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, VIC 3010, Australia
J. P. Monty
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, VIC 3010, Australia
D. Chung
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, VIC 3010, Australia
I. Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, VIC 3010, Australia
*
†Email address for correspondence: [email protected]
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Abstract

In this study we examine the impact of the strength of the large-scale motions on the amplitude and frequency of the small scales in high-Reynolds-number turbulent boundary layers. Time series of hot-wire data are decomposed into large- and small-scale components, and the impact of the large scale on the amplitude and frequency of the small scales is considered. The amplitude modulation effect is examined by conditionally averaging the small-scale intensity (${ u}_{S}^{2} $) for various values of the large-scale fluctuation (${u}_{L} $). It is shown that ${ u}_{S}^{2} $ increases with increasing value of ${u}_{L} $ in the near-wall region, whereas, farther away from the wall, ${ u}_{S}^{2} $ decreases with increasing ${u}_{L} $. The rate of increase in small-scale intensity with the strength of the large-scale signal is neither symmetric (about ${u}_{L} = 0$) nor linear. The extent of the frequency modulation is examined by counting the number of occurrences of local maxima or minima in the small-scale signal. It is shown that the frequency modulation effect is confined to the near-wall region and its extent diminishes rapidly beyond ${y}^{+ } = 100$. A phase lag between the large- and small-scale fluctuations, in terms of amplitude modulation, has also been identified, which is in agreement with previous studies. The phase lag between large- and small-scale fluctuations for frequency modulation is comparable to that of amplitude modulation in the near-wall region. The combined effect of both amplitude and frequency modulation is also examined by computing conditional spectra of the small-scale signal conditioned on the large scales. In the near-wall region, the results indicate that the peak value of pre-multiplied spectra increases with increasing value of ${u}_{L} $, indicating amplitude modulation, while the frequency at which this peak occurs also increases with increasing value of ${u}_{L} $, revealing frequency modulation. The overall trends observed from the conditional spectra are consistent with the results obtained through statistical analyses. Finally, a physical mechanism that can capture most of the above observations is also presented.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 61 - 91
Copyright
©2012 Cambridge University Press

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