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Amplitude and frequency modulation in wall turbulence

  • B. Ganapathisubramani (a1), N. Hutchins (a2), J. P. Monty (a2), D. Chung (a2) and I. Marusic (a2)...

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.

Copyright

Corresponding author

Email address for correspondence: G.Bharath@soton.ac.uk

References

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Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 153.
Bailey, S. C. C., Hultmark, M., Smits, A. & Schultz, M. P. 2008 Azimuthal structure of turbulence in high Reynolds number pipe flow. J. Fluid Mech. 615, 121138.
Bandyopadhyay, P. R. & Hussain, A. K. M. F. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 22212228.
Bernardini, M. & Pirozzoli, S. 2011 Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys. Fluids 23 (6), 061701.
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Time scales and correlations in a turbulent boundary layer. Phys. Fluids 15, 15451554.
Brown, G. R. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20, S243S251.
Chung, D. & McKeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341364.
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Mech. 4, 151.
Del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41L44.
Del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
Dennis, D. J. C. & Nickels, T. B. 2008 On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197206.
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 3546.
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.
Guala, M., Metzger, M. & McKeon, B. J. 2011 Interactions within the turbulent boundary layer at high Reynolds number. J. Fluid Mech. 666, 573604.
Hunt, J. C. R. & Morrison, J. F. 2000 Eddy structure in turbulent boundary layers. Eur. J. Mech (B/Fluids) 19, 673694.
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering structures in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. 365, 647664.
Hutchins, N., Monty, J. P., Ganapathisubramani, B., Ng, H. & Marusic, I. 2011 Three-dimensional conditional structure of a high Reynolds number turbulent boundary layer. J. Fluid Mech. 673, 255285.
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 632, 431442.
Kailashnath, K. & Sreenivasan, K. R. 1993 Zero crossings of velocity fluctuations in turbulent boundary layers. Phys. Fluids 5 (11), 28792885.
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283326.
Ligrani, P. M. & Bradshaw, P. 1987 Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp. Fluids 5, 407417.
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193196.
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311337.
Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537566.
Meinhart, C. D. & Adrian, R. J. 1995 On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7 (4), 694696.
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.
Nagib, H. & Chauhan, K. 2008 Variations of Von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the ${k}^{\ensuremath{-} 1} $ law in high-Reynolds number turbulent boundary layer. Phys. Rev. Lett. 95, 074501.
Nickels, T. B., Marusic, I., Hafez, S., Hutchins, N. & Chong, M. S. 2007 Some predictions of the attached eddy model for a high Reynolds number boundary layer. Phil. Trans. R. Soc. Lond. 265, 807822.
Rao, K. N., Narasimha, R. & Narayanan, M. A. B. 1971 The phenomenon in a turbulent boundary layer. J. Fluid Mech. 48, 339352.
Repetto, M. P. 2005 Cycle counting methods for bi-modal stationary Gaussian processes. Prob. Engng Mech. 20 (3), 229238.
Rychlik, I. 1993 Characterisation of random fatigue loads. In Stochastic Approach to Fatigue (ed. Sobczyk, K), CISM Courses and Lectures , vol. 334. Springer.
Schlatter, P. & Örlü, R. 2010 Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution. Phys. Fluids 22, 051704.
Sreenivasan, K. R. 1985 On the fine-scale intermittency of turbulence. J. Fluid Mech. 151, 81103.
Sreenivasan, K. R., Prabhu, A. & Narasimha, R. 1983 Zero-crossings in turbulent signals. J. Fluid Mech. 137, 251272.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Wark, C. E. & Nagib, H. M. 1991 Experimental investigation of coherent structures in turbulent boundary layers. J. Fluid Mech. 230, 183208.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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