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Relation between a singly-periodic roughness geometry and spatio-temporal turbulence characteristics

Morgan, J. and McKeon, B. J. (2018) Relation between a singly-periodic roughness geometry and spatio-temporal turbulence characteristics. International Journal of Heat and Fluid Flow, 71 . pp. 322-333. ISSN 0142-727X.

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The structure of a turbulent boundary layer over a singly-periodic roughness of large wavelength is shown to give insight into the physics of rough-wall boundary layers. To this end, a roughness consisting of a single spanwise-varying mode and a single streamwise-varying mode was 3D printed with wavelengths on the order of the boundary layer thickness. The large length scale introduced by such a roughness creates spatial inhomogeneity of the mean velocity field throughout the entire boundary layer. A hot-wire probe was used to take time series of streamwise velocity at a grid of points in the x,y, and z directions, covering the volume over a single period of roughness, and allowing Fourier transforms of field variables to isolate the spatial variations correlating to the periodic geometry. The pre-multiplied Taylor-transformed wavelength power spectrum of streamwise velocity λTΦ(y, λT, x, z) can be Fourier-transformed in space to reveal that the portion of the power spectrum which varies most strongly in the streamwise direction is the portion with Taylor-transformed wavelength λT equal to the roughness wavelength λx. The spatial variation of the power spectrum at this wavelength exhibits a systematic change in phase across the boundary layer, which can be correlated to the phase of the spatially-varying time-averaged velocity field to reveal amplitude modulation of particular wavelengths by a roughness-induced synthetic scale. In a canonical smooth-wall boundary layer, the spatial variation of the mean velocity and the power spectrum would be identically zero due to translational symmetry. The introduction of a periodic roughness introduces the spatial variation in the power spectrum, but not directly. The roughness creates a stationary time-averaged velocity mode, but this mode does not appear in the power spectrum as it does not convect. The connection to the power spectrum must therefore be through non-linear interactions. It is shown that the correlation between the mean velocity and the power spectrum can be interpreted exactly as a measure of phase organization between pairs of convecting velocity modes which are triadically consistent with the stationary roughness velocity mode, analogously to amplitude modulation in canonical flows. Implications for real-world roughness are discussed.

Item Type:Article
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McKeon, B. J.0000-0003-4220-1583
Additional Information:© 2018 Elsevier Inc. Received 22 November 2017, Revised 17 February 2018, Accepted 9 April 2018, Available online 5 May 2018.
Subject Keywords:Turbulent boundary layer; Amplitude modulation; Rough wall; Periodic roughness
Record Number:CaltechAUTHORS:20180507-091749221
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Official Citation:J. Morgan, B.J. McKeon, Relation between a singly-periodic roughness geometry and spatio-temporal turbulence characteristics, International Journal of Heat and Fluid Flow, Volume 71, June 2018, Pages 322-333, ISSN 0142-727X, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86238
Deposited By: Tony Diaz
Deposited On:07 May 2018 17:08
Last Modified:03 Oct 2019 19:41

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