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 .
http://resolver.caltech.edu/CaltechAUTHORS:20180507-091749221

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## Abstract

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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Additional Information: | © 2018 Elsevier Inc. Received 22 November 2017, Revised 17 February 2018, Accepted 9 April 2018, Available online 5 May 2018. | ||||||

Group: | GALCIT | ||||||

Subject Keywords: | Turbulent boundary layer; Amplitude modulation; Rough wall; Periodic roughness | ||||||

Record Number: | CaltechAUTHORS:20180507-091749221 | ||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20180507-091749221 | ||||||

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, https://doi.org/10.1016/j.ijheatfluidflow.2018.04.005. (https://www.sciencedirect.com/science/article/pii/S0142727X17311086) | ||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||

ID Code: | 86238 | ||||||

Collection: | CaltechAUTHORS | ||||||

Deposited By: | Tony Diaz | ||||||

Deposited On: | 07 May 2018 17:08 | ||||||

Last Modified: | 07 May 2018 17:08 |

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