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Interactions between scales in wall turbulence: Phase relationships, amplitude modulation and the importance of critical layers

Jacobi, I and Chung, D and Duvvuri, S and McKeon, BJ (2021) Interactions between scales in wall turbulence: Phase relationships, amplitude modulation and the importance of critical layers. In: Journal of Fluid Mechanics .

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Official URL: https://doi.org/10.1017/jfm.2020.770


We present a framework for predicting the interactions between motion at a single scale and the underlying stress fluctuations in wall turbulence, derived from approximations to the Navier-Stokes equations. The dynamical equations for an isolated scale and stress fluctuations at the same scale are obtained from a decomposition of the governing equations and formulated in terms of a transfer function between them. This transfer function is closely related to the direct correlation coefficient of Duvvuri & McKeon (J. Fluid Mech., vol. 767, 2015, R4), and approximately to the amplitude modulation coefficient described in Mathis et al. (J. Fluid Mech., vol. 628, 2009, pp. 311-337), by consideration of interactions between triadically consistent scales. In light of the agreement between analysis and observations, the modelling approach is extended to make predictions concerning the relationship between very-large motions and small-scale stress in the logarithmic region of the mean velocity. Consistent with experiments, the model predicts that the zero-crossing height of the amplitude modulation statistic coincides with the wall-normal location of the very large-scale peak in the one-dimensional premultiplied spectrum of streamwise velocity fluctuations, the critical layer location for the very large-scale motion. Implications of fixed phase relationships between small-scale stresses and larger isolated scales for closure schemes are briefly discussed. © The Author(s), 2021. Published by Cambridge University Press.

Item Type: Journal Article
Publication: Journal of Fluid Mechanics
Publisher: Cambridge University Press
Additional Information: The copyright for this article belongs to Cambridge University Press
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 23 Mar 2021 10:14
Last Modified: 23 Mar 2021 10:14
URI: http://eprints.iisc.ac.in/id/eprint/68548

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