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A foundation for analytical developments in the logarithmic region of turbulent channels

Moarref, Rashad and Sharma, Ati S. and Tropp, Joel A. and McKeon, Beverley J. (2014) A foundation for analytical developments in the logarithmic region of turbulent channels. . (Unpublished)

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An analytical framework for studying the logarithmic region of turbulent channels is formulated. We build on recent findings (Moarref et al., J. Fluid Mech., 734, 2013) that the velocity fluctuations in the logarithmic region can be decomposed into a weighted sum of geometrically self-similar resolvent modes. The resolvent modes and the weights represent the linear amplification mechanisms and the scaling influence of the nonlinear interactions in the Navier-Stokes equations (NSE), respectively (McKeon & Sharma, J. Fluid Mech., 658, 2010). Originating from the NSE, this framework provides an analytical support for Townsend’s attached-eddy model. Our main result is that self-similarity enables order reduction in modeling the logarithmic region by establishing a quantitative link between the self-similar structures and the velocity spectra. Specifically, the energy intensities, the Reynolds stresses, and the energy budget are expressed in terms of the resolvent modes with speeds corresponding to the top of the logarithmic region. The weights of the triad modes -the modes that directly interact via the quadratic nonlinearity in the NSE- are coupled via the interaction coefficients that depend solely on the resolvent modes (McKeon et al., Phys. Fluids, 25, 2013). We use the hierarchies of self-similar modes in the logarithmic region to extend the notion of triad modes to triad hierarchies. It is shown that the interaction coefficients for the triad modes that belong to a triad hierarchy follow an exponential function. The combination of these findings can be used to better understand the dynamics and interaction of flow structures in the logarithmic region. The compatibility of the proposed model with theoretical and experimental results is further discussed.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Sharma, Ati S.0000-0002-7170-1627
Tropp, Joel A.0000-0003-1024-1791
McKeon, Beverley J. 0000-0003-4220-1583
Additional Information:The support of Air Force Office of Scientific Research under grants FA 9550-09-1-0701 (P.M. Rengasamy Ponnappan) and FA 9550-12-1-0469 (P.M. Doug Smith) is gratefully acknowledged.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA 9550-09-1-0701
Air Force Office of Scientific Research (AFOSR)FA 9550-12-1-0469
Record Number:CaltechAUTHORS:20180831-112157832
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89344
Deposited By: George Porter
Deposited On:04 Sep 2018 14:42
Last Modified:03 Oct 2019 20:15

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