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On the shape of resolvent modes in wall-bounded turbulence

Dawson, Scott T. M. and McKeon, Beverley J. (2019) On the shape of resolvent modes in wall-bounded turbulence. . (Unpublished)

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The resolvent formulation of the Navier--Stokes equations gives a means for the characterization and prediction of features of turbulent flows---such as statistics, structures and their nonlinear interactions---using the singular value decomposition of the resolvent operator based on the appropriate turbulent mean, following the framework developed by McKeon & Sharma (2010). This work will describe a methodology for approximating leading resolvent (i.e., pseudospectral) modes for shear-driven turbulent flows using prescribed analytic functions. We will demonstrate that these functions, which arise from the consideration of wavepacket pseudoeigenmodes of simplified linear operators (Trefethen 2005), in particular give an accurate approximation of the class of nominally wall-detached modes that are centered about the critical layer. Focusing in particular on modeling wall-normal vorticity modes, we present a series of simplifications to the governing equations that result in scalar differential operators that are amenable to such analysis. We demonstrate that the leading wall-normal vorticity response mode for the full Navier--Stokes equations may be accurately approximated by considering a second order scalar operator, equipped with a non-standard inner product. The variation in mode shape as a function of wavenumber and Reynolds number may be captured by evolving a low dimensional differential equation in parameter space. This characterization provides a theoretical framework for understanding the origin of observed structures, and allows for rapid estimation of dominant resolvent mode characteristics without the need for operator discretization or large numerical computations. We relate our findings to classical lift-up and Orr amplification mechanisms in shear-driven flows.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:The authors acknowledge support from the Air Force Office of Scientific Research grant FA9550-16-1-0232 (program manager Ivett Leyva). The authors also thank Peter Schmid, Anthony Leonard, and Kevin Rosenberg for valuable discussions, and Xiaohua Wu for allowing us to use his turbulent boundary layer database.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0232
Record Number:CaltechAUTHORS:20190429-080541243
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95062
Deposited By: Tony Diaz
Deposited On:29 Apr 2019 15:55
Last Modified:29 Apr 2019 15:55

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