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Self-sustained elastoinertial Tollmien-Schlichting waves

Shekar, Ashwin and McMullen, Ryan M. and McKeon, Beverley J. and Graham, Michael D. (2020) Self-sustained elastoinertial Tollmien-Schlichting waves. Journal of Fluid Mechanics, 897 . Art. No. A3. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20200128-134130309

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Abstract

Direct simulations of two-dimensional plane channel flow of a viscoelastic fluid at Reynolds number Re = 3000 reveal the existence of a family of attractors whose structure closely resembles the linear Tollmien–Schlichting (TS) mode, and in particular exhibits strongly localized stress fluctuations at the critical layer position of the TS mode. At the parameter values chosen, this solution branch is not connected to the nonlinear TS solution branch found for Newtonian flow, and thus represents a solution family that is nonlinearly self-sustained by viscoelasticity. The ratio between stress and velocity fluctuations is in quantitative agreement for the attractor and the linear TS mode, and increases strongly with Weissenberg number, Wi. For the latter, there is a transition in the scaling of this ratio as Wi increases, and the Wi at which the nonlinear solution family comes into existence is just above this transition. Finally, evidence indicates that this branch is connected through an unstable solution branch to two-dimensional elastoinertial turbulence (EIT). These results suggest that, in the parameter range considered here, the bypass transition leading to EIT is mediated by nonlinear amplification and self-sustenance of perturbations that excite the TS mode.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/jfm.2020.372DOIArticle
https://arxiv.org/abs/1910.11419arXivDiscussion Paper
ORCID:
AuthorORCID
McMullen, Ryan M.0000-0003-1371-7150
McKeon, Beverley J.0000-0003-4220-1583
Graham, Michael D.0000-0003-4983-4949
Additional Information:© 2020 The Author(s), Published by Cambridge University Press. Received 23 October 2019; revised 29 April 2020; accepted 5 May 2020. This work was supported by (University of Wisconsin) NSF CBET-1510291, AFOSR FA9550-18-1-0174, and ONR N00014-18-1-2865, and (Caltech) ONR N00014-17-1-3022. The authors report no conflict of interest.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NSFCBET-1510291
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0174
Office of Naval Research (ONR)N00014-18-1-2865
Office of Naval Research (ONR)N00014-17-1-3022
Subject Keywords:drag reduction, turbulent transition
Record Number:CaltechAUTHORS:20200128-134130309
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200128-134130309
Official Citation:Shekar, A., McMullen, R., McKeon, B., & Graham, M. (2020). Self-sustained elastoinertial Tollmien–Schlichting waves. Journal of Fluid Mechanics, 897, A3. doi:10.1017/jfm.2020.372
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100968
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Jan 2020 23:26
Last Modified:25 Jun 2020 18:09

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