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Tollmien-Schlichting route to elastoinertial turbulence in channel flow

Shekar, Ashwin and McMullen, Ryan M. and McKeon, Beverley J. and Graham, Michael D. (2021) Tollmien-Schlichting route to elastoinertial turbulence in channel flow. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210504-093917792

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Abstract

Direct simulations of two-dimensional channel flow of a viscoelastic fluid have revealed the existence of a family of Tollmien-Schlichting (TS) attractors that is nonlinearly self-sustained by viscoelasticity [Shekar et al., J.Fluid Mech. 893, A3 (2020)]. Here, we describe the evolution of this branch in parameter space and its connections to the Newtonian TS attractor and to elastoinertial turbulence (EIT). At Reynolds number Re=3000, there is a solution branch with TS-wave structure but which is not connected to the Newtonian solution branch. At fixed Weissenberg number, Wi and increasing Reynolds number from 3000-10000, this attractor goes from displaying a striation of weak polymer stretch localized at the critical layer to an extended sheet of very large polymer stretch. We show that this transition is directly tied to the strength of the TS critical layer fluctuations and can be attributed to a coil-stretch transition when the local Weissenberg number at the hyperbolic stagnation point of the Kelvin cat's eye structure of the TS wave exceeds 1/2. At Re=10000, unlike 3000, the Newtonian TS attractor evolves continuously into the EIT state as Wi is increased from zero to about 13. We describe how the structure of the flow and stress fields changes, highlighting in particular a "sheet-shedding" process by which the individual sheets associated with the critical layer structure break up to form the layered multisheet structure characteristic of EIT.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2104.10257arXivDiscussion 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:This work was supported by (UW) NSF CBET-1510291, AFOSR FA9550-18-1-0174, and ONR N00014-18-1-2865, and (Caltech) ONR N00014-17-1-3022. Declaration of interests: none.
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
Record Number:CaltechAUTHORS:20210504-093917792
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210504-093917792
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108959
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 May 2021 18:39
Last Modified:05 May 2021 18:39

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