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Closing the loop: nonlinear Taylor vortex flow through the lens of resolvent analysis

Barthel, Benedikt and Zhu, Xiaojue and McKeon, Beverley J. (2021) Closing the loop: nonlinear Taylor vortex flow through the lens of resolvent analysis. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20210315-104125027

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Abstract

We present an optimization-based method to efficiently calculate accurate nonlinear models of Taylor vortex flow. We use the resolvent formulation of McKeon & Sharma (2010) to model these Taylor vortex solutions by treating the nonlinearity not as an inherent part of the governing equations but rather as a triadic constraint which must be satisfied by the model solution. We exploit the low rank linear dynamics of the system to calculate an efficient basis for our solution, the coefficients of which are then calculated through an optimization problem where the cost function to be minimized is the triadic consistency of the solution with itself as well as with the input mean flow. Our approach constitutes, what is to the best of our knowledge, the first fully nonlinear and self-sustaining, resolvent-based model described in the literature. We compare our results to direct numerical simulation of Taylor Couette flow at up to five times the critical Reynolds number, and show that our model accurately captures the structure of the flow. Additionally, we find that as the Reynolds number increases the flow undergoes a fundamental transition from a classical weakly nonlinear regime, where the forcing cascade is strictly down scale, to a fully nonlinear regime characterized by the emergence of an inverse (up scale) forcing cascade. Triadic contributions from the inverse and traditional cascade destructively interfere implying that the accurate modeling of a certain Fourier mode requires knowledge of its immediate harmonic and sub-harmonic. We show analytically that this finding is a direct consequence of the structure of the quadratic nonlinearity of the governing equations formulated in Fourier space. Finally, we show that using our model solution as an initial condition to a higher Reynolds number DNS significantly reduces the time to convergence.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/2102.09141arXivDiscussion Paper
ORCID:
AuthorORCID
McKeon, Beverley J.0000-0003-4220-1583
Additional Information:We thank Kevin Rosenberg for many inspiring and helpful discussions and gratefully acknowledge the support of the U.S. Office of Naval Research under grants ONR N00014-17-1-2307 and N00014-17-1-3022.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-17-1-2307
Office of Naval Research (ONR)N00014-17-1-3022
Subject Keywords:Taylor-Couette flow, low-dimensional models, nonlinear instability, transition to turbulence
Record Number:CaltechAUTHORS:20210315-104125027
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210315-104125027
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108428
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Mar 2021 00:39
Last Modified:19 Mar 2021 00:39

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