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Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

Published online by Cambridge University Press:  12 September 2017

Jeffrey Tithof Open the ORCID record for Jeffrey Tithof [Opens in a new window] ,
Balachandra Suri ,
Ravi Kumar Pallantla ,
Roman O. Grigoriev Open the ORCID record for Roman O. Grigoriev [Opens in a new window]  and
Michael F. Schatz
Jeffrey Tithof*
Affiliation:
Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
Balachandra Suri
Affiliation:
Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
Ravi Kumar Pallantla
Affiliation:
Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
Roman O. Grigoriev
Affiliation:
Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
Michael F. Schatz
Affiliation:
Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a two-dimensional (2D) model (Suri et al., Phys. Fluids, vol. 26 (5), 2014, 053601), derived from first principles by depth-averaging the full three-dimensional Navier–Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 837 - 866
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Copyright
© 2017 Cambridge University Press 

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Tithof et al. supplementary movie

A side-by-side animation comparing the time-periodic flows observed in the experiment and the NPS (with depth-averaged parameters). In each case, the Reynolds number was chosen above the onset of the secondary instability so that the oscillations are clearly visible.

Download Tithof et al. supplementary movie(Video)
Video 24.1 MB