Symmetry-breaking bifurcations in two-dimensional square vortex flows

Suri, B (2021) Symmetry-breaking bifurcations in two-dimensional square vortex flows. In: Physics of Fluids, 33 (9).

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Abstract

We present a theoretical study of spatial symmetries and bifurcations in a laterally bounded two-dimensional flow composed of approximately square vortices. The numerical setting simulates a laboratory experiment wherein a shallow electrolyte layer is driven by a plane-parallel force that is nearly sinusoidal in both extended directions. Choosing an integer or half-integer number of forcing wavelengths along each direction, we generate square vortex flows invariant under different spatial symmetries. We then map out the sequence of symmetry-breaking bifurcations leading to the formation of fully asymmetric flows. Our analysis reveals a gallery of pitchfork and Hopf bifurcations, both supercritical and subcritical in nature, resulting in either steady or time-dependent asymmetric flows. Furthermore, we demonstrate that different types of flows (steady, periodic, pre-periodic, or quasi-periodic), at times with twofold multiplicity, emerge as a result of symmetry-breaking bifurcations. Our results also provide new theoretical insights into previous experimental observations in quasi-two-dimensional square vortex flows. © 2021 Author(s).

Item Type:	Journal Article
Publication:	Physics of Fluids
Publisher:	American Institute of Physics Inc.
Additional Information:	The copyright for this article belongs to American Institute of Physics Inc.
Keywords:	Electrolytes; Hopf bifurcation, A-plane; Asymmetric flows; Electrolyte layers; Laboratory experiments; Spatial bifurcation; Spatial symmetry; Symmetry-breaking bifurcations; Theoretical study; Two-dimensional; Two-dimensional flow, Vortex flow
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	29 Nov 2021 09:40
Last Modified:	29 Nov 2021 09:40
URI:	http://eprints.iisc.ac.in/id/eprint/70288

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