Breaking of symmetry in shallow rotating flows -

Abstract

We show theoretically and experimentally that the breaking of symmetry of shallow rotating Taylor-Couette (TC) flow is spontaneous and does not require forcing under certain flow parameters. To do this we build a novel experiment, in which a cylindrical container of radius R is placed in a set of electromagnets generating a uniform magnetic field in the z-direction. KOH solution is poured into the cylinder with a depth h, and a current is passed in it. The Lorentz force, J X B , drives the rotation of the flow. Three flow regimes are explored. At shallow depth, or large aspect ratio Γ=R-h, and low Reynold's number Re=hVθ-ν the flow is laminar. At lower Γs and higher Re the flow is subject to a TC instability due to the boundary layer near the outer edge of the flow. Finally, above a Reynold’s number Re = 241, the symmetry of the TC flow is broken, and non-axisymmetric vortices are formed. The source of the secondary structures is a shear layer in the (r-z) plane. These results are also confirmed using theoretical analysis of the flow, where we modeled the TC flow by two counter rotating vortices. We perform linear stability analysis on this base flow, and we find that the conditions for the instabilities are close to those of the experiment. We conclude that the symmetry of shallow rotating flows is naturally broken, due to the primary flow dynamics, if the Reynold's number is high enough.