Experimental and numerical investigation of bistability in rotating permanent magnet-generated electrolyte flow in a ring-shaped container

Abstract

Here, the stability of a transversely magnetized rotating permanent magnet-generated flow in a concentric cylindrical ring channel is studied. Numerical calculations show that the steady-state solution becomes asymmetric through a pitchfork bifurcation at a Reynolds number (Re) of 60. The two new antisymmetric steady-state solutions become cyclic at Re = 90. Nonlinearities develop at larger Re values and the limit cycle solutions are destabilized at Re = 250, enabling random transition events between the two pitchfork branches. Such transitions have been observed in all kinds of natural phenomena, spanning from neuroscientific to astrophysical systems, which are often too complex to be directly computed. Our presented system is physical yet simple enough to be used to conduct a parametric study with full three-dimensional direct numerical simulations. It raises the possibility of numerically and experimentally analyzing transitions in more detail. Experimental measurements indicated the existence of long-lived states and suitability for the proposed system for future studies of such phenomenon. However, the experimental results did not conclusively observe bistability.