The effect of seam imperfections on the unsteady flow within a fluid-filled torus

Abstract

We consider the behaviour of the flow within a fluid-filled torus when there is a sudden change in the rotation rate of the torus. Experimental work on this problem by Madden & Mullin (J. Fluid Mech., vol. 265, 1994, p. 217) demonstrated a flow with a rich and complex dynamics. In particular, planar (top-down) flow visualisation images show a well-defined laminar band at both the inner and outer bend of the toroidal pipe. Hewitt et al. (J. Fluid Mech., vol. 688, 2011, pp. 88–119) demonstrated the existence of finite-time singularities in the resulting viscous boundary layers, and linked the post-singularity structure to one of the laminar bands identified in experiments (Madden & Mullin J. Fluid Mech., vol. 265, 1994, p. 217; del Pino et al. Phys. Fluids, vol. 20 (12), 2008, 124104). The second band (or laminar front) identified by Madden & Mullin was conjectured by Hewitt et al. to be the result of a centrifugal instability, perhaps generated by small imperfections in the experimental apparatus. Here we explore this conjecture further, demonstrating that a small seam imperfection can generate substantial secondary motion but with considerably different dynamics than the centrifugally driven instability of Hewitt et al.