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

The unsteady flow due to an impulsively rotated sphere

  Sophie Calabretto | Research

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) 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) 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; del Pino et al. Phys. Fluids, vol. 20 (12), 2008). 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.

Collaborators: T. Mattner and J. Denier

We consider the flow induced by a sphere, contained in an otherwise quiescent body of fluid, that is suddenly imparted with angular momentum. This classical problem is known to exhibit a finite-time singularity in the boundary-layer equations, due to the viscous boundary layer, induced by the sudden rotation, colliding at the sphere’s equator.We consider this flow from the perspective of the post-collision dynamics, showing that the collision gives rises to a radial jet headed by a swirling toroidal starting vortex pair. The starting vortex propagates away from the sphere and, in doing so, loses angular momentum. The jet, in turn, develops an absolute instability, which propagates back towards the sphere’s equator. The starting vortex pair detaches from the jet and expands as a coherent (non-swirling) toroidal vortex pair.We also present results of some new experiments, which show good qualitative agreement with our computational results.

Collaborators: B. Levy, J. Denier and T. Mattner