Axisymmetric pulse train solutions in narrow-gap spherical Couette flow

We numerically compute the flow induced in a spherical shell by fixing the outer sphere and rotating the inner one. The aspect ratio epsilon = (r(o) - r(i))/r(i) is set at 0.04 and 0.02, and in each case the Reynolds number measuring the inner spheres rotation rate is increased to similar to 10% beyond the first bifurcation from the basic state flow. For epsilon = 0.04 the initial bifurcations are the same as in previous numerical work at epsilon = 0.154, and result in steady one- and two-vortex states. Further bifurcations yield travelling wave solutions similar to previous analytic results valid in the epsilon -> 0 limit. For epsilon = 0.02 the steady one-vortex state no longer exists, and the first bifurcation is directly to these travelling wave solutions, consisting of pulse trains of Taylor vortices travelling toward the equator from both hemispheres, and annihilating there in distinct phase-slip events. We explore these time-dependent solutions in detail, and find that they can be both equatorially symmetric and asymmetric, as well as periodic or quasi-periodic in time. (C) 2017 Elsevier B.V. All rights reserved.