  The squirmer is a popular model to analyse the fluid mechanics of a
self-propelled object, such as a micro-organism. We demonstrate that some
fore-aft symmetric squirmers can spontaneously self-propel above a critical
Reynolds number. Specifically, we numerically study the effects of inertia on
spherical squirmers characterised by an axially and fore-aft symmetric
`quadrupolar' distribution of surface-slip velocity; under creeping-flow
conditions, such squirmers generate a pure stresslet flow, the stresslet sign
classifying the squirmer as either a `pusher' or `puller.' Assuming axial
symmetry, and over the examined range of the Reynolds number $Re$ (defined
based upon the magnitude of the quadrupolar squirming), we find that
spontaneous symmetry breaking occurs in the pusher case above $Re \approx
14.3$, with steady swimming emerging from that threshold consistently with a
supercritical pitchfork bifurcation and with the swimming speed growing
monotonically with $Re$.
