Linear stability of the flow past a spheroidal bubble

The linear stability of the axisymmetric flow past a fixed-shape spheroid with free-slip boundary conditions is studied numerically to gain some insight into the path instability of bubbles rising in liquids. Qualitatively, the results are similar to those for a solid sphere. The m = 1 mode gives rise to a double-threaded wake and proves to be the most unstable mode, with a first regular bifurcation followed by a Hopf bifurcation. The importance of the base-flow vorticity is highlighted by a stability analysis of the axisymmetric base flow ‘frozen’ before reaching steady state. Setting viscosity to zero in the perturbation equations results in a faster growth of the primary instability, which indicates its root in inertial effects.