  Recent studies on viscous streaming flows in two dimensions have elucidated
the impact of body curvature variations on resulting flow topology and
dynamics, with opportunities for microfluidic applications. Following that, we
present here a three-dimensional characterization of streaming flows as
function of changes in body geometry and topology, starting from the well-known
case of a sphere to progressively arrive at toroidal shapes. We leverage direct
numerical simulations and dynamical systems theory to systematically analyze
the reorganization of streaming flows into a dynamically rich set of regimes,
the origins of which are explained using bifurcation theory.
