  Viscous streaming flows generated by objects of constant curvature (circular
cylinders, infinite plates) have been well understood. Yet, characterization
and understanding of such flows when multiple body length-scales are involved
has not been looked into, in rigorous detail. We propose a simplified setting
to understand and explore the effect of multiple body curvatures on streaming
flows, analyzing the system through the lens of bifurcation theory. Our setup
consists of periodic, regular lattices of cylinders characterized by two
distinct radii, so as to inject discrete curvatures into the system, which in
turn affect the streaming field generated due to an oscillatory background
flow. We demonstrate that our understanding based on this system can be then
generalized to a variety of individual convex shapes presenting a spectrum of
curvatures, explaining prior experimental and computational observations. Thus,
this study illustrates a route towards the rational manipulation of viscous
streaming flow topology, through regulated variation of object geometry.
