Emergence of upstream swimming via a hydrodynamic transition.

We demonstrate that upstream swimming of sperm emerges via an orientation disorder-order transition. The order parameter, the average orientation of the sperm head against the flow, follows a 0.5 power law with the deviation from the critical flow shear rate (γ-γ_{c}). This transition is successfully explained by a hydrodynamic bifurcation theory, which extends the sperm upstream swimming to a broad class of near surface microswimmers that possess front-back asymmetry and circular motion.