  Many motile biological cells navigate along concentration gradients of
signaling molecules: This chemotaxis guides for instance sperm cells from
marine invertebrates, which have to find egg cells in the ocean. While
chemotaxis has been intensively studied for idealized conditions of
rotationally symmetric gradients in still water, natural gradients are usually
distorted, e.g., by turbulent flows in the ocean. Recent experiments and direct
numerical simulations with sperm cells and bacteria surprisingly suggest the
existence of an optimal flow strength at which chemotaxis is more effective
than for still water. We use sperm chemotaxis in simple shear flow as a
prototypical example to understand the origin of such an optimal flow strength
theoretically: We quantify how flow accelerates spreading of signaling
molecules released by the egg, but distorts the resulting concentration field
into long and thin filaments. The competition between these two effects sets an
optimal flow strength that maximizes sperm-egg encounter. We characterize how
sperm cells `surf' along concentration filaments, typical for scalar
turbulence, revealing a general navigation paradigm in the presence of flow. We
compare both simulation and theory with previous experimental results and find
good agreement.
