Abstract: In this talk, I will introduce two seemingly unrelated topics: kinetic Brownian motion, and fluid mechanics. The former is a geometric random perturbation of the geodesic flow. In its simplest form, it is the motion described by someone walking at unit speed, but in a direction that continuously and randomly changes in time. The latter, in some special case, has been shown by Arnol'd to be equivalent to a geodesic equation in an infinite-dimensional manifold, where each point represents a configuration of a fluid. I will show that it is possible to construct "kinetic Brownian (inviscid incompressible) fluids", and that, in some sense, they degenerate into "Brownian fluids" as the noise diverges.