  We identify most probable flows for Kunita Brownian motions, i.e. stochastic
flows with Eulerian noise and deterministic drifts. Such stochastic processes
appear for example in fluid dynamics and shape analysis modelling coarse scale
deterministic dynamics together with fine-grained noise. We treat this infinite
dimensional problem by equipping the underlying domain with a Riemannian metric
originating from the noise. The resulting most probable flows are compared with
the non-perturbed deterministic flow, both analytically and experimentally by
integrating the equations with various choice of noise structures.
