  The splitting scheme (the Kato-Trotter formula) is applied to stochastic
flows with common noise of the type introduced by Th.E.~Harris. The case of
possibly coalescing flows with continuous infinitesimal covariance is
considered and the weak convergence of the corresponding finite-dimensional
motions is established. As applications, results for the convergence of the
associated pushforward measures and dual flows are given. Similarities between
splitting and the Euler-Maruyama scheme yield estimates of the speed of the
convergence under additional regularity assumptions.
