We analyze from first principles the advection of particles in a velocity fie with Hamiltonian H(x, y) = V1BAR, y - V2BAR x + w, (y) - W2(x), where W(i), i = 1, 2, are random functions with stationary, independent increments. In the absence of molecular diffusion, the particle dynamics are very sensitive to the streamline topology, which depends on the mean-to-fluctuations ratio rho = max(\V1BAR\/UBAR; \V2BAR\/UBAR), with UBAR = [\W1'\2]1/2 = rms fluctuations. Remarkably, the model is exactly solvable for rho greater-than-or-equal-to 1 and well suited for Monte Carlo simulations for all rho, providing a nice setting for, studying seminumerically the influence of streamline topology on large-scale transport. First, we consider the statistics of streamlines for rho = 0, deriving power laws for p(nc)(L) and [lambda(L)], which are, respectively, the escape probability and the length of escaping trajectories for a box of size L, L much greater than 1. We also obtain a characterization of the ''statistical topography'' of the Hamiltonian H. Second, we study the large-scale transport of advected particles with rho > 0. For 0 < rho < 1, a fraction of particles is trapped in closed field lines and another fraction undergoes unbounded motions; while for rho greater-than-or-equal-to 1 all particles evolve in open streamlines. The fluctuations of the free particle positions about their mean is studied in terms of the normalized variables t-nu/2[x(t) - [x(t)]] and t-nu/y(5) - [y(t)]]. The large-scale motions are shown to be either Fickian (v = 1), or superdiffusive (nu = 3/2) with a non-Gaussian coarse-grained probability, according to the direction of the mean velocity relative to the underlying lattice. These results are obtained analytically for rho greater-than-or-equal-to 1 and extended to the regime 0 < rho < 1 by Monte Carlo simulations. Moreover, we show that the effective diffusivity blows up for resonant values of (V1BAR, V2BAR) for which stagnation regions in the flow exist. We compare the results with existing predictions on the topology of streamlines based on percolation theory, as well as with mean-field calculations of effective diffusivities. The simulations are carried out with a CM 200 massively parallel computer with 8192 SIMD processors.
