Dynamics of particles in the steady flows of an inviscid fluid

Advection of small particles with inertia in two-dimensional ideal flows is studied both numerically and analytically. It is assumed that the flow disturbance around the particle corresponds to a potential dipole, so that the motion is driven by pressure gradient, inertial, and added-mass forces. It is found that in general the motion is nonintegrable, but particular exact solutions can be obtained. The problem is then studied for the cases of axisymmetric flow, when the motion proves to be completely integrable, and of a cellular flow, for which both regular and stochastic (bounded and unbounded) trajectories are calculated. In the latter case, the unbounded stochastic motion is of Brownian-like character, and the results derived show that the particle dispersion process is generally anomalous.