CHAOTIC ADVECTION IN A CUBIC STOKES-FLOW

A stationary incompressible Stokes flow in a sphere is considered. The flow was introduced by Stone et al, (1991) as a flow inside a neutral ly buoyant spherical drop immersed in a linear flow, The velocity fiel d of the how is a result of a small perturbation of an integrable velo city field with almost all streamlines closed, Under arbitrarily small perturbation a large domain of chaotic advection within the sphere ar ises. This phenomenon is explained by quasirandom changes in the adiab atic invariant of the flow, which occur as a streamline crosses the tw o-dimensional separatrix of the unperturbed flow. Phase portraits of t he averaged system are constructed. An asymptotic formula for the chan ge in the adiabatic invariant due to the separatrix crossing is derive d. The process of diffusion of the adiabatic invariant due to multiple separatrix crossings is described.