Chaotic advection in a cubic Stokes flow

✍ Scribed by A.I. Neishtadt; D.L. Vainshtein; A.A. Vasiliev

• Book ID: 104297413
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 999 KB
• Volume: 111
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(97)80013-9

✦ Synopsis

A stationary incompressible Stokes flow in a sphere is considered. The flow was introduced by Stone et al. (1991) as a flow inside a neutrally buoyant spherical drop immersed in a linear flow. The velocity field of the flow is a result of a small perturbation of an integrable velocity field with almost all streamlines closed. Under arbitrarily small perturbation a large domain of chaotic advection within the sphere arises. This phenomenon is explained by quasirandom changes in the adiabatic invariant of the flow, which occur as a streamline crosses the two-dimensional separatrix of the unperturbed flow. Phase portraits of the averaged system are constructed. An asymptotic formula for the change in the adiabatic invariant due to the separatrix crossing is derived. The process of diffusion of the adiabatic invariant due to multiple separatrix crossings is described.