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Title:Chaotic advection in cubic stokes flow
Author(s):Neishtadt, Anatoly I; Vainshtein, Dmitri L.; Vasiliev, Alexei A.
Subject(s):Chaotic Advection
Cubic Stokes Flow
Abstract:A stationary incompressible Stokes flow in a sphere is considered. The flow was introduced by H. A. Stone, A. Nadim and S. H. Strogatz in 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.
Issue Date:1997-06
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 857
Genre:Technical Report
Sponsor:Russian Basic Research Foundation 97/06; US Civilian Research & Development Foundation 97/06 RM 1 184 97/06
Rights Information:Copyright 1997 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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