University of Illinois Urbana-Champaign

Chaotic advection in cubic stokes flow

Neishtadt, Anatoly I; Vainshtein, Dmitri L.; Vasiliev, Alexei A.

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https://hdl.handle.net/2142/112560

Description

Title
Chaotic advection in cubic stokes flow
Author(s)
  • Neishtadt, Anatoly I
  • Vainshtein, Dmitri L.
  • Vasiliev, Alexei A.
Issue Date
1997-06
Keyword(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.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 857
  • 1997-6018
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112560
Sponsor(s)/Grant Number(s)
Russian Basic Research Foundation 97/06; US Civilian Research & Development Foundation 97/06 RM 1 184 97/06
Copyright and License Information
Copyright 1997 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
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.