Estimating stable and unstable sets and their role as transport barriers in stochastic flows

Sanjeeva Balasuriya and Georg A. Gottwald
Phys. Rev. E 98, 013106 – Published 24 July 2018

Abstract

We consider the situation of a large-scale stationary flow subjected to small-scale fluctuations. Assuming that the stable and unstable manifolds of the large-scale flow are known, we quantify the mean behavior and stochastic fluctuations of particles close to the unperturbed stable and unstable manifolds and their evolution in time. The mean defines a smooth curve in physical space, while the variance provides a time- and space-dependent quantitative estimate where particles are likely to be found. This allows us to quantify transport properties such as the expected volume of mixing as the result of the stochastic fluctuations of the transport barriers. We corroborate our analytical findings with numerical simulations in both compressible and incompressible flow situations. We moreover demonstrate the intimate connection of our results with finite-time Lyapunov exponent fields, and with spatial mixing regions.

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  • Received 2 April 2018

DOI:https://doi.org/10.1103/PhysRevE.98.013106

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsNonlinear DynamicsFluid Dynamics

Authors & Affiliations

Sanjeeva Balasuriya*

  • School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia

Georg A. Gottwald

  • School of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, Australia

  • *sanjeevabalasuriya@yahoo.com
  • georg.gottwald@sydney.edu.au

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Issue

Vol. 98, Iss. 1 — July 2018

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