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Type: Journal article
Title: Estimating stable and unstable sets and their role as transport barriers in stochastic flows
Author: Balasuriya, S.
Gottwald, G.
Citation: Physical Review E, 2018; 98(1):013106-1-013106-17
Publisher: American Physical Society
Issue Date: 2018
ISSN: 2470-0045
Statement of
Sanjeeva Balasuriya, Georg A. Gottwald
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.
Rights: ©2018 American Physical Society
RMID: 0030095682
DOI: 10.1103/PhysRevE.98.013106
Grant ID:
Appears in Collections:Mathematical Sciences publications

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