NDLI: Designing a Finite-Time Mixer: Optimizing Stirring for Two-Dimensional Maps

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Meiss, J. D. Mitchell, R. A.
Copyright Year	2017
Abstract	Mixing of a passive scalar in a fluid flow results from a two part process in which large gradients are first created by advection and then smoothed by diffusion. We investigate methods of designing efficient stirrers to optimize mixing of a passive scalar in a two-dimensional, nonautonomous, incompressible flow over a finite-time interval. The flow is modeled by a sequence of area-preserving maps whose parameters change in time, defining a mixing protocol. Stirring efficiency is measured by a negative Sobolev seminorm; its decrease implies creation of fine-scale structure. A Perron--Frobenius operator is used to numerically advect the scalar for two examples: compositions of Chirikov standard maps and of Harper maps. In the former case, we find that a protocol corresponding to a single vertical shear composed with horizontal shearing at all other steps is nearly optimal. For the Harper maps, we devise a predictive, one-step scheme to choose appropriate fixed point stabilities and to control the Fourier spectrum evolution to obtain a near-optimal protocol.
Sponsorship	Division of Mathematical Sciences
Starting Page	1514
Ending Page	1542
Page Count	29
File Format	PDF
DOI	10.1137/16M1107139
e-ISSN	15360040
Issue Number	3
Volume Number	16
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-08-17
Access Restriction	Subscribed
Subject Keyword	area-preserving maps chaotic advection mixing Dynamical systems in fluid mechanics, oceanography and meteorology Nonautonomous smooth dynamical systems Symplectic mappings, fixed points
Content Type	Text
Resource Type	Article

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