A Shell Model for Optimal Mixing View Full Text


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Article Info

DATE

2018-12

AUTHORS

Christopher J. Miles, Charles R. Doering

ABSTRACT

What is the maximum mixing efficiency of an incompressible flow? To address this question we introduce a shell model—a reduced model mimicking the kinematics of advection and diffusion—to study the evolution of an initially inhomogeneous tracer concentration carried by a given incompressible fluid on a periodic spatial domain. We pose the mixing task as an optimization problem: Find the divergence-free velocity field (the control variable) that produces a well-mixed tracer concentration field (the state variable). We consider two alternative objectives: local-in-time optimization (maximize the instantaneous mixing rate) and global-in-time optimization (maximize mixing at a prescribed final time). Throughout, we use a shell-model analog of the H-1 mix-norm to measure mixing. In addition, lower bounds on the mix-norm are obtained and rule out perfect mixing in finite time in particular cases. More... »

PAGES

2153-2186

References to SciGraph publications

  • 2000-06. Scalar turbulence in NATURE
  • 1994. Principles of Quantum Mechanics in NONE
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