Abstract
We consider wall-to-wall transport of a passive tracer by divergence-free velocity vector fields . Given an enstrophy budget we construct steady two-dimensional flows that transport at rates in the large enstrophy limit. Combined with the known upper bound for any such enstrophy-constrained flow, we conclude that maximally transporting flows satisfy up to possible logarithmic corrections. Combined with known transport bounds in the context of Rayleigh-Bénard convection, this establishes that while suitable flows approaching the “ultimate” heat transport scaling exist, they are not always realizable as buoyancy-driven flows. The result is obtained by exploiting a connection between the wall-to-wall optimal transport problem and a closely related class of singularly perturbed variational problems arising in the study of energy-driven pattern formation in materials science.
- Received 21 December 2016
DOI:https://doi.org/10.1103/PhysRevLett.118.264502
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