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CATEGORIES:Geophysical and Environmental Processes
SUMMARY:Optimizing scalar transport using branching flows
- Anuj Kumar\, University of California Santa Cruz
DTSTART;TZID=Europe/London:20221024T130000
DTEND;TZID=Europe/London:20221024T140000
UID:TALK185138AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/185138
DESCRIPTION:We consider the problem of "wall-to-wall optimal t
ransport\," in which we attempt to maximize the tr
ansport of a passive temperature field between hot
and cold plates. Specifically\, we are interested
in the design of forcing in the forced Navier--St
okes equation that maximizes this transport for a
given power supply budget. One can equivalently fo
rmulate this problem as the design of a divergence
-free flow field that maximizes scalar transport u
nder an enstrophy constraint (which can be underst
ood as a constraint on the power supply). Previous
work established that the transport cannot scale
faster than 1/3-power of the power supply. Recentl
y\, Tobasco & Doering (Phys. Rev. Lett. vol.118\,
2017\, p.264502) and Doering & Tobasco (Comm. Pure
Appl. Math. vol.72\, 2019\, p.2385--2448) constru
cted self-similar two-dimensional steady branching
flows saturating this upper bound up to a logarit
hmic correction to scaling. This logarithmic corre
ction appears to arise due to a topological obstru
ction inherent to two-dimensional steady branching
flows. We present a construction of three-dimensi
onal "branching pipe flows" that eliminates the po
ssibility of this logarithmic correction and for w
hich the corresponding passive scalar transport sc
ales as a clean 1/3-power law in power supply. Our
flows resemble previous numerical studies of the
three-dimensional wall-to-wall problem by Motoki\,
Kawahara & Shimizu (J. Fluid Mech. vol.851\, 2018
\, p.R4). However\, using an unsteady branching fl
ow construction\, it appears that the 1/3 scaling
is also optimal in two dimensions. This unsteady f
low design challenges the general belief that stea
dy flows are optimal for transporting heat in the
family of all incompressible flows. After carefull
y examining these designs\, we extract the underly
ing physical mechanism that makes the branching fl
ows "efficient." We present the relevance of branc
hing in naturally occurring buoyancy-driven flows
and discuss if these flows are optimal for transpo
rting a scalar. We also present a design of mechan
ical apparatus\, which in principle\, can achieve
the best possible case scenario of heat transfer.\
n
LOCATION:MR5\, CMS
CONTACT:
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