4,247 research outputs found
A Heuristic Framework for Next-Generation Models of Geostrophic Convective Turbulence
Many geophysical and astrophysical phenomena are driven by turbulent fluid
dynamics, containing behaviors separated by tens of orders of magnitude in
scale. While direct simulations have made large strides toward understanding
geophysical systems, such models still inhabit modest ranges of the governing
parameters that are difficult to extrapolate to planetary settings. The
canonical problem of rotating Rayleigh-B\'enard convection provides an
alternate approach - isolating the fundamental physics in a reduced setting.
Theoretical studies and asymptotically-reduced simulations in rotating
convection have unveiled a variety of flow behaviors likely relevant to natural
systems, but still inaccessible to direct simulation. In lieu of this, several
new large-scale rotating convection devices have been designed to characterize
such behaviors. It is essential to predict how this potential influx of new
data will mesh with existing results. Surprisingly, a coherent framework of
predictions for extreme rotating convection has not yet been elucidated. In
this study, we combine asymptotic predictions, laboratory and numerical
results, and experimental constraints to build a heuristic framework for
cross-comparison between a broad range of rotating convection studies. We
categorize the diverse field of existing predictions in the context of
asymptotic flow regimes. We then consider the physical constraints that
determine the points of intersection between flow behavior predictions and
experimental accessibility. Applying this framework to several upcoming devices
demonstrates that laboratory studies may soon be able to characterize
geophysically-relevant flow regimes. These new data may transform our
understanding of geophysical and astrophysical turbulence, and the conceptual
framework developed herein should provide the theoretical infrastructure needed
for meaningful discussion of these results.Comment: 36 pages, 8 figures. CHANGES: in revision at Geophysical and
Astrophysical Fluid Dynamic
Improved Fourier restriction estimates in higher dimensions
We consider Guth's approach to the Fourier restriction problem via polynomial
partitioning. By writing out his induction argument as a recursive algorithm
and introducing new geometric information, known as the polynomial Wolff
axioms, we obtain improved bounds for the restriction conjecture, particularly
in high dimensions. Consequences for the Kakeya conjecture are also considered.Comment: 43 pages, 5 figures. A number of typos have been corrected and
additional points of clarification added. To appear in Cambridge Journal of
Mathematic
Origin and Detection of Microstructural Clustering in Fluids with Spatial-Range Competitive Interactions
Fluids with competing short-range attractions and long-range repulsions mimic
dispersions of charge-stabilized colloids that can display equilibrium
structures with intermediate range order (IRO), including particle clusters.
Using simulations and analytical theory, we demonstrate how to detect cluster
formation in such systems from the static structure factor and elucidate links
to macrophase separation in purely attractive reference fluids. We find that
clusters emerge when the thermal correlation length encoded in the IRO peak of
the structure factor exceeds the characteristic lengthscale of interparticle
repulsions. We also identify qualitative differences between the dynamics of
systems that form amorphous versus micro-crystalline clusters.Comment: 6 pages, 5 figure
On the measurability of a numerical function with respect to a family of sets
The following document is a translation (from French to English) of: Gabriele
H. Greco, Sur la mesurabilit\'e d'une fonction num\'erique par rapport \`a une
famille d'ensembles, Rendiconti del Seminario Matematico della Universit\`a di
Padova}, tome 65 (1981), pp. 163--176. Translated by: Jonathan M. Keith, School
of Mathematics, Monash University, [email protected]. With thanks to:
Prof. Andrea D'Agnolo, Editor-in-Chief of the above journal, for permission to
publish this translation
A nonlinear model for rotationally constrained convection with Ekman pumping
It is a well established result of linear theory that the influence of
differing mechanical boundary conditions, i.e., stress-free or no-slip, on the
primary instability in rotating convection becomes asymptotically small in the
limit of rapid rotation. This is accounted for by the diminishing impact of the
viscous stresses exerted within Ekman boundary layers and the associated
vertical momentum transport by Ekman pumping. By contrast, in the nonlinear
regime recent experiments and supporting simulations are now providing evidence
that the efficiency of heat transport remains strongly influenced by Ekman
pumping in the rapidly rotating limit. In this paper, a reduced model is
developed for the case of low Rossby number convection in a plane layer
geometry with no-slip upper and lower boundaries held at fixed temperatures. A
complete description of the dynamics requires the existence of three distinct
regions within the fluid layer: a geostrophically balanced interior where fluid
motions are predominately aligned with the axis of rotation, Ekman boundary
layers immediately adjacent to the bounding plates, and thermal wind layers
driven by Ekman pumping in between. The reduced model uses a classical Ekman
pumping parameterization to alleviate the need for spatially resolving the
Ekman boundary layers. Results are presented for both linear stability theory
and a special class of nonlinear solutions described by a single horizontal
spatial wavenumber. It is shown that Ekman pumping allows for significant
enhancement in the heat transport relative to that observed in simulations with
stress-free boundaries. Without the intermediate thermal wind layer the
nonlinear feedback from Ekman pumping would be able to generate a heat
transport that diverges to infinity. This layer arrests this blowup resulting
in finite heat transport at a significantly enhanced value.Comment: 38 pages, 14 figure
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