46 research outputs found
Kelvin–Helmholtz instability in a Hele-Shaw cell
A linear stability analysis is presented for the Kelvin–Helmholtz instability in a Hele-Shaw cell, an analysis based on the Navier–Stokes equation to improve on the previous Euler–Darcy study that Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] made of their own experiments
Kelvin–Helmholtz instability in a Hele-Shaw cell: Large effect from the small region near the meniscus
In an attempt to improve the poor prediction of our previous theory, we examine corrections from the small region in a Hele-Shaw cell near the meniscus where the flow is three dimensional. At larger Reynolds numbers, we find an O(1) change to the effective boundary condition for mass conservation which is to be applied to the large scale flow outside the small region
Spreading fronts and fluctuations in sedimentation
International audienceA diffuse interface or ''front'' at the top of the suspension is investigated experimentally and numerically. The width of the front is found to grow linearly in time, mainly due to a polydispersity of particle size in the very dilute experiments, and due only to fluctuations in particle density in the simulations. Away from the front, the fluctuations in the particle velocities are found not to decay
On stratification control of the velocity fluctuations in sedimentation
International audienceWe have tested whether stratification can govern local velocity fluctuations in suspensions of sedimenting spheres. Comparison of the proposed scaling for local control of fluctuations by stratification to experimental data demonstrates that this mechanism cannot account for the reduction of the observed velocity fluctuations
Fluctuations and stratification in sedimentation of dilute suspensions of spheres
International audienceWe have tested in experiments and simulations whether stratification can control velocity fluctuations in suspensions of sedimenting spheres. The initial value and early decay of the velocity fluctuations are not affected by stratification. On the other hand, in the descending front where the stratification is strong and well defined, the velocity fluctuations are inhibited according to a previously proposed scaling. In between, after the initial decay and before the arrival of the front, the local value of the stratification does not always play a role
Spreading fronts in sedimentation of dilute suspension of spheres
International audienceThe thickness of the diffuse front between a sedimenting dilute suspension and the clear fluid above grows linearly in time due to polydispersity in the size of the particles and due to a hydrodynamic effect in which randomly heavy clusters fall out of the front leaving it depleted. Experiments and simplified point-particle numerical simulations agree that these two effects are not simply linearly additive
The S shape of a granular pile in a rotating drum
The shape of a granular pile in a rotating drum is investigated. Using
Discrete Elements Method (DEM) simulations we show that the "S shape" obtained
for high rotation speed can be accounted for by the friction on the end plates.
A theoretical model which accounts for the effect of the end plates is
presented and the equation of the shape of the free surface is derived. The
model reveals a dimensionless number which quantifies the influence of the end
plates on the shape of the pile. Finally, the scaling laws of the system are
discussed and numerical results support our conclusions
The Local Effects of Cosmological Variations in Physical 'Constants' and Scalar Fields I. Spherically Symmetric Spacetimes
We apply the method of matched asymptotic expansions to analyse whether
cosmological variations in physical `constants' and scalar fields are
detectable, locally, on the surface of local gravitationally bound systems such
as planets and stars, or inside virialised systems like galaxies and clusters.
We assume spherical symmetry and derive a sufficient condition for the local
time variation of the scalar fields that drive varying constants to track the
cosmological one. We calculate a number of specific examples in detail by
matching the Schwarzschild spacetime to spherically symmetric inhomogeneous
Tolman-Bondi metrics in an intermediate region by rigorously construction
matched asymptotic expansions on cosmological and local astronomical scales
which overlap in an intermediate domain. We conclude that, independent of the
details of the scalar-field theory describing the varying `constant', the
condition for cosmological variations to be measured locally is almost always
satisfied in physically realistic situations. The proof of this statement
provides a rigorous justification for using terrestrial experiments and solar
system observations to constrain or detect any cosmological time variations in
the traditional `constants' of Nature.Comment: 30 pages, 3 figures; corrected typo
Simple Viscous Flows: from Boundary Layers to the Renormalization Group
The seemingly simple problem of determining the drag on a body moving through
a very viscous fluid has, for over 150 years, been a source of theoretical
confusion, mathematical paradoxes, and experimental artifacts, primarily
arising from the complex boundary layer structure of the flow near the body and
at infinity. We review the extensive experimental and theoretical literature on
this problem, with special emphasis on the logical relationship between
different approaches. The survey begins with the developments of matched
asymptotic expansions, and concludes with a discussion of perturbative
renormalization group techniques, adapted from quantum field theory to
differential equations. The renormalization group calculations lead to a new
prediction for the drag coefficient, one which can both reproduce and surpass
the results of matched asymptotics
Observable Effects of Scalar Fields and Varying Constants
We show by using the method of matched asymptotic expansions that a
sufficient condition can be derived which determines when a local experiment
will detect the cosmological variation of a scalar field which is driving the
spacetime variation of a supposed constant of Nature. We extend our earlier
analyses of this problem by including the possibility that the local region is
undergoing collapse inside a virialised structure, like a galaxy or galaxy
cluster. We show by direct calculation that the sufficient condition is met to
high precision in our own local region and we can therefore legitimately use
local observations to place constraints upon the variation of "constants" of
Nature on cosmological scales.Comment: Invited Festscrift Articl