5,579 research outputs found
Selection of dune shapes and velocities. Part 2: A two-dimensional modelling
We present in this paper a simplification of the dune model proposed by
Sauermann et al. which keeps the basic mechanisms but allows analytical and
parametric studies. Two kinds of purely propagative two dimensional solutions
are exhibited: dunes and domes, which, by contrast to the former, do not show
avalanche slip face. Their shape and velocity can be predicted as a function of
their size. We recover in particular that dune profiles are not scale invariant
(small dunes are flatter than the large ones), and that the inverse of the
velocity grows almost linearly with the dune size. We furthermore get the
existence of a critical mass below which no stable dune exists. However, the
linear stability analysis of a flat sand sheet shows that it is unstable at
large wavelengths and suggests a mechanism of dune initiation.Comment: submitted to Eur. Phys. J. B, 13 pages, 17 figure
Comment on "Minimal size of a barchan dune"
It is now an accepted fact that the size at which dunes form from a flat sand
bed as well as their `minimal size' scales on the flux saturation length. This
length is by definition the relaxation length of the slowest mode toward
equilibrium transport. The model presented by Parteli, Duran and Herrmann
[Phys. Rev. E 75, 011301 (2007)] predicts that the saturation length decreases
to zero as the inverse of the wind shear stress far from the threshold. We
first show that their model is not self-consistent: even under large wind, the
relaxation rate is limited by grain inertia and thus can not decrease to zero.
A key argument presented by these authors comes from the discussion of the
typical dune wavelength on Mars (650 m) on the basis of which they refute the
scaling of the dune size with the drag length evidenced by Claudin and
Andreotti [Earth Pla. Sci. Lett. 252, 30 (2006)]. They instead propose that
Martian dunes, composed of large grains (500 micrometers), were formed in the
past under very strong winds. We show that this saltating grain size, estimated
from thermal diffusion measurements, is not reliable. Moreover, the microscopic
photographs taken by the rovers on Martian aeolian bedforms show a grain size
of 87 plus or minus 25 micrometers together with hematite spherules at
millimetre scale. As those so-called ``blueberries'' can not be entrained by
reasonable winds, we conclude that the saltating grains on Mars are the small
ones, which gives a second strong argument against the model of Parteli et al.Comment: A six page comment on ``Minimal size of a barchan dune'' by Parteli,
Duran and Herrmann [Phys. Rev. E 75, 011301 (2007) arXiv:0705.1778
The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator
We establish the existence of the asymptotic expansion of the Bergman kernel
associated to the spin-c Dirac operators acting on high tensor powers of line
bundles with non-degenerate mixed curvature (negative and positive eigenvalues)
by extending the paper " On the asymptotic expansion of Bergman kernel "
(math.DG/0404494) of Dai-Liu-Ma. We compute the second coefficient b_1 in the
asymptotic expansion using the method of our paper "Generalized Bergman kernels
on symplectic manifolds" (math.DG/0411559).Comment: 21 pages, to appear in Internat. J. Math. Precisions added in the
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Evidence of Raleigh-Hertz surface waves and shear stiffness anomaly in granular media
Due to the non-linearity of Hertzian contacts, the speed of sound in granular
matter increases with pressure. Under gravity, the non-linear elastic
description predicts that acoustic propagation is only possible through surface
modes, called Rayleigh-Hertz modes and guided by the index gradient. Here we
directly evidence these modes in a controlled laboratory experiment and use
them to probe the elastic properties of a granular packing under vanishing
confining pressure. The shape and the dispersion relation of both transverse
and sagittal modes are compared to the prediction of non-linear elasticity that
includes finite size effects. This allows to test the existence of a shear
stiffness anomaly close to the jamming transition.Comment: 4 pages 4 figure
Barchan dune corridors: field characterization and investigation of control parameters
The structure of the barchan field located between Tarfaya and Laayoune
(Atlantic Sahara, Morocco) is quantitatively investigated and compared to that
in La Pampa de la Joya (Arequipa, Peru). On the basis of field measurements, we
show how the volume, the velocity and the output sand flux of a dune can be
computed from the value of its body and horn widths. The dune size distribution
is obtained from the analysis of aerial photographs. It shows that these fields
are in a statistically homogeneous state along the wind direction and present a
`corridor' structure in the transverse direction, in which the dunes have a
rather well selected size. Investigating the possible external parameters
controlling these corridors, we demonstrate that none among topography,
granulometry, wind and sand flux is relevant. We finally discuss the dynamical
processes at work in these fields (collisions and wind fluctuations), and
investigate the way they could regulate the size of the dunes. Furthermore we
show that the overall sand flux transported by a dune field is smaller than the
maximum transport that could be reached in the absence of dunes, i.e. in
saltation over the solid ground.Comment: revised version for JGR-ES, 36 pages, 21 figure
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