4,225 research outputs found
Numerical study of geometrical dispersion in self-affine rough fractures
We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-affine surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefficient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-affine curve whose exponent is equal to that of the fracture surface
Tracer Dispersion in Rough Open Cracks
Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface.This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained
Topology and field strength in spherical, anelastic dynamo simulations
Numerical modelling of convection driven dynamos in the Boussinesq
approximation revealed fundamental characteristics of the dynamo-generated
magnetic fields and the fluid flow. Because these results were obtained for an
incompressible fluid, their validity for gas planets and stars remains to be
assessed. A common approach is to take some density stratification into account
with the so-called anelastic approximation. The validity of previous results
obtained in the Boussinesq approximation is tested for anelastic models. We
point out and explain specific differences between both types of models, in
particular with respect to the field geometry and the field strength, but we
also compare scaling laws for the velocity amplitude, the magnetic dissipation
time, and the convective heat flux. Our investigation is based on a systematic
parameter study of spherical dynamo models in the anelastic approximation. We
make use of a recently developed numerical solver and provide results for the
test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and
multipolar dynamos identified in Boussinesq simulations is also present in our
sample of anelastic models. Dipolar models require that the typical length
scale of convection is an order of magnitude larger than the Rossby radius.
However, the distinction between both classes of models is somewhat less
explicit than in previous studies. This is mainly due to two reasons: we found
a number of models with a considerable equatorial dipole contribution and an
intermediate overall dipole field strength. Furthermore, a large density
stratification may hamper the generation of dipole dominated magnetic fields.
Previously proposed scaling laws, such as those for the field strength, are
similarly applicable to anelastic models. It is not clear, however, if this
consistency necessarily implies similar dynamo processes in both settings.Comment: 14 pages, 11 figure
First Passage Time in a Two-Layer System
As a first step in the first passage problem for passive tracer in stratified
porous media, we consider the case of a two-dimensional system consisting of
two layers with different convection velocities. Using a lattice generating
function formalism and a variety of analytic and numerical techniques, we
calculate the asymptotic behavior of the first passage time probability
distribution. We show analytically that the asymptotic distribution is a simple
exponential in time for any choice of the velocities. The decay constant is
given in terms of the largest eigenvalue of an operator related to a half-space
Green's function. For the anti-symmetric case of opposite velocities in the
layers, we show that the decay constant for system length crosses over from
behavior in diffusive limit to behavior in the convective
regime, where the crossover length is given in terms of the velocities.
We also have formulated a general self-consistency relation, from which we have
developed a recursive approach which is useful for studying the short time
behavior.Comment: LaTeX, 28 pages, 7 figures not include
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