831 research outputs found
Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
A new transient regime in the relaxation towards absolute equilibrium of the
conservative and time-reversible 3-D Euler equation with high-wavenumber
spectral truncation is characterized. Large-scale dissipative effects, caused
by the thermalized modes that spontaneously appear between a transition
wavenumber and the maximum wavenumber, are calculated using fluctuation
dissipation relations. The large-scale dynamics is found to be similar to that
of high-Reynolds number Navier-Stokes equations and thus to obey (at least
approximately) Kolmogorov scaling.Comment: 4 pages, 5 figures new version with only 4 figures; title changed;
manuscript changed; accepted by PR
Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem
Numerical simulations of the incompressible Euler equations are performed
using the Taylor-Green vortex initial conditions and resolutions up to
. The results are analyzed in terms of the classical analyticity strip
method and Beale, Kato and Majda (BKM) theorem. A well-resolved acceleration of
the time-decay of the width of the analyticity strip is observed at
the highest resolution for while preliminary 3D visualizations
show the collision of vortex sheets. The BKM criterium on the power-law growth
of supremum of the vorticity, applied on the same time-interval, is not
inconsistent with the occurrence of a singularity around .
These new findings lead us to investigate how fast the analyticity strip
width needs to decrease to zero in order to sustain a finite-time singularity
consistent with the BKM theorem. A new simple bound of the supremum norm of
vorticity in terms of the energy spectrum is introduced and used to combine the
BKM theorem with the analyticity-strip method. It is shown that a finite-time
blowup can exist only if vanishes sufficiently fast at the
singularity time. In particular, if a power law is assumed for then
its exponent must be greater than some critical value, thus providing a new
test that is applied to our Taylor-Green numerical simulation.
Our main conclusion is that the numerical results are not inconsistent with a
singularity but that higher-resolution studies are needed to extend the
time-interval on which a well-resolved power-law behavior of takes
place, and check whether the new regime is genuine and not simply a crossover
to a faster exponential decay
A New Family of Planets ? "Ocean Planets"
A new family of planets is considered which is between rochy terrestrial
planets and gaseous giant ones: "Ocean-Planets". We present the possible
formation, composition and internal models of these putative planets, including
that of their ocean, as well as their possible Exobiology interest. These
planets should be detectable by planet detection missions such as Eddington and
Kepler, and possibly COROT (lauch scheduled in 2006). They would be ideal
targets for spectroscopic missions such as Darwin/TPF.Comment: 15 pages, 3 figures submitted to Icarus notes (10 july 2003
Three regularization models of the Navier-Stokes equations
We determine how the differences in the treatment of the subfilter-scale
physics affect the properties of the flow for three closely related
regularizations of Navier-Stokes. The consequences on the applicability of the
regularizations as SGS models are also shown by examining their effects on
superfilter-scale properties. Numerical solutions of the Clark-alpha model are
compared to two previously employed regularizations, LANS-alpha and Leray-alpha
(at Re ~ 3300, Taylor Re ~ 790) and to a DNS. We derive the Karman-Howarth
equation for both the Clark-alpha and Leray-alpha models. We confirm one of two
possible scalings resulting from this equation for Clark as well as its
associated k^(-1) energy spectrum. At sub-filter scales, Clark-alpha possesses
similar total dissipation and characteristic time to reach a statistical
turbulent steady-state as Navier-Stokes, but exhibits greater intermittency. As
a SGS model, Clark reproduces the energy spectrum and intermittency properties
of the DNS. For the Leray model, increasing the filter width decreases the
nonlinearity and the effective Re is substantially decreased. Even for the
smallest value of alpha studied, Leray-alpha was inadequate as a SGS model. The
LANS energy spectrum k^1, consistent with its so-called "rigid bodies,"
precludes a reproduction of the large-scale energy spectrum of the DNS at high
Re while achieving a large reduction in resolution. However, that this same
feature reduces its intermittency compared to Clark-alpha (which shares a
similar Karman-Howarth equation). Clark is found to be the best approximation
for reproducing the total dissipation rate and the energy spectrum at scales
larger than alpha, whereas high-order intermittency properties for larger
values of alpha are best reproduced by LANS-alpha.Comment: 21 pages, 8 figure
Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
We investigate the ideal and incompressible magnetohydrodynamic (MHD)
equations in three space dimensions for the development of potentially singular
structures. The methodology consists in implementing the four-fold symmetries
of the Taylor-Green vortex generalized to MHD, leading to substantial computer
time and memory savings at a given resolution; we also use a re-gridding method
that allows for lower-resolution runs at early times, with no loss of spectral
accuracy. One magnetic configuration is examined at an equivalent resolution of
points, and three different configurations on grids of
points. At the highest resolution, two different current and vorticity sheet
systems are found to collide, producing two successive accelerations in the
development of small scales. At the latest time, a convergence of magnetic
field lines to the location of maximum current is probably leading locally to a
strong bending and directional variability of such lines. A novel analytical
method, based on sharp analysis inequalities, is used to assess the validity of
the finite-time singularity scenario. This method allows one to rule out
spurious singularities by evaluating the rate at which the logarithmic
decrement of the analyticity-strip method goes to zero. The result is that the
finite-time singularity scenario cannot be ruled out, and the singularity time
could be somewhere between and More robust conclusions will
require higher resolution runs and grid-point interpolation measurements of
maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review
Intraperitoneal mesh repair of small ventral abdominal wall hernias with a Ventralex hernia patch
BACKGROUND: Various surgical procedures have been described in the treatment of small ventral abdominal wall hernias. Mesh repair is becoming popular because of a low recurrence rate.
AIM: The aim of this prospective study was to evaluate an open intraperitoneal technique using the Bard Ventralex hernia patch in the treatment of small midline ventral hernias.
METHODS: 101 patients were operated on (59 male, 42 female) with a mean age of 54.5 years (range 17-85). Mean operative time was 33 min (range 16-65). The median hospital stay was 2 days (range 1-15).
RESULTS: Two patients had a hematoma without wound infection. There were 2 recurrences (2%). Mean postoperative follow-up time was 28.5 months (range 6-55).
CONCLUSIONS: Our preliminary results suggest that Ventralex hernia patch repair for ventral hernias can be performed with minimal postoperative morbidity and a low recurrence rate
Transformation kinetics of alloys under non-isothermal conditions
The overall solid-to-solid phase transformation kinetics under non-isothermal
conditions has been modeled by means of a differential equation method. The
method requires provisions for expressions of the fraction of the transformed
phase in equilibrium condition and the relaxation time for transition as
functions of temperature. The thermal history is an input to the model. We have
used the method to calculate the time/temperature variation of the volume
fraction of the favored phase in the alpha-to-beta transition in a zirconium
alloy under heating and cooling, in agreement with experimental results. We
also present a formulation that accounts for both additive and non-additive
phase transformation processes. Moreover, a method based on the concept of path
integral, which considers all the possible paths in thermal histories to reach
the final state, is suggested.Comment: 16 pages, 7 figures. To appear in Modelling Simul. Mater. Sci. En
Highly turbulent solutions of LANS-alpha and their LES potential
We compute solutions of the Lagrangian-Averaged Navier-Stokes alpha-model
(LANS) for significantly higher Reynolds numbers (up to Re 8300) than have
previously been accomplished. This allows sufficient separation of scales to
observe a Navier-Stokes (NS) inertial range followed by a 2nd LANS inertial
range. The analysis of the third-order structure function scaling supports the
predicted l^3 scaling; it corresponds to a k^(-1) scaling of the energy
spectrum. The energy spectrum itself shows a different scaling which goes as
k^1. This latter spectrum is consistent with the absence of stretching in the
sub-filter scales due to the Taylor frozen-in hypothesis employed as a closure
in the derivation of LANS. These two scalings are conjectured to coexist in
different spatial portions of the flow. The l^3 (E(k) k^(-1)) scaling is
subdominant to k^1 in the energy spectrum, but the l^3 scaling is responsible
for the direct energy cascade, as no cascade can result from motions with no
internal degrees of freedom. We verify the prediction for the size of the LANS
attractor resulting from this scaling. From this, we give a methodology either
for arriving at grid-independent solutions for LANS, or for obtaining a
formulation of a LES optimal in the context of the alpha models. The fully
converged grid-independent LANS may not be the best approximation to a direct
numerical simulation of the NS equations since the minimum error is a balance
between truncation errors and the approximation error due to using LANS instead
of the primitive equations. Furthermore, the small-scale behavior of LANS
contributes to a reduction of flux at constant energy, leading to a shallower
energy spectrum for large alpha. These small-scale features, do not preclude
LANS to reproduce correctly the intermittency properties of high Re flow.Comment: 37 pages, 17 figure
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