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 $4096^3$. 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 $\delta(t)$ is observed at the highest resolution for $3.7<t<3.85$ 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 $t \simeq 4$. 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 $\delta(t)$ vanishes sufficiently fast at the singularity time. In particular, if a power law is assumed for $\delta(t)$ then its exponent must be greater than some critical value, thus providing a new test that is applied to our $4096^3$ 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 $\delta(t)$ 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 $6144^3$ points, and three different configurations on grids of $4096^3$ 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 $t=2.33$ and $t=2.70.$ 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