Characterizing most irregular small-scale structures in turbulence using local Hölder exponents.

Two scalar fields characterizing respectively pseudo-Hölder exponents and local energy transfers are used to capture the topology and the dynamics of the velocity fields in areas of lesser regularity. The present analysis is conducted using velocity fields from two direct numerical simulations of the Navier-Stokes equations in a triply periodic domain. A typical irregular structure is obtained by averaging over the 213 most irregular events. Such structure is similar to a Burgers vortex, with nonaxisymmetric corrections. A possible explanation for such asymmetry is provided by a detailed time-resolved analysis of birth and death of the irregular structures, which shows that they are connected to vortex interactions, possibly vortex reconnection.

Local estimates of Hölder exponents in turbulent vector fields.

It is still not known whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is Hölder continuous with some exponent h<1 (i.e., not necessarily differentiable) at small scales. Different methods have already been proposed to explore the regularity properties of the velocity field and the estimate of its Hölder exponent h. A first method is to detect potential singularities via extrema of an "inertial" dissipation D*=lim_{ℓ→0}D_{ℓ}^{I} that is independent of viscosity [Duchon and Robert, Nonlinearity 13, 249 (2000)0951-771510.1088/0951-7715/13/1/312]. Another possibility is to use the concept of multifractal analysis that provides fractal dimensions of the subspace of exponents h. However, the multifractal analysis is a global statistical method that only provides global information about local Hölder exponents, via their probability of occurrence. In order to explore the local regularity properties of a velocity field, we have developed a local statistical analysis that estimates locally the Hölder continuity. We have compared outcomes of our analysis with results using the inertial energy dissipation D_{ℓ}^{I}. We observe that the dissipation term indeed gets bigger for velocity fields that are less regular according to our estimates. The exact spatial distribution of the local Hölder exponents however shows nontrivial behavior and does not exactly match the distribution of the inertial dissipation.

Attached flow structure and streamwise energy spectra in a turbulent boundary layer.

On the basis of (i) particle image velocimetry data of a turbulent boundary layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum E_{11}(k_{x}) in a wave-number range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers Re_{τ} considered here which are between 10^{3} and 10^{4}. Instead, we find E_{11}(k_{x})∼k_{x}^{-1-p} where p varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent p characterizes the turbulence levels inside wall-attached streaky structures conditional on the length of these structures. A particular consequence is that the skin friction velocity is not sufficient to scale E_{11}(k_{x}) for wave numbers directly affected by the wall.

Subcritical dynamo bifurcation in the Taylor-Green flow.

We report direct numerical simulations of dynamo generation for flow generated using a Taylor-Green forcing. We find that the bifurcation is subcritical and show its bifurcation diagram. We connect the associated hysteretic behavior with hydrodynamics changes induced by the action of the Lorentz force. We show the geometry of the dynamo magnetic field and discuss how the dynamo transition can be induced when an external field is applied to the flow.

Influence of turbulence on the dynamo threshold.

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale, and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold and increases it for any noise at large scale. For small-scale noise, the result depends on its correlation time and on the magnetic Prandtl number.

Forced stratified turbulence: successive transitions with Reynolds number.

Numerical simulations are made for forced turbulence at a sequence of increasing values of Reynolds number Re keeping fixed a strongly stable, volume-mean density stratification. At smaller values of Re, the turbulent velocity is mainly horizontal, and the momentum balance is approximately cyclostrophic and hydrostatic. This is a regime dominated by so-called pancake vortices, with only a weak excitation of internal gravity waves and large values of the local Richardson number Ri everywhere. At higher values of Re there are successive transitions to (a) overturning motions with local reversals in the density stratification and small or negative values of Ri; (b) growth of a horizontally uniform vertical shear flow component; and (c) growth of a large-scale vertical flow component. Throughout these transitions, pancake vortices continue to dominate the large-scale part of the turbulence, and the gravity wave component remains weak except at small scales.

Scaling laws and vortex profiles in two-dimensional decaying turbulence.

We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A scaling regime is detected when the scaling laws are expressed in units of mean vorticity and integral scale, like predicted in Carnevale et al., Phys. Rev. Lett. 66, 2735 (1991), and it is observed that viscous effects spoil this scaling regime. The exponent controlling the decay of the number of vortices shows some trends toward xi=1, in agreement with a recent theory based on the Kirchhoff model [C. Sire and P. H. Chavanis, Phys. Rev. E 61, 6644 (2000)]. In terms of scaled variables, the vortices have a similar profile with a functional form related to the Fermi-Dirac distribution.

[Computerized management of anticancer chemotherapy]. / Gestion informatisée des soins de chimiothérapie anticancéreuse.

Control of anti-cancer chemotherapeutic management is facilitated by the use of micro-computers. The authors have devised a program in which are entered, as separate records, all data required concerning the patient, the drugs administered, the therapeutic regimens and the controls to be applied during treatment. The computer commands appointments, examinations to be performed, prescriptions and protocols, making all the calculations needed and taking into account those data which restrict the use of drugs. At the end of each course, each record is updated by entering control parameters and new events, so that a detailed history of all the treatments received by all patients is obtained. This last record can be used for statistical purposes and to test compliance with, and response to treatment. The program, produced and distributed by a data-processing service firm, can be used with various micro-computers. It is available to medical groups interested in the treatment of cancer.

Secretion of labelled proteins by the isolated dog pancreas in the response to secretin and cholecystokinin.

We compared the effects of secretin (10 clinical units/hur.) and cholecystokinin-pancreiozymin (CCK-PZ 10 Ivy units/hr.) from G.I.H. Laboratory in Stockholm, Sweden, on the secretion of radioactively labelled proteins in the pancreatic juice. This was carried out on isolated dog pancreas perfused "ex-vivo" with whole heparinized oxygenated blood. CCK-PZ and secretin were infused together and the results compared with a second series of experiments where secretin alone was administered, at the same dose. Both hormones caused a discharge of labelled proteins, which was linear over 55 minutes. Secretin increased the flow rate of the pancreatic juice and to a lesser extent the enzymatic protein output. CCK-PZ stimulated the mass flow of secretory proteins.