The effect of modeled drag reduction on the wall region

The low-dimensional model derived for the wall region of a turbulent boundary layer (Aubry et al., 1988) is applied to a drag-reduced flow. In agreement with some experimental results, drag reduction is modeled by thickening the wall region, which is achieved by applying stretching transformations to the original flow. By application of a Galerkin projection, a set of ordinary differential equations (ODEs) is obtained whose structure is identical to the set corresponding to the unmodified flow. The coefficients of the ODEs are modified in a nontrivial way. The bifurcation diagrams plotted for different values of the stretching parameter are different in detail but the structure is globally the same. In particular, the intermittent behavior which Aubry et al. identified with the cyclic bursting events experimentally observed is still present. The scenario by which intermittency appears through a subcritical Hopf bifurcation in which a heteroclinic cycle is created and disappears through a bifurcation to traveling waves is identical. These results hold for values of the stretching between 1 and 2.65, the value at which the top of the buffer layer reaches the centerline of the pipe. This is in agreement with experimental results for flows whose drag is reduced but which still display intermittency. The bifurcations occur in the stretched flow at increased levels of dissipation (relative to the unstretched flow), consistent with theoretical pictures of drag reduction, in which the increase of scale is due to stabilization by an increase of dissipation in the turbulent part of the flow. Moreover, this method is a systematic way to perturb the coefficients of the ODEs of Aubry et al. (1988). Under this kind of perturbation, the behavior of the solution (in the part of the bifurcation diagram physically relevant) is found to be extremely robust.     

On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer

In this paper we establish some rigorous connections between the dynamics of coherent structures in the wall region of the turbulent boundary layer and the low-dimensional models of the type studied by Aubry et al. (1988). An important first step is to determine what sort of connection is feasible. We choose to study the energy budget of the models in comparison with the energy budget of the real flow. This is done by comparing the respective kinetic energy equations. In the process we reexamine some of the assumptions and approximations of Aubry et al. (1988) and perform order of magnitude analyses to determine when they hold. We find that, for the models developed in that paper, involving modes which do not vary in the streamwise direction, the energy production lies within positive, experimentally determined, bounds. Moreover, the dissipation due to neglected modes may be reproduced correctly with an order 1 value of the Heisenberg parameter , as assumed by Aubry et al. This work was supported by AFOSR F49620-92-J-0287.     

Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

The determination of 5 anticoccidial drugs (nicarbazin,lasalocid, monensin,salinomycin and narasin) in animal livers and eggs by liquid chromatography linked with tandem mass spectrometry (LC-MS-MS)

A method has been developed for the simultaneous extraction and determination of five of the most commonly used anticoccidial drugs (nicarbazin, lasalocid, monensin, narasin and salinomycin) from livers and eggs by LC-MS-MS. Results show good repeatability, with mean spiked recoveries for nicarbazin, lasalocid, monensin, narasin and salinomycin in poultry livers in the average range of 92-118%, and 86-110% in eggs. The detection limit is at 1 ng ml(-1) for all the named compounds and a quantitation level of 2.5 ng g(-1) has been achieved. A high throughput of samples is achievable using this method which allows the analysis of up to 40 samples by one analyst in a day.     

Extension of Heisenberg's model for spectral transfer to second order fluids in turbulent flow

A generalization of the eddy viscosity concept permits an extension of the Heisenberg model for spectral energy transfer. The results are applied to the isotropic homogeneous turbulent flow of an incompressible second order fluid. This work was supported by the U.S. Office of Naval Research, Fluid Mechanics Branch, under Contract Nonr 656(33) and is taken from the Ph.D. Dissertation of the first author in the department of Aerospace Engineering, March 1966.     

Precipitation and solute distribution in an interrupted-aged Al–Mg–Si–Cu alloy

Quantitative analysis of the precipitate species and solute distribution was carried out on Al–Mg–Si–Cu alloy 6061 aged to peak hardness using a conventional T6 heat treatment and the so-called T6I6 heat treatments. In this latter, a dwell period at reduced temperature (65°C) is introduced into the T6 ageing cycle (at 177°C or 150°C) which modifies the microstructure and results in the simultaneous improvement of both tensile properties and fracture toughness. Analysis of three-dimensional atom probe data reveals that the superior mechanical properties of the T6I6/177 temper are achieved by a combined effect of a greater consumption of solute atoms by precipitates, an increased number density of fine precipitates and the presence of greater fractions of the effective strengthening precipitates in the final microstructure. Three types of precipitates were found to be characteristic of the peak aged conditions: β′′ precipitates, Guinier–Preston zones and Mg–Si(–Cu) co-clusters. The composition of the strengthening precipitates was found to vary over a wide range for the different heat treatment schedules, corresponding to a variation in the number density of stable nuclei, without any accompanying change in their morphology. All precipitates were found to contain substantial quantities of aluminium. The results also indicate that the strengthening precipitates are preferentially formed from Si-rich nuclei that contain Cu atoms, as opposed to Cu-free nuclei.     

A Century of Turbulence

A brief, superficial survey of some very personal nominations for highpoints of the last hundred years in turbulence. Some conclusions can be dimly seen. This field does not appear to have a pyramidal structure, like the best of physics. We have very few great hypotheses. Most of our experiments are exploratory experiments. What does this mean? We believe it means that, even after 100 years, turbulence studies are still in their infancy. We are naturalists, observing butterflies in the wild. We are still discovering how turbulence behaves, in many respects. We do have a crude, practical, working understanding of many turbulence phenomena but certainly nothing approaching a comprehensive theory, and nothing that will provide predictions of an accuracy demanded by designers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stereocontrolled synthesis of lepadiformine A

In this paper we present results of a study into whether the tricyclic core of the lepadiformines A-C can be accessed via intramolecular hetero-Diels-Alder cycloaddition. We are able to demonstrate that such a process is possible and that the reaction proceeds in an endo-selective fashion, providing the correct relative stereochemistry for this family of natural products. By employing this approach we have been able to develop a short (7 step) synthesis of (+/-)-lepadiformine A, starting from commercially-available trans-2-nonenal.