The inertial subrange in turbulent pipe flow: centreline

The inertial-subrange scaling of the axial velocity component is examined for the centreline of turbulent pipe flow for Reynolds numbers in the range 249⩽Reλ⩽986. Estimates of the dissipation rate are made by both integration of the one-dimensional dissipation spectrum and the third-order moment of the structure function. In neither case does the non-dimensional dissipation rate asymptote to a constant; rather than decreasing, it increases indefinitely with Reynolds number. Complete similarity of the inertial range spectra is not evident: there is little support for the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 32, 1941a, pp. 16–18; Dokl. Akad. Nauk SSSR, vol. 30, 1941b, pp. 301–305) and the effects of Reynolds number are not well represented by Kolmogorov’s ‘extended similarity hypothesis’ (J. Fluid Mech., vol. 13, 1962, pp. 82–85). The second-order moment of the structure function does not show a constant value, even when compensated by the extended similarity hypothesis. When corrected for the effects of finite Reynolds number, the third-order moments of the structure function accurately support the ‘four-fifths law’, but they do not show a clear plateau. In common with recent work in grid turbulence, non-equilibrium effects can be represented by a heuristic scaling that includes a global Reynolds number as well as a local one. It is likely that non-equilibrium effects appear to be particular to the nature of the boundary conditions. Here, the principal effects of the boundary conditions appear through finite turbulent transport at the pipe centreline, which constitutes a source or a sink at each wavenumber

Study of the structure of turbulent shear flows at supersonic speeds and high Reynolds number

A major effort to improve the accuracies of turbulence measurement techniques is described including the development and testing of constant temperature hot-wire anemometers which automatically compensate for frequency responses. Calibration and data acquisition techniques for normal and inclined wires operated in the constant temperature mode, flow geometries, and physical models to explain the observed behavior of flows are discussed, as well as cooperation with computational groups in the calculation of compression corner flows

A new friction factor relationship for fully developed pipe flow

The friction factor relationship for high-Reynolds-number fully developed turbulent pipe flow is investigated using two sets of data from the Princeton Superpipe in the range 31×10^3 ≤ ReD ≤ 35×10^6. The constants of Prandtl’s ‘universal’ friction factor relationship are shown to be accurate over only a limited Reynolds-number range and unsuitable for extrapolation to high Reynolds numbers. New constants, based on a logarithmic overlap in the mean velocity, are found to represent the high-Reynolds-number data to within 0.5%, and yield a value for the von Kármán constant that is consistent with the mean velocity profiles themselves. The use of a generalized logarithmic law in the mean velocity is also examined. A general friction factor relationship is proposed that predicts all the data to within 1.4% and agrees with the Blasius relationship for low Reynolds numbers to within 2.0%

A semi-Lagrangian scheme for the game pp-Laplacian via pp-averaging

We present and analyze an approximation scheme for the two-dimensional game $p$-Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian scheme which exploits the idea of $p$-averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game $p$-Laplacian. We also present a numerical implementation of the scheme for different values of $p$; the numerical tests show that the scheme is accurate.Comment: 34 pages, 3 figures. To appear on Applied Numerical Mathematic

Longitudinal spin-relaxation in nitrogen-vacancy centers in electron irradiated diamond

We present systematic measurements of longitudinal relaxation rates ($1/T_1$) of spin polarization in the ground state of the nitrogen-vacancy (NV$^-$) color center in synthetic diamond as a function of NV$^-$ concentration and magnetic field $B$. NV$^-$ centers were created by irradiating a Type 1b single-crystal diamond along the [100] axis with 200 keV electrons from a transmission electron microscope with varying doses to achieve spots of different NV$^-$ center concentrations. Values of ($1/T_1$) were measured for each spot as a function of $B$.Comment: 4 pages, 8 figure

Theoretical He I Emissivities in the Case B Approximation

We calculate the He I case B recombination cascade spectrum using improved radiative and collisional data. We present new emissivities over a range of electron temperatures and densities. The differences between our results and the current standard are large enough to have a significant effect not only on the interpretation of observed spectra of a wide variety of objects but also on determinations of the primordial helium abundance.Comment: Accepted to ApJ

European Private Law: A Plea for a Spontaneous Legal Order

This contribution focuses on European integration through private law. After a sketch of the existing European acquis in the field of the law of contract, tort and property, the question is discussed whether there is a need for harmonisation in view of the goals the European Union set itself. Subsequently, the question of how to design a future European private law is answered. In the field of contract law, the European Commission now follows a two-track policy: it intends to draft a ‘Common Frame of Reference’ (‘CFR’) as well as furthering the debate on the possibility of an optional code. It is debated what the contents of these two instruments should be and how they should be created, but also the more fundamental question as to whether they will really contribute to the solving of the present problems with the European acquis is touched upon. Finally, the influence of ‘Europe’ on national private law is looked at from a critical perspective. The author adopts the view that uniform private law should come about in a Hayekian way of a spontaneous legal order

Defining adaptation in a generic multi layer model : CAM: the GRAPPLE conceptual adaptation model

Authoring of Adaptive Hypermedia is a difficult and time consuming task. Reference models like LAOS and AHAM separate adaptation and content in different layers. Systems like AHA! offer graphical tools based on these models to allow authors to define adaptation without knowing any adaptation language. The adaptation that can be defined using such tools is still limited. Authoring systems like MOT are more flexible, but usability of adaptation specification is low. This paper proposes a more generic model which allows the adaptation to be defined in an arbitrary number of layers, where adaptation is expressed in terms of relationships between concepts. This model allows the creation of more powerful yet easier to use graphical authoring tools. This paper presents the structure of the Conceptual Adaptation Models used in adaptive applications created within the GRAPPLE adaptive learning environment, and their representation in a graphical authoring tool