ALBERT

Description: In forensic sciences, radiocarbon found in modern human nails and hair is evaluated to determine the year of death. However, 14C analyses presented herein of fingernails and hair from the same infant demonstrated 14C values of hair that were lower than would be expected (e.g. depleted relative to the fingernails by at least 10‰). These results prompted a series of 14C measurements on infant hair strands, fingernails, and infant shampoo, which suggested the presence of C contamination due to cosmetic products. To further evaluate these discrepancies, several hair strands and fingernail samples from multiple donors were collected, pretreated by several approaches, and measured using isotopic analysis (δ13C, δ15N, and C/N as well as 14C accelerator mass spectrometry). SEM images of the surface of chemically pretreated hair strands were also taken to inspect the performance of the chemical pretreatments applied. Our 14C and stable isotope results show that modern human hair is likely contaminated with fossil-fuel-derived carbon, which is found in most hair care products. Currently, the various chemical pretreatments available in the literature and presented herein show that it is not possible to completely remove foreign carbon contaminates. Thus, the human 14C and δ13C values between keratinous tissues (fingernails and hair) arc not in agreement. From these observations, it becomes apparent that isotopic interpretations using human hair should be used with extreme caution and additional work is needed for its use in forensic and dietary research.

Description: Intended as a contribution towards understanding the multiple processes entailed in the development of coastal sand bars due to wave action, this theoretical and experimental study deals with the Bragg reflection of long-crested surface waves in a water channel whose bed is corrugated sinusoidally. The present findings complement and in a few respects improve upon those in previous investigations, particularly Davies & Heathershaw (1984). In §2 a linearized theory is presented, being directed to the elucidation of experimental situations where monochromatic waves propagate into a channel with a limited stretch of corrugations on its bed and an imperfectly absorbing beach at its far end. Allowance is made fully for dispersive effects (§2.2) and approximately for small frictional effects (§2.3). Points of interpretation (§2.4) include accounts of degenerate but non-trivial solutions that apply at frequencies terminating the stopping band, wherein the spatial wavefield has an exponential envelope. The experimental results presented in §4 derive from measurements of the wavefield over a stretch of 24 corrugations, at various frequencies both inside and outside the stopping band. Quantitative comparisons (§§4.2 and 4.3) demonstrate close agreements with the theory. © 1987, Cambridge University Press. All rights reserved.

Description: A theoretical study is made of shearing flows bounded by a simple-harmonic wavy surface, the main object being to calculate the normal and tangential stresses on the boundary. The type of flow considered is approximately parallel in the absence of the waves, being exemplified by two-dimensional boundary layers over a plane. Account is taken of viscosity; but, as the Reynolds number is assumed to be large, its effects are seen to be confined within narrow ‘friction layers’, one of which adjoins the wave and another surrounds the ‘critical point’ where the velocity of flow equals the wave velocity. The boundary conditions are made as general as possible by including the three cases where respectively the boundary is rigid, flexible yet still solid, or completely mobile as if it were the interface with a second fluid.The theory is developed on the model of stable laminar flow, although it is proposed that the same theory may usefully be applied also to examples of turbulent flow considered as ‘pseudo-laminar’ with velocity profiles corresponding to the mean-velocity distribution. Use is made of curvilinear co-ordinates which follow the contour of the wave-train. This admits a linearized form of the problem whose validity requires only that the wave amplitude be small in comparison with the wavelength, even when large velocity gradients exist close to the boundary. The analysis is made largely without restriction to particular forms of the velocity profile; but eventually consideration is given to the example of a linear profile and the example of a boundary-layer profile approximated by a quarter-period sinusoid. In § 7 some general methods are set out for the treatment of disturbed boundary-layer proses: these apply with greatest precision to thin boundary layers, but are also useful for the initially very steep but on the whole fairly diffuse profiles which occur in most practical instances of turbulent flow over waves.The phase relationships found between the stresses and the wave elevation are discussed for several examples, and their interest in connexion with problems of wave generation by wind is pointed out. It is shown that in most circumstances the stresses are distributed in much the same way as if the leeward slopes of the waves were sheltered. For instance, the pressure distribution often has a substantial component in phase with the wave slope, just as if a wake were formed behind each wave crest—although of course actual separation effects are outside the scope of the present theory. In this aspect, the analysis amplifies the work of Miles (1957).

Description: The theoretical study presented in this paper was inspired by the recent report (Krämer 1960) of experiments showing that considerable reductions in the drag of an underwater solid body were achieved by covering it with a skin of flexible material; apparently this effect was due to the boundary layer being stabilized in the presence of the skin, so that transition to a turbulent condition of flow was prevented or at least delayed. The stability problem for flow past a flexible boundary is here formulated in a general way which allows a full exploration of the possibility of a stabilizing effect without the need to assign specific properties to the flexible medium; the collective properties of possible boundaries are represented by a ‘response coefficient’ α (a sort of ‘effective compliance’) measuring the deflexion of the surface under a travelling sinusoidal distribution of pressure.A remarkably simple analytical connexion is established between the present general problem and the corresponding stability problem for the boundary layer on a rigid plane wall, and hence many details of the existing theory of hydrodynamic stability are immediately useful. However, the presence of the flexible boundary admits possible modes of instability additional to those which already exist when the boundary is rigid, and clearly every mode must be considered with regard to practical measures for stabilization—that is to say, it might be useless to inhibit one mode by a device which lets in another. What is believed to be an essentially complete interpretation of the over-all possibilities is deduced on recognizing three more or less distinct forms of instability. The first comprises waves resembling the unstable waves which can arise in the presence of a rigid boundary, but now being modified by the effects of flexibility. These waves tend to be stabilized when the boundary has a compliant response to them, which means the respective wave velocity has to be less than the velocity of free surface waves on the boundary; but it is found that the effect of internal friction in the flexible medium is actually destabilizing. The second form of instability is essentially a resonance effect and comprises waves travelling at very nearly the velocity of free surface waves. These waves can only be excited when the latter velocity falls below the free-stream velocity; they are scarcely affected by the viscosity of the fluid since the ‘wall friction layer’ is largely cancelled, so that damping due to the medium itself becomes the only stabilizing factor. The third form is akin to Kelvin–Helmholtz instability.This interpretation of the theoretical results seems to point to the essential factors in the operation of a flexible skin as a stabilizing device, and accordingly in the concluding secttion of the paper two alternative sets of criteria are proposed each of which would provide a logical basis for designing such a device. The principle of the first alternative explains the success of Gamer's invention, but the second appears equally promising and the relative advantages of the two can really be proved only by further experiment.

Description: This paper discusses the general idea that in systems where a flexible solid is coupled with a flowing fluid three different types of instability are possible. These were originally designated by Brooke Benjamin (1960) as ‘class A’, ‘class B’ and ‘Kelvin-Helmholtz’ instability, and their collective significance has been clarified recently by Landahl (1962). Class A and class B disturbances are essentially oscillations involving conservative energy-exchanges between the fluid and solid, but their stability is determined by the net effect of irreversible processes, which include dissipation and energy-transfer to the solid by non-conservative hydrodynamic forces. Dissipation in the solid tends to stabilize class B distrbances but to destabilize class A ones. Class C instability (i.e. the ‘Kelvin-Helmholtz’ type) occurs when conservative hydrodynamic forces cause a unidirectional transfer of energy to the solid. In § 2 this idea is examined fundamentally by way of the Lagrangian method of generalized co-ordinates, and in § 3 the example of inviscid-fluid flow past a flexible plane boundary is considered. The treatment of this example amplifies the work of Landahl, in particular by including the effect of non-conservative forces of the kind investigated by Miles in his series of papers on water-wave generation by wind. © 1963, Cambridge University Press. All rights reserved.

Description: This paper presents a broad investigation into the properties of steady gravity currents, in so far as they can be represented by perfect-fluid theory and simple extensions of it (like the classical theory of hydraulic jumps) that give a rudimentary account of dissipation. As usually understood, a gravity current consists of a wedge of heavy fluid (e.g. salt water, cold air) intruding into an expanse of lighter fluid (fresh water, warm air); but it is pointed out in § 1 that, if the effects of viscosity and mixing of the fluids at the interface are ignored, the hydrodynamical problem is formally the same as that for an empty cavity advancing along the upper boundary of a liquid. Being simplest in detail, the latter problem is treated as a prototype for the class of physical problems under study: most of the analysis is related to it specifically, but the results thus obtained are immediately applicable to gravity currents by scaling the gravitational constant according to a simple rule.In § 2 the possible states of steady flow in the present category between fixed horizontal boundaries are examined on the assumption that the interface becomes horizontal far downstream. A certain range of flows appears to be possible when energy is dissipated; but in the absence of dissipation only one flow is possible, in which the asymptotic level of the interface is midway between the plane boundaries. The corresponding flow in a tube of circular cross-section is found in § 3, and the theory is shown to be in excellent agreement with the results of recent experiments by Zukoski. A discussion of the effects of surface tension is included in § 3. The two-dimensional energy-conserving flow is investigated further in § 4, and finally a close approximation to the shape of the interface is obtained. In § 5 the discussion turns to the question whether flows characterized by periodic wavetrains are realizable, and it appears that none is possible without a large loss of energy occurring. In § 6 the case of infinite total depth is considered, relating to deeply submerged gravity currents. It is shown that the flow must always feature a breaking ‘head wave’, and various properties of the resulting wake are demonstrated. Reasonable agreement is established with experimental results obtained by Keulegan and others.

Description: A theoretical and experimental investigation is reported dealing with the onset of buckling in a horizontal layer of highly viscous liquid. The layer floats on a heavier liquid with negligible viscosity, and at rest is stabilized by gravity and surface tension. When sheared at a sufficient rate, the flat configuration of the layer becomes unstable; and the aim of the investigation is to establish the relation between critical values of the shearing rate and values of the layer’s thickness and other physical parameters. A primitive theory based on membrane approximations is first reviewed and its deficiencies are appreciated. Then a more reliable theory is developed, providing estimates of values taken by a dimensionless shear stress f at the threshold of instability. The values fcare found to depend primarily on a dimensionless number H proportional to the thickness of the layer. Experiments on sheared layers of silicone oil with various high viscosities are then described. Measured values offc plotted against H over a wide range are shown to be in satisfactory agreement with the theory. Finally, discrepancies between previous experimental results and ours are discussed. © 1988, Cambridge University Press. All rights reserved.

Description: Standard approximations expressing the drag of a sphere as a function of Reynolds number are reappraised in the light of the evident requirement that drag reverses with the direction of motion. It is thereby highlighted that the relation between the drag and the velocity of a sphere is not analytic. Another, simpler example is cited to illustrate a non-analytic relation between physical properties, which is appreciated to be a common feature of hydrodynamic models that rely on the abstract notion of an infinite incompressible fluid. © 1993, Cambridge University Press. All rights reserved.

Description: The exact problem of steady periodic waves (Stokes waves) on the surface of an ideal liquid above a horizontal bottom is reconsidered in order to confirm a general property conjectured by Benjamin&Lighthill (1954). Specifically, in terms of parameters r and s proportional respectively to the total-head and flow-force constants for steady flows, such waves are proved to realize points (r, s) inside the region of the (r, s)-plane that is bounded by the cusped curve representing all possible uniform streams. A corresponding attribute of steady periodic waves on the surface of an infinitely deep ideal liquid will also be demonstrated. The concluding discussion refers to steady water waves that are not periodic Stokes waves, and comments with reference to Appendix B on the significance of the flow-force invariant s in Hamiltonian representations of the steady-wave problem. © 1995, Cambridge University Press. All rights reserved.

Description: Several new results on the bifurcation and instability of nonlinear periodic travelling waves, at the interface between two fluids in relative motion, in a parametric neighbourhood of a Kelvin-Helmholtz unstable equilibrium are presented. The organizing centre for the analysis is a canonical Hamiltonian formulation of the Kelvin-Helmholtz problem presented in Part 1. When the density ratio of the upper and lower fluid layers exceeds a critical value, and surface tension is present, a pervasive superharmonic instability is found, and as u → u0, where u is the velocity difference between the two layers and u0 is the Kelvin-Helmholtz threshold, the amplitude at which the superharmonic instability occurs scales like (u0 - u)1/2 with u 〈 u0. Other results presented herein include (a) new results on the structure of the superharmonic instability, (b) the discovery of isolated branches and intersecting branches of travelling waves near a critical density ratio, (c) the appearance of Benjamin-Feir instability along branches of waves near the Kelvin-Helmholtz instability threshold and (d) the interaction between the Kelvin-Helmholtz, superhar-monic and Benjamin-Feir instability at low amplitude.