bluuebunny/crossref_metadata_2025 huggingface dataset:
COERCED FIRST SEXUAL INTERCOURSE AND SELECTED REPRODUCTIVE HEALTH OUTCOMES AMONG YOUNG WOMEN IN KWAZULU-NATAL, SOUTH AFRICA
Authors: MAHARAJ PRANITHA , MUNTHREE CHANTAL
Published: March 2006

Coercion may play an important role in compelling young women to engage in sexual intercourse at an early age. With a decline in age at first intercourse and increased reporting of coercive first sex, concerns of adverse reproductive health outcomes such as unintended pregnancy and sexually transmitted infections (STIs), including HIV, have become important issues, particularly in the context of a high HIV prevalence. This paper uses data collected in 2001 from the second round of a longitudinal study of 1130 sexually experienced young women in KwaZulu-Natal to investigate the relationship between coerced first intercourse and selected reproductive health outcomes and behaviours. Nearly 46% of all sexually experienced young women had reported that their first sexual encounter had been coerced. Young women who reported being coerced at first sex were significantly more likely to be Black and living in an urban area. Those who had been coerced at first sex were also more likely to report having had an STI and having experienced unintended pregnancy, than those who had not been coerced at first sex. Coercion at first sex is an important social and public health problem that has a serious impact on the reproductive health and behaviours of young women. Interventions should directly address the issue of sexual coercion by ensuring young women are aware of their reproductive rights.
Effects of prepartum milking on postpartum reproduction, udder health and production performance in first-calf dairy heifers
Authors: Bowers Susan , Gandy Scott , Graves Kenneth , Eicher Susan , Willard Scott
Published: March 2006

Postpartum production performance of dairy heifers may be enhanced by prepartum milking by alleviating the stress of the periparturient period. The objective of this study was to determine the impact of prepartum milking of dairy heifers on postpartum reproduction, udder health, milk production and other associated production characteristics. Pregnant heifers (Holstein, n=21; Jersey n=10) were assigned to either a prepartum milked (premilked, n=15) or control (n=16) group. Premilked heifers were milked twice daily starting 3 weeks prior to anticipated calving dates, and milk yield recorded at each milking. All heifers were evaluated on days 21, 14 and 7 before calving, and udder oedema scores and milk conductivity readings were recorded. Following calving, measurements were taken twice weekly to assess udder oedema, milk conductivity (indicative of udder infection), and reproductive health, which included palpation for uterine tone and uterine position, vaginal electrical impedance (VEI) and the quantification of cross-sectional area of the uterine horns (uterine difference) by transrectal ultrasonography. Uterine tone, uterine position, uterine difference, and VEI did not differ (P>0·10) with treatment. Overall, up to week six inclusive, postpartum premilked heifers had lower (P<0·01) udder oedema scores than control heifers and up to week five inclusive, had lower (P<0·01) milk conductivity readings (indicative of fewer incidences of udder infections) than control heifers. The premilked heifers of both breeds produced more milk (P<0·01) at calving and more milk overall from calving to day 60 postpartum than the control heifers. In summary, udder health and milk production were improved post calving in premilked heifers compared with controls. However, no overt differences in reproductive characteristics were observed between the premilked and control heifers.
Biosensor assay for determination of haptoglobin in bovine milk
Authors: Åkerstedt Maria , Björck Lennart , Persson Waller Karin , Sternesjö Åse
Published: March 2006

Despite more than 30 years of research into mastitis diagnostics, there are few alternatives to the somatic cell count (SCC) in practical use for identification of cows with subclinical mastitis. Mastitis is not only an animal welfare problem, but also affects the yield, composition and technological properties of milk. Hence, dairy cooperatives give farmers a premium quality payment to encourage low SCC although there is no clear scientific data defining the level of SCC in bulk tank milk that is associated with additional benefits in terms of milk quality. Recent research on alternative markers for inflammatory reactions in the lactating cow, e.g. in mastitis, includes investigations of the acute phase protein, haptoglobin (Hp). So far, the content of Hp in milk has mainly been studied in relation to mastitis diagnostics, with little attention given to its importance for milk composition and technological properties. At present, Hp in milk is measured using ELISA, but this technique is not suitable for routine large-scale analysis. In recent years, optical biosensor technology has been used for automated and rapid quantitative analysis of different components in milk, but so far not for analysis of acute phase proteins. The aim of the present study was to develop a rapid and sensitive biosensor method to determine Hp in milk. An affinity sensor assay based on the interaction between Hp and haemoglobin was developed using surface plasmon resonance (SPR) biosensor technology. The assay was used to analyse Hp in composite milk samples from cows without any clinical signs of mastitis and quarter milk samples with a weak to strong reaction in the California Mastitis Test (CMT). A commercial ELISA for determination of Hp in milk was used for comparison. The limit of detection (LOD) of the biosensor assay was determined as 1·1 mg/l. Within-assay and between-day variations were determined both with bulk tank milk spiked with human Hp and with composite milk samples containing bovine Hp. Coefficients of variation varied between 3·6 and 8·6% at concentrations between 4·0 and 12 mg/l, respectively. Agreement between the results obtained by the biosensor assay and the ELISA was satisfactory; however, the results obtained by the biosensor were generally lower than the results obtained by the ELISA. Possible explanations for this observation are discussed.
Hypertonic NaCl infusions affect milk composition in goats
Authors: Olsson Kerstin , Mengistu Urge , Stein Jennie , Bekele Tafesse , Bruckmaier Rupert M
Published: March 2006

The capability of goats to maintain milk production during water deprivation is remarkable and not yet fully understood. The aim of the present study was to investigate whether intravenous infusions of hypertonic NaCl cause release of both vasopressin and oxytocin and whether the peptides, in combination with the hyperosmolality, affect milk flow and milk composition. Six Swedish domestic landrace goats in their first to third lactation were milked every 30 min during experiments. Hypertonic NaCl (HNaCl) or isotonic NaCl (IsoNaCl) were infused for 90 min. Goats were not allowed to drink during infusions. Plasma vasopressin concentration increased during HNaCl infusions, and did not change in response to IsoNaCl infusions. Plasma oxytocin concentration did not change during either infusion. Milk flow was maintained during the infusions. Milk fat concentration decreased in the three samples taken before onset of the infusions, but then increased gradually during HNaCl infusions, while it continued to fall during the IsoNaCl infusions. Milk osmolality followed the rise in plasma osmolality during the HNaCl infusions and did not change in IsoNaCl experiments. Milk lactose concentration increased throughout both series of experiments, the concentration being higher during HNaCl infusions. Milk protein concentration did not change during HNaCl infusions, but fell in the IsoNaCl experiments. It is concluded that the hyperosmolality in combination with elevated plasma vasopressin levels did not disturb the secretory activity of the mammary cells, but rather facilitated emptying of the alveolar milk. Such a mechanism may help to explain the sustained milk production in water deprived goats.
The refraction of sea waves in shallow water
Authors: Longuet-Higgins M. S.
Published: March 2006

This paper considers the changes that occur in the character of short-crested sea waves when they are refracted by a shallowing depth of water. Besides a change in mean wave-length and direction there is also a change (usually an increase) in the mean length of the crests. If the waves approach obliquely they become skew, that is, the crests become staggered one behind another.

When a short-crested sea is superposed on a long-creasted swell, refraction tends to amplify the longer waves more than the shorter ones. This also produces an increase in the mean length of the crests.

Numerical examples are given.
On steady laminar flow with closed streamlines at large Reynolds number
Authors: Batchelor G. K.
Published: March 2006

Frictionless flows with finite voticity are usually made determinate by the imposition of boundary conditions specifying the distribution of vorticity ‘at infinity’. No such boundary conditions are available in the case of flows with closed streamlines, and the velocity distributions in regions where viscous forces are small (the Reynolds number of the flow being assumed large) cannot be made determinate by considerations of the fluid as inviscid. It is shown that if the motion is to be exactly steady there is an integral condition, arising from the existence of viscous forces, which must be satisfied by the vorticity distribution no matter how small the viscosity may be. This condition states that the contribution from viscous forces to the rate of change of circulation round any streamline must be identically zero. (In cases in which the vortex lines are also closed, there is a similar condition concerning the circulation round vortex lines.)

The inviscid flow equations are then combined with this integral condition in cases for which typical streamlines lie entirely in the region of small viscous forces. In two-dimensional closed flows, the vorticity is found to be uniform in a connected region of small viscous forces, with a value which remains to be determined—as is done explicitly in one simple case—by the condition that the viscous boundary layer surrounding this region must also be in steady motion. Analogous results are obtained for rotationally symmetric flows without azimuthal swirl, and for a certain class of flows with swirl having no interior boundary to the streamlines in an axial plane, the latter case requiring use of the fact that the vortex lines are also closed. In all these cases, the results are such that the Bernoulli constant, or ‘total head’, varies linearly with the appropriate stream function, and the effect of viscosity on the rate of change of vorticity at any point vanishes identically.
On the flow in channels when rigid obstacles are placed in the stream
Authors: Benjamin T. Brooke
Published: March 2006

A previous paper drew attention to the collective importance of three physical quantities Q, R, S associated with ideal fluid flow in a horizontal channel. Invariability of these quantities at different cross-sections of the flow implies respectively conservation of flow rate, energy and momentum; and their values determine a wave-train uniquely. The properties of Q, R, S are recalled in the present paper to account for the various effects of lowering a rigid obstacle into a stream. The conditions giving rise to dissimilar types of flow are examined; in particular, the circumstances causing stationary waves on the downstream side are clearly distinguished from those under which the receding stream assumes a uniform ‘supercritical’ state. A well-known result in the theory of the solitary wave is shown to apply to the receding stream even when the extreme conditions for the wave are exceeded; although it fails to account for a region close to the obstacle where the curvature of the streamlines becomes large. In passing, a feature of the theory is shown to bear on the practical problem of producing a uniform stream. Precise calculations are made for the flow under a vertical sluice-gate and under an inclined plane. To account for the region near the bottom edge of the sluice-gate, a method based on conformal transformation is used whereby an unknown curve in the hodograph plane is approximated by an arc of an ellipse. The accuracy of the results is more than sufficient for practical purposes, and they compare favourably with solutions previously obtained by relaxation methods. A number of experiments with water streams are described.
Forces, moments, and added masses for Rankine bodies
Authors: Landweber L. , Yih C. S.
Published: March 2006

The dynamical theory of the motion of a body through an inviscid and incompressible fluid has yielded three relations: a first, due to Kirchhoff, which expresses the force and moment acting on the body in terms of added masses; a second, initiated by Taylor, which expresses added masses in terms of singularities within the bòdy; and a third, initiated by Lagally, which expresses the forces and moments in terms of these singularities. The present investigation is concerned with generalizations of the Taylor and Lagally theorems to include unsteady flow and arbitrary translational and rotational motion of the body, to present new and simple derivations of these theorems, and to compare the Kirchhoff and Lagally methods for obtaining forces and moments. In contrast with previous generalizations, the Taylor theorem is derived when other boundaries are present; for the added-mass coefficients due to rotation alone, for which no relations were known, it is shown that these relations do not exist in general, although approximate ones are found for elongated bodies. The derivation of the Lagally theorem leads to new terms, compact expressions for the force and moment, and the complete expressions of the forces and moments in terms of singularities for elongated bodies.
The wave drag at zero lift of slender delta wings and similar configurations
Authors: Lighthill M. J.
Published: March 2006

Ward's slender-body theory of supersonic flow is applied to bodies terminating in either (i) a single trailing edge at right angles to the oncoming supersonic stream, or (ii) two trailing edges at right angles to one another as well as to the oncoming stream, or (iii) a cylindrical section with two or four identical fins equally spaced round it. The wave drag at zero lift, D, is given by the expression
$\frac {D}{\frac {1}{2}\rho U^2} &=& \frac {1}{2\pi}\int^l_0 \int^l_0 log\frac{1}{|s-z|}S^{\prime \prime}(s)S^{\prime \prime}(z)dsdz - \\ &-& \frac{S^\prime (l)}{\pi}\int^l_0 log \frac {l}{l-z}S^{\prime \prime}(z)dz + \frac{S^{\prime 2}(l)}{2\pi} \{ log \frac{l}{(M^2-1)^{1|2}b}+k \} $
where l is the length of the body, b the semi-span of the trailing edge (or length of trailing edge of a single fin), and S(z) is the cross-sectional area of the body at a distance z behind the apex. The constant k depends on the distribution of trailing-edge angle along the span for each trailing-edge configuration. In case (i) it is 1·5 for a uniform distribution of trailing-edge angle and 1·64 for an elliptic distribution. In case (ii) it is 1·28 for a uniform distribution and 1·44 for an elliptic distribution. Study of case (iii) indicates that interference effects due to the presence of the body reduce the drag of the fins. For example, with a uniform distribution of trailing-edge angle, k for two fins falls from 1·5 in the absence of a body to 1·06 when the body radius equals the trailing-edge semi-span, while k for four fins falls from 1·28 to 0·45 under the same conditions.

Where ordinary finite-wing theory is applicable, the present method must agree with it for small $(M^2-1)^{1|2}b|l$, and this is confirmed by two examples (§3), but within the limit imposed by slenderness the present method is of course more widely applicable, as well as simpler, than finite-wing theory.

It is not known experimentally whether slender-body theory gives accurate predictions of drag at zero lift, for the shapes here discussed, under the conditions for which on theoretical grounds it might be expected to do so. It should be noted that, although tests have not yet been made on ideally suitable bodies, no clear the drag is therefore twice that of a wing made up of two of them. The final stages of the process cannot be represented by slender-body theory, but the initial trend may well be indicated fairly accurately.
A proposal concerning laminar wakes behind bluff bodies at large Reynolds number
Authors: Batchelor G. K.
Published: March 2006

This note advocates a model of the steady flow about a bluff body at large Reynolds number which is different from the classical free-streamline model of Helmholtz and Kirchhoff. It is suggested that, although the free-streamline model may be a proper solution of the Navier-Stokes equation with μ = 0, it is unlikely to be the limit, as μ → 0, of the solution describing the steady flow due to the presence of a bluff body in an otherwise uniform stream. The limit solution proposed here is one which gives a closed wake.

A closed wake contains a standing eddy, or eddies, whose general features can be inferred from the results of an earlier investigation of steady flow in a closed region at large Reynolds number. In all cases, the drag (coefficient) on the body tends to zero as the Reynolds number tends to infinity. The proccedure for finding the details of the closed wake behind two-dimensional and axisymmetrical bodies is described, although no particular case has yet been worked out.
The method of characteristics for steady supersonic rotational flow in three dimensions
Authors: Holt Maurice
Published: March 2006

The method of characteristics for steady supersonic flow problems in three dimensions, due to Coburn & Dolph (1949), is extended so that flow with shocks and entropy changes may be treated. Equations of motion based on Coburn & Dolph's characteristic coordinate system are derived and a scheme is described for solving these by finite differences.

A linearized method of characteristics is developed for calculating perturbations of a given three-dimensional field of flow. This is a generalization of the method evolved by Ferri (1952) for perturbations of plane flow and conical flow.
The influence of radiative transfer on cellular convection
Authors: Goody R. M.
Published: March 2006

This paper presents an approximate solution of the problem of the onset of convection between plane-parallel plates heated from below when the fluid between them absorbs and emits thermal radiation. A complete solution to this problem would be extremely difficult, and the equation of radiative transfer is therefore developed in two approximate forms, one appropriate to an opaque medium, the other to a transparent medium. This equation is then combined with the dynamical equations of the problem.

The initial static state is investigated by use of the Milne-Eddington approximation, and it is shown that there can be very large variations of temperature near to the boundaries.

The conditions for marginal stability are investigated both for motions which are restricted to the temperature boundary layer, and for motions which take place in the body of the fluid. In the former case it is found that a complete solution is provided by the approximate form for a transparent medium, and in the latter case a reasonable interpolation has to be made between results for the two approximate forms in order to complete the solution.

The effect of radiative transfer both on the initial static state and on the dynamical equations is such that the fluid is stabilized. This stabilization could probably be detected in the laboratory under certain conditions. In the earth's atmosphere the critical Rayleigh number for large scale motions may be increased by a factor 105, while at the surface of the solar photosphere the factor may be as large as 1012.
An inequality concerning the production of vorticity in isotropic turbulence
Authors: Betchov R.
Published: March 2006

An inequality is demonstrated involving the rate of production S of mean-square vorticity in isotropic turbulence and a factor γ which may be said to allow for intermittency or for the non-vanishing of fourth-order cumulants. An extreme state, corresponding to equality of this relationship, occurs if S = 0·64 and γ = 2·14. The experimental values are S = 0·4 and γ = 4. Another kinematical relation shows that the mechanism of vorticity production resembles collision between fluid particles rather than the swirling of contracting jets.
The almost-rigid rotation of viscous fluid between concentric spheres
Authors: Proudman Ian
Published: March 2006

Two concentric spheres are supposed to rotate about the same axis with almost the same angular velocity, so that the viscous stresses over the surfaces of the spheres induce a flow which may be represented by a small perturbation superimposed upon a rigid body rotation of the fluid as a whole. The governing equations are therefore linearized in the magnitude of the perturbation, and it appears that the validity of this linearization is independent of the Reynolds number of the primary rotation. Attention is then restricted to the case in which the Reynolds number is large, the principal object of the note being to exemplify some of the properties of rotating systems at large Reynolds numbers in terms of a particularly simple mathematical model.

It is found that the cylindrical surface that touches the inner sphere (the axis being the axis of rotation) is a singular surface in which velocity gradients are very large. Everywhere outside this cylinder, the fluid rotates as a rigid body with the same angular velocity as the outer sphere. Inside the cylinder, the velocity distribution in the central (inviscid) core of the motion is shown to be determined by the velocity distribution in the boundary layers over the spheres, and explicit solutions are obtained for all these velocity distributions. The mechanics of the cylindrical shear layer itself is also discussed, though no explicit solution is obtained in this case.
The speed of drifting bodies in a stream
Authors: Francis J. R. D.
Published: March 2006

The speed of free floating bodies on the surface of a water stream in a sloping channel has been found to be sensibly the same as the mean speed of the layer of water in which the bodies are floating, contrary to some recorded opinions.
The Saha equation and the adiabatic exponent in shock wave calculations
Authors: Alpher Ralph A.
Published: March 2006

The purpose of this note is to comment on the calculation of equilibrium gas dynamic parameters behind strong shock waves. The writer has been aroused by the appearance of a paper by Guman (1956) presenting a generalized computing scheme for ionizing shock waves in monatomic gases. In that paper the reader is not cautioned about including excited states in the Saha equation for the computation of the degree of ionization behind shock fronts at appropriate temperatures and densities. The same paper treats the adiabatic exponent γ = cp/cv as constant across strong shocks when at the same time it is implied that the computing scheme is of general validity. Hence, the unwary reader might attempt to apply the scheme in a regime where γ is not only no longer constant but is no longer a useful quantity for characterizing the shock conditions. Other authors (see, for example, Glass, Martin & Patterson (1953)) characterize flows in which a shock has excited internal degrees of freedom in terms of a variable specific heat ratio when in fact one cannot use this quantity in calculating shock front conditions.
Buoyant plumes in a moist atmosphere
Authors: Morton B. R.
Published: March 2006

This paper describes a simple model which can be used to investigate the transport of water vapour by thermal plumes in the atmosphere. For an approximate treatment of these plumes, it is assumed (as in a previous paper) that the vertical velocity, temperature and specific humidity are constant across the ascending column, and that the inflow velocity due to mixing at the edge of the plume is proportional to the vertical velocity within the plume. The behaviour of the rising air is then investigated by means of equations representing the conservation of mass, momentum, heat and water vapour, and numerical solutions are obtained for representative cases.

It is shown that in a stably stratified atmosphere the plume air will become saturated if the source is sufficiently strong, and that the height of this saturation level can be determined in terms of dimensionless parameters representative of the source and the environment. Above the saturation level the analysis is continued by taking into account both vapour and liquid phases of water, and an approximate treatment is given for the behaviour of small plume clouds. It is found that there is a critical size for these; smaller clouds remain characteristic of the plume, but larger ones extend upwards to heights which do not depend on the previous parameters.
Damping of surface waves in an incompressible liquid
Authors: Case K. M. , Parkinson W. C.
Published: March 2006

The damping of surface waves of small amplitude in liquid contained in cylinders has been calculated. Viscous dissipation in an assumed laminar boundary layer was taken to be the primary cause of damping. Experimental results were obtained for the logarithmic decrement as a function of the ratio of liquid height to cylinder radius for several water-filled cylinders. Theory and experiment were found to be in good agreement.
Diffusion from a fixed source at a height of a few hundred feet in the atmosphere
Authors: Hay J. S. , Pasquill F.
Published: March 2006

The results of measurements of the vertical distribution of airborne particles, released usually at a height of 500 ft., and sampled for periods of about 30 minutes at downwind distances of 100, 300 and 500 metres, are presented and discussed.

At all distances the frequency distributions of the particle elevation with respect to the site of release are closely similar in shape and size to the frequency distribution of wind inclination at the site of release. This is interpreted as showing that, despite the uncorrelated effects of small eddies, high correlation was maintained in the motion of a particle, for periods of 1 minute or more, by the dominant action of persistent eddies which contributed heavily to the turbulent energy. In contrast to this result, the wind observations showed that the Eulerian auto-correlation coefficient (Rr) fell to about 0.2 in 10 seconds.
Static pressure distribution in the free turbulent jet
Authors: Miller David R. , Comings Edward W.
Published: March 2006

Measurements of mean velocity, turbulent stress and static pressure were made in the mixing region of a jet of air issuing from a slot nozzle into still air. The velocity was low and the two-dimensional flow was effectively incompressible. The results are examined in terms of the unsimplified equations of fluid motion, and comparisons are drawn with the common assumptions and simplifications of free jet theory. Appreciable deviations from isobaric conditions exist and the deviations are closely related to the local turbulent stresses. Negative static pressures were encountered everywhere in the mixing field except in the potential wedge region immediately adjacent to the nozzle. Lateral profiles of mean longitudinal velocity conformed closely to an error curve at all stations further than 7 slot widths from the nozzle mouth. An asymptotic approach to complete self-preservation of the flow was observed.
The reflection of pressure waves of finite amplitude from an open end of a duct
Authors: Rudinger George
Published: March 2006

When plane pressure waves in a duct reach an open end, they establish a complicated three-dimensional wave pattern in the vicinity of the exit which tends to readjust the exit pressure to its steady-flow level. This adjustment process is continually modified by further incident waves, so that the effective instantaneous boundary conditions which determine the reflected wave depend on the flow history. In the analysis of a nonsteady-flow problem by means of a wave diagram, it has been customary to assume that the steady-flow boundary conditions are instantaneously established. While this simplifying assumption appears reasonable, the resulting errors have been undetermined. It is the purpose of the present investigation to obtain improved boundary conditions. The results of a previous study of the reflection of shock waves from an open end have now been extended to other waves of finite amplitude. The reflected waves computed by means of the new procedure are in good agreement with experimental data observed in a shock tube for a variety of flow conditions. The pressure variations in a reflected wave lag behind those derived in the conventional manner by the time in which a sound wave travels about one or two duct diameters. Such lags are small, but may occasionally become significant. As a consequence of the lag, certain discontinuities of the incident wave do not reappear in the reflected wave. This improved understanding of the reflection process has made it possible to clarify some previously unexplained experimental observations.
A note on Mott-Smith's solution of the Boltzmann equation for a shock wave
Authors: Sakurai Akira
Published: March 2006

After a Modification, the interpolation formula of Mott-Smith (1951) for the shock wave problem is found to be a solution of the Boltzmann equation at large Mach number in a finite region of molecular velocity space. This modification gives a unique determination of the shock wave thickness, removing the ambiguity for this in Mott-Smith's formula.
The flow of swirling water through a convergentdivergent nozzle
Authors: Binnie A. M. , Hookings G. A. , Kamel M. Y. M.
Published: March 2006

Experiments with Perspex nozzles, which were arranged to discharge vertically downwards and in which the convergent part was followed by a short divergency, showed that at low swirls the flow was unstable. When the swirl was sufficiently large for an air core to be established, its effective magnitude was estimated from measurements, at the throat, of the core diameter and of the wall pressure. The former were in closer accord with inviscid theory than the latter. The results are presented in terms of dimensionless discharge and swirl coefficients. Measurements of core diameter and wall pressure were also made throughout one of the nozzles and compared with the theory. Reversed axial flow in the upper part of the nozzles was easily produced, and the limits of its appearance were determined. Low pressure tests with the reservoir top alternately submerged and uncovered revealed that the top had a marked influence on the nature of the flow in the nozzle; and measurements of the tangential and axial velocities in the upper part of the nozzle proved the inviscid theory to be seriously in error at high swirls. For purposes of comparison, similar experiments were performed on a convergent nozzle.
On fully-dispersed shock waves in carbon dioxide
Authors: Griffith Wayland C. , Kenny Anne
Published: March 2006

A dispersed shock wave may be defined as one in which finite changes occur over distances large compared to the mean free path in the gas. In contrast a shock wave in air extends over only a few mean free paths. When internal motions in a molecule are excited rather slowly by collisions, as is the case for molecular vibration, the shock wave may be partly dispersed; then, the sharp shock front is followed by a diffuse tail leading to complete thermal equilibrium. Alternatively, it may be fully dispersed, so that adjustments in the energy in all the degrees of freedom proceed slowly and in parallel. The purpose of this note is to point out that within a narrow speed range, from a shock Mach number of 1 to 1.042, shocks in carbon dioxide are fully-dispersed in the above sense. Such waves have been observed experimentally using a shock tube and interferometer. The possible existence of such waves was first pointed out by Bethe & Teller (1941) purely as a matter of academic interest. This note treats the problem in the same spirit.
The effect of a magnetic field on Stokes flow in a conducting fluid
Authors: Chester W.
Published: March 2006

Low Reynolds number flow of a conducting fluid past a sphere is considered. The classical Stokes solution is modified by a magnetic field which, at infinity, is uniform and in the direction of flow of the fluid.

The formula for the drag is found to be
$D = D_S \{ 1+\frac{3}{8}M+\frac{7}{960}M^2-\frac{43}{7680}M^3+O(M^4) \},$
Where DS is the Stokes drag and M is the Hartmann number.
Dynamics of a dissociating gas Part I Equilibrium flow
Authors: Lighthill M. J.
Published: March 2006

Atmospheric dissociation will be appreciable in the neighbourhood of projectiles travelling at speeds greater than 2 km/sec. This introductory paper on possible effects of dissociation on the airflow, and hence on the drag, stability and aerodynamic heating of such projectiles, is intended mainly as a source of ideas for later, more comprehensive investigations.
Transition processes in shock wave interactions
Authors: Jahn Robert G.
Published: March 2006

This paper is a discussion of recent experiments in shock-wave refraction which have clarified a special type of shock outflow process appearing to have relevance to other shock interactions, and notably to shock reflection from an oblique wall. For certain incident shock strengths and angles of incidence α, the air/methane refraction problem simulates closely the situation in the trouble-some range of the reflection problem, in which α lies between the value αe at which the theoretical solutions terminate and the value α0 that marks the onset of Mach reflection, and in which the flow deflections cannot be reconciled with theoretically permissible reflected shock strengths. In the analogous refraction cases, the reflected shock is observed to increase in strength along its length to a maximum value at the intersection point, and to be followed by a subsonic rarefaction zone which also increases in severity near the intersection. In fact, this zone appers to coalesce into a subsonic discontinuity, just at the intersection point—a feature which would contradict one of the basic assumptions of the regular reflection and refraction theories. Other refraction experiments suggest that a similar process is relevant to the Mach reflection configuration, and may account for the discrepancies in the three-shock theory for weak incident shocks.
A simple derivation of Lighthill's heat transfer formula
Authors: Liepmann H. W.
Published: March 2006

In the following it will be shown that a simple argument based on the use of the energy integral equation of the laminar boundary layer permits the derivation of a heat transfer formula valid for non-uniform temperature distribution and non-zero pressure gradients. The formula is then shown to be identical in structure with Lighthill's (1950) well-known results. Lighthill obtained his formula by solving the boundary layer equations in the von Mises form using operational methods. An elegant way to obtain the same results using exact similarity consideration was given by Lagerstrom (not yet published). The derivation given here is probably the most simple-minded one and the method may be useful for other applications as well. Furthermore, it is shown that the approach can be slightly modified to permit application of the formula to flow near separation. The latter result is applied to the Falkner-Skan solution for just separating flows and is found to be in excellent agreement with the exact solutions.
The minimum Reynolds number for a turbulent boundary layer and the selection of a transition device
Authors: Preston J. H.
Published: March 2006

In the case of turbulent flow in a pipe there is a lower experimental number to the Reynolds limit for which fully developed turbulent flow occurs. From the similarity and close agreement of the curves showing the coefficient of skin friction cf as a function of the Reynolds number Rθ (based on the momentum thickness θ) for the circular pipe and flat plate, it is suggested that there should be a lower limit to Rθ for fully developed turbulent flow on a flat plate. Rather limited experimental data confirm this and place the lower limit at Rθ = 320. The choice and size of transition device is examined in relation to this minimum Rθ and an approximate theory leads to a ‘wire’ Reynolds number in fair agreement with experience.
Slow motion of a paraboloid of revolution in a rotating fluid
Authors: Sarma L. V. K. Viswanadha
Published: March 2006

The slow uniform motion, after an impulsive start from relative rest, of a paraboloid of revolution along the axis of a rotating fluid is investigated by using a perturbation method. The principal purpose of the note is to illustrate the mechanism by which the fluid is not subjected to any substantial radial displacement, which is a direct consequence of the requirement that the circulation round material circuits should be constant when the perturbation velocities due to the motion of the paraboloid remain small. It appears that the mechanism is an oscillatory one in which the distance between any fluid particle and the axis of rotation oscillates sinusoidally in time with small amplitude. As time progresses, the amplitude of the oscillation decays to zero everywhere except on the paraboloid. The ultimate motion is then a rigid body rotation everywhere except on the paraboloid and the axis of rotation, where the perturbation velocities continue to oscillate indefinitely with small amplitude.
On the non-linear mechanics of hydrodynamic stability
Authors: Stuart J. T.
Published: March 2006

In most work on the theory of stability of laminar flow, infinitesimal disturbances only have been considered, so that only the initial growth of the disturbance has been determined. It is the object of the present paper to extend the theory to larger amplitudes and to study the mechanics of disturbance growth with the inherent non-linearity of the hydrodynamical system taken into account.

The Reynolds stress (where averages are taken with respect to some suitable space coordinate) is the fundamental consequence of the non-linearity, and its effects can be anticipated as follows. Initially a disturbance grows exponentially with time according to the linear theory, but eventually it reaches such a size that the transport of momentum by the finite fluctuations is appreciable and the associated mean stress (the Reynolds stress) then has an appreciable effect on the mean flow. This distortion of the mean flow modifies the rate of transfer of energy from the mean flow to the disturbance and, since this energy transfer is the cause of the growth of the disturbance, there is a modification of the rate of growth of the latter.

It is suggested that, in many cases, an equilibrium state may be possible in which the rate of transfer of energy from the (distorted) mean flow to the disturbance balances precisely the rate of viscous dissipation of the energy of disturbance. A theory based on certain assumptions about the energy flow is given to describe both the growth of the disturbance and the final equilibrium state, and application is made to the cases of Poiseuille flow between parallel planes and flow between rotating cylinders. The distorted mean flow in the equilibrium state can be calculated and from this, in the latter case, the torque required to maintain the cylinders in motion. Good agreement is obtained with G. I. Taylor's measurements of the torque for the case when the inner cylinder rotates and the outer cylinder is at rest.
The stability of a two-dimensional laminar jet
Authors: Tatsumi T. , Kakutani T.
Published: March 2006

This paper deals with the stability of a two-dimensional laminar jet against the infinitesimal antisymmetric disturbance. The curve of the neutral stability in the (α, R)-plane (α, the wave-number; R, Reynolds number) is calculated using two different methods for the different parts of the curve; the solution is developed in powers of (αR)−1 for obtaining the upper branch of the curve and in powers of αR for the lower branch.

The asymptotic behaviour of these branches is that for branch I,$\alpha \rightarrow 2, \;\; c \rightarrow \frac{2}{3}$ for $R \rightarrow \infty$; and for branch II, $R \sim 1\cdot12\alpha^{-1|2},\; c \sim 1\cdot 20 \alpha^2$ for α → 0. Some discussion is given on the validity of the basic assumption of the stability theory in relation to the numerical result obtained here.
The thermal boundary layer on a non-isothermal surface with non-uniform free stream velocity
Authors: Sparrow E. M.
Published: March 2006

A formally exact solution for the thermal boundary layer on a non-isothermal surface subjected to non-uniform free stream velocity is presented in the form of a series. It is demonstrated that the solution can be recast in terms of universal functions, which are independent of the wall temperature data of particular problems, and which depend only on a single parameter characterizing the variation of the free stream velocity.
On the breaking of water waves of finite amplitude on a sloping beach
Authors: Greenspan H. P.
Published: March 2006

In a recent paper Carrier & Greenspan (1958) showed that, within the framework of the non-linear shallow-water theory, there exist waves which do not break as they climb a sloping beach. The formation of a shock or bore is dependent on a variety of factors (wave shape, particle velocity, etc.) and, as yet, no general criteria for breaking have been found. In this paper, we consider waves which propagate shoreward into quiescent water; it is shown that any compressive wave (a wave of positive amplitude) which has a non-zero slope at the wave-front eventually breaks before reaching the coastline. In fact, an explicit relation is obtained between the initial conditions and the position where breaking occurs.
A note on shock flow in a channel
Authors: Gundersen Roy
Published: March 2006

A shock wave is generated by a uniform compressive piston motion and passes into a channel of slowly varying cross-section. A relation in closed form is obtained between shock strength and the area of the channel and is used to discuss converging cylindrical and spherical shocks.
Two-dimensional incompressible magneto-hydrodynamic flow across an elliptical solenoid
Authors: Kemp Nelson H. , Petschek Harry E.
Published: March 2006

An analysis has been made of the two-dimensional flow of an incompressible constant-conductivity fluid through an elliptically shaped solenoid containing a constant magnetic field directed normal to the flow plane. The effect of both Hall current and ion slip has been included in the generalized Ohm's law used for the fluid. The analysis is based on a perturbation procedure in two parameters, one being the magnetic Reynolds number Rm and the other the ratio S of magnetic force per unit area to dynamic pressure. Calculations have been carried to the first order in each parameter, and closed-form analytic expressions have been obtained for the force and moment on the solenoid, the current density, stream function, magnetic field and other pertinent physical quantities.

It was found that, to the zeroth order, there is a force but no moment on the solenoid. To the first order in S, where the flow field is modified but the magnetic field is not, there is a moment and a force, the latter being anti-parallel to the zeroth order force. To the first order in Rm, where the magnetic field is modified but the flow field is not, there is a moment but no force. Thus, to the first order the lift to drag ratio is the same as in the zeroth order. Graphs which illustrate some of the effects of angle of attack, fineness ratio of the ellipse, Hall current and ion slip, on the forces and moments are presented.
A note on the compression of air through repeated shock waves
Authors: Stollery J. L. , Maull D. J.
Published: March 2006

The results of calculations of the compression of air by repeated shock waves are compared with the perfect-gas values given by Evans & Evans (1956). The comparison emphasizes the increasing divergence of real from perfect-gas results as shock strengths are raised. The equations relating conditions across a shock wave are obtained in a convenient form for solution using a Mollier diagram.
A new approach to problems of shock dynamics Part 2. Three-dimensional problems
Authors: Whitham G. B.
Published: March 2006

This paper gives the extension of the approximate theory developed in Part 1 (Whitham 1957) to three-dimensional problems. The basic equations are derived in §1, using the original assumption of a functional relation between the strength of the shock wave at any point and the area of the ray tube. An analogy with steady supersonic flow is found. For the diffraction of a plane shock wave by an obstacle, the equations and boundary conditions are exactly the same as those for steady supersonic potential flow past that obstacle, with a special choice of the density-speed relation. The successive positions of the shock wave are the equipotential surfaces of the supersonic flow. The 'shock-shocks’ introduced in Part 1, i.e. discontinuities in the slope and Mach number of the shock wave, correspond to the steady oblique shock waves in the supersonic flow problem. They arise when Mach reflexion occurs.

In §2 the theory is applied in detail to the diffraction of a plane shock wave by a cone. Then, in §3, a small perturbation theory is applied to the two typical problems of (i) diffraction by a slender axi-symmetrical body of general shape, and (ii) the stability of a plane shock. Many further applications would be possible and some brief comments on these are made in §4.
Cellular convection with finite amplitude in a rotating fluid
Authors: Veronis G.
Published: March 2006

When a rotating layer of fluid is heated uniformly from below and cooled from above, the onset of instability is inhibited by the rotation. The first part of this paper treats the stability problem as it was considered by Chandrasekhar (1953), but with particular emphasis on the physical interpretation of the results. It is shown that the time-dependent (overstable) motions occur because they can reduce the stabilizing effect of rotation. It is also shown that the boundary of a steady convection cell is distorted by the rotation in such a way that the wave length of the cell measured along the distorted boundary is equal to the wavelength of the non-rotating cell. This conservation of cellular wavelength is traced to the constancy of horizontal vorticity in the rotating and non-rotating systems. In the finite-amplitude investigation the analysis, which is pivoted about the linear stability problem, indicates that the fluid can become unstable to finite-amplitude disturbances before it becomes unstable to infinitesimal perturbations. The finite-amplitude motions generate a non-linear vorticity which tends to counteract the vorticity generated by the imposed constraint of rotation. Under experimental conditions the two fluids, mercury and air, which are considered in this paper, will not exhibit this finite amplitude instability. However, a fluid with a sufficiently small Prandtl number will become unstable to finite-amplitude perturbations. The special role of viscosity as an energy releasing mechanism in this problem and in the Orr-Sommerfeld problem suggests that the occurrence of a finite-amplitude instability depends on this dual role of viscosity (i.e. as an energy releasing mechanism as well as the more familiar dissipative mechanism). The relative stability criterion developed by Malkus & Veronis (1958) is used to determine the preferred type of cellular motions which can occur in the fluid. This preferred motion is a function of the Prandtl number and the Taylor number. In the case of air it is shown that overstable square cells become preferred in finite amplitude, even though steady convective motions occur at a lower Rayleigh number.