ALBERT

Beschreibung: The radiocarbon age measurements reported on in this article were made during a period from May, 1957, through May, 1958. During this time the laboratory was operated by the Department of Anthropology, under the direction of Dr. Emil W. Haury. On July 1, 1958, the Carbon-14 laboratory, under the supervision of Dr. Paul E. Damon with Dick Shutler, Jr. as laboratory technician, was transferred to the Geochronology Laboratories.

Beschreibung: The radiocarbon laboratory at the University of Pennsylvania is sponsored jointly by the University Museum and the Physics Department. In this laboratory our primary function is to date archaeologic samples from those four regions of the world in which the University Museum studies are concentrated, namely, the Near East, South America, Central America, and the Arctic. Dates for sites in the first two regions are included in this list, and a long series of temple lintels from Tikal, Guatamala is now being processed. Dates for the Arctic were obtained intermittently from 1953 through 1955 (with solid-carbon counting); others, more recently. The materials for many of the Arctic dates, however, were not reliable; that is, they were physically contaminated before processing in the laboratory. We hope that better samples can be found for future Arctic dating. Our Arctic dates which now furnish tentative age ranges for Punuk, Birnirk, Kachemak Bay III, Okvik, Old Bering Sea, Ipiutak, Norton, Dorset, Kachemak Bay I, Choris, Firth River (Early Mountain Phase), Sarqaq, and Denbigh Flint Complex Periods have been submitted to American Antiquity (Rainey and Ralph, in press) along with detailed discussions of possible contaminations.

Beschreibung: The Kelvin-Helmholtz model for the formation of surface waves at the interface between two fluids in relative motion is generalized for parallel shear flows. It is assumed that phase changes across the flow are negligible and hence that the aerodynamic pressure on the wave is in phase with its displacement (rather than its slope). A variational formulation is established and leads to the determination of appropriately weighted means for the velocity profiles. The principal application is to flow of a light inviscid fluid over a viscous liquid; it is shown that the principle of exchange of stabilities is applicable to such a configuration, and a critical wind speed in satisfactory agreement with observation is predicted for an air-oil interface. The results also are applied to an air-water interface and lead to the conclusion that Kelvin-Helmholtz instability of such an interface is unlikely at commonly observed wind speeds. A more general formulation of the Kelvin-Helmholtz boundary-value problem and variational principle, allowing for variations in both velocity and density, is given in two appendices.

Beschreibung: A procedure is given for translating boundary-value problems of gas dynamics from microscopic form into approximately equivalent continuum form. The continuum formulations involve state-variables that are either half-space moments, or complete moments of the molecular distribution functions. Moment equations derived from the kinetic equations are reduced to a determinate set by representing the distribution functions as sums of ‘modified Maxwellian functions based on various characteristic temperatures and velocities’. The particular choice of such a representation depends on the Knudsen number and on the nature of the microscopic boundary conditions.

Beschreibung: A previous analysis for the generation of surface waves by a parallel shear flow (Miles 1957 a) is extended by: (a) presenting results based on a more accurate solution of the differential equation; (b) imposing the boundary condition at the surface wave, rather than at the mean surface; and (c) including the dominant viscous term in the complete Orr-Sommerfeld equation. The modification (a) yields an energy transfer somewhat smaller than that predicted previously but of the same order of magnitude as, and in rather better agreement with, observation, while (b) has no effect and (c) only a small effect for gravity waves. The analysis is based on the equations of motion in intrinsic co-ordinates (rather than the usual Orr-Sommerfeld equation) and may be of interest in other problems of hydrodynamic stability.

Beschreibung: The effects of density variation in the absence of gravity on the stability of a horizontal shear layer between two streams of uniform velocities is investigated. The density is assumed to decrease exponentially with height and the velocity is represented by U(y) = tanh y.The method of small disturbances is employed to obtain the neutral stability curve. It is demonstrated that disturbances with wave-numbers larger than the width of the transition layer are attenuated.Qualitative agreement with experimental evidence is obtained.

Beschreibung: First, from a volumetric formulation of the momentum theorem of linearized theory, a general analytic proof is presented of the invariance of the drag of an arbitrary spatial distribution of horseshoe vortices and sources under reversal of the undisturbed flow. By consideration of the interference drag of two such singularity distributions, a reverse-flow relation for steady subsonic or supersonic flow is then obtained. This relation, a generalization of the Ursell-Ward theorem, may be applied to configurations with bodies whose surfaces are not quasi-cylindrical and whose surface pressures are quadratically related to the perturbation velocity.The relation is used to discuss several interfering two-body arrangements in supersonic flow. It is shown that, in certain cases, the drag and lift may be determined without knowledge of the interference flow field associated with the arbitrarily prescribed body geometry. The simplicity of the results permits the formulation of optimum problems. The invariance of the drag under flow reversal with unchanged geometry is also established.

Beschreibung: To determine experimentally the mean value of a randomly fluctuating quantity, it may be necessary to measure the average value over a considerable interval of time. This problem arose in a recent study of the temperature fluctuations over a heated horizontal plate, and a system was used that depended on the counting of electrical pulses generated at a rate proportional to the quantity being measured. The advantage of this technique is that mean values may be measured over time intervals of almost unlimited length with little added difficulty for the experimenter. Circuits are described which measure: (a) the mean square of a fluctuating quantity and of its time-derivative, (b) the statistical distribution of the fluctuations, (c) the mean frequency of the fluctuation assuming a particular value, and (d) the mean product of two fluctuating quantities. Over the range of use, the stability and linearity of the calibrations is better than 1%, more than sufficient for work on natural convection. In its present form, the equipment responds uniformly to all frequencies below 100 c/s, but it would not be difficult to extend this range of response to higher frequencies.

Beschreibung: On the assumption that the rotational oscillations of a rigid plane are small, boundary-layer type solutions of the Navier-Stokes equations are attempted by an expansion of the velocity components in power series of the amplitude. First-and third-order approximations to the transverse velocity are obtained, from which a correction to the moment on a disk of finite radius is found.The first non-vanishing approximation to the radial-axial flow (a second-order term) is seen to have a steady component and a component with frequency twice that of the plate. The former component appears to persist outside the boundary layer, and at large distances from the plate to have the character of an irrotational stagnation flow. A re-examination not involving the series approximation reveals that although steady radial flow does exist outside the boundary layer, it is a viscous flow and is confined within a secondary layer. The ratio of the thicknesses of the two layers is found to be inversely proportional to the amplitude of the oscillations. These results indicate that a second-order flow in a region where the first-order flow field vanishes should not be accepted without further discussion.

Beschreibung: Some ablating bodies entering the atmosphere will melt or soften. Under deceleration, the soft or melted surface will tend to develop instabilities of the Lamb-Taylor type. Two situations involving viscous incompressible fluids are investigated here: one where the liquid layer has constant viscosity and finite thickness, and the other, where the viscosity increases exponentially with distance away from the interface, and the layer is semi-infinite in extent.It can be demonstrated, that if one neglects gradients in the flow direction, the rate of growth of interface disturbances in a plane normal to the axis of an axially symmetric blunt body is independent of the flow velocity. The fact that the deceleration and liquid thickness vary with time along a trajectory is also included in the analysis. Results of calculations for the amplification factor and the most amplified wavelength are given.A mechanism due to the deceleration is postulated, which would cause the formation of longitudinal grooves on the surface of an axially symmetric blunt body while entering the atmosphere.

Beschreibung: A hinged vane and a sensitive electrical system for recording the motion of the vane have been developed for the observation of fluctuating y-components of velocity in boundary layers. An approximate theory of the natural oscillations of such vanes is presented and experimentally verified. Using vanes as resonant detectors, meassurements have been made of oscillations injected into the laminar boundary layer on a flat plate in a wind tunnel with 0·3% free-stream turbulence. Points on the neutral Tollmien-Schlichting curve have thereby been obtained which lie close to the theoretical neutral curve.

Beschreibung: The uniform steady flow of an incompressible, viscous, electrically conducting fluid is distorted by the presence of a symmetrically oriented semi-infinite flat plate. The ambient magnetic field is coincident with the ambient velocity field. The description of the resulting fields depends on the physical co-ordinates measured in units of Reynolds number and on the two parameters ε = ωμν and β = μH2/ρv2. This description of the fields is approximated in three different ways and essentially covers the full range of ε and β. In particular, when β [Gt ] 1, no steady flow which is uniform at large distances from the plate exists.

Beschreibung: Exact transfer calculations for boundary layers with longitudinal pressure gradients are very complicated, but in the literature several approximate methods are known for the rapid calculation of both the wall friction and the heat transfer. A ‘wedge method’ propounded by Meksyn turns out to be one of the most rapid methods, being no less accurate than other approximate methods. A way of refining this method is proposed.This paper also shows that asymptotic expansions provide convenient relations which are capable of expressing the Nusselt number explicitly in terms of the Prandtl number.It is shown that, together with the asymptotic expansions, Meksyn's method permits rapid calculation of local heat transfer numbers. Some examples of application are given for elliptical cylinders and spheres for several values of the Prandtl number.

Beschreibung: A physical theory is proposed for the skin friction on a flat plate at zero incidence in the transition flow regime, i.e. in the flow of a moderately rarefied gas. The ratio of the molecular mean free path to the characteristic size of the plate is assumed of order unity or larger. A general formula for the perturbation to the well-known friction of the free-molecule theory is given. This perturbation is attributed to the intermolecular collisions which are neglected on the basis of the free-molecule hypothesis. The expected rate of collisions are calculated for rigid spheres, using the classical kinetic theory.Although this is intended as an approximate theory, the theoretical results check surprisingly well with the limited experimental data that are available. The present theory shows that the ratio of the Reynolds number to the Mach number squared is the governing parameter for determining the intermolecular collision effect on skin friction in the transition flow regime.

Beschreibung: Measurements are described of the static pressures and velocities of detonation waves in hydrogen-oxygen mixtures, together with the pressures arising on their normal reflexion at the closed end of the explosion tube. Two explosion tubes, of diameter 10 and 1·6 cm, were employed to study the diameter effect on the wave pressures. The experimental results are compared with calculated values of the wave properties for a range of hydrogen-oxygen mixtures initially at atmospheric pressure. In the 10 cm tube the static pressures and velocities are found to agree well with theory for mixtures with hydrogen content in the approximate range 50-75%; the evidence from pressure profiles and wave velocities indicates that mixtures outside this range may not be able to support ideal C–J waves. Detonation waves in all the mixtures studied in the 1·6 cm tube are found to be subideal. A possible explanation, in terms of energy loss to the tube wall, of the discrepancy between experiment and theory is discussed. Spinning occurs in mixtures near the limits of detonation in the smaller tube; the measured frequencies are found to be in reasonable agreement with the values predicted by the theories of Manson (1947) and Fay (1952).

Beschreibung: A small-disturbance solution is obtained for the steady two-dimensional flow over a sinusoidal wall of an inviscid gas in vibrational or chemical non-equilibrium. The results are based on a single, linear, third-order partial differential equation, which plays the same role here as does the Prandtl–Glauert equation in equilibrium flow. The solution is valid throughout the range from subsonic to supersonic speeds and for all values of the rate parameter from equilibrium to frozen flow (in both of which limits it reduces to Ackert's classical solution of the Prandtl–Glauert equation). The results illustrate in simple fashion some of the properties of non-equilibrium flow, such as the occurrence of pressure drag at subsonic speeds and the absence of the discontinuous phenomena that characterize the Prandtl–Glauert theory when the flow changes from subsonic to supersonic.

Beschreibung: The motion of a fluid inside a rotating annulus of square cross-section, whose dimensions are small compared with the distance from the axis of rotation, is considered. The rigid side walls are held at different constant temperatures and the fluid motions that occur are strongly influenced by Coriolis accelerations. A detailed study is made of the azimuthally independent state, a Hadley cell, in the limit of small thermal Rossby number. It is convenient to employ a boundary layer type analysis, essentially with respect to the Taylor number and all the imposed boundary conditions are rigorously satisfied.An entirely geostrophic thermal wind is found to obtain over the main body of the fluid. The circulation in the plane of the annular cross-section is entirely confined within narrow boundary layers and consists of a superposition of three cellular motions: a cell occupying the cross-section and two additional cells confined to the side-wall boundary layers. These motions are intimately related to the rotational constraint. The temperature distribution and its relation to the conductive and convective processes are determined.

Beschreibung: Part I describes measurements of the drag on circular cylinders, made by observing the bending of quartz fibres, in a stream with the Reynolds number range 0·5-100. Comparisons are made with other experimental values (which cover only the upper part of this range) and with the various theoretical calculations.Part II advances experimental evidence for there being a transition in the mode of the vortex street in the wake of a cylinder at a Reynolds number around 90. Investigations of the nature of this transition and the differences between the flows on either side of it are described. The interpretation that the change is between a vortex street originating in the wake and one originating in the immediate vicinity of the cylinder is suggested.

Beschreibung: For wings with supersonic edges and with arbitrary dihedral, twist, camber and thickness distribution, the pressure distribution on the wing exterior to and along the two Mach lines emanating from the vertex of the wing is equal to the corresponding pressure distribution for a planar wing. The problem is to find the pressure distribution inside the two Mach lines. In the present paper, the unknown pressure distribution is approximated by an elementary function of the two surface variables. The (as yet undetermined) constants in the function are then found by the conditions: (i) that the function takes on the corresponding planar values along the two Mach lines, (ii) that it fulfils certain generalized integral relationships (Ting 1959), and (iii) that it satisfies the averaging property of solutions of the wave equation to be developed in this paper. The generalized integral relationship relates the integral of the pressure distribution along the line of intersection of a Mach plane with the wing to the integral along the same line of the prescribed normal velocity. The averaging property relates the pressure distribution along the line of intersection of the surface of the dihedral wing to that on a planar wing.

Beschreibung: An analytic solution for the velocity field of a vortex street generated in a viscous fluid is developed. A method is presented for the determination of the true transverse spacing of vortices. Experimental geometry and velocity data, obtained by hot-wire techniques, are presented.The experimental results verified the validity of the analytic solution. The vortices of a real viscous vortex street were found to resemble very closely the exponential solution of the Navier-Stokes equations for an isolated axisymmetric rectilinear vortex. Three basic regions of vortex street behaviour were apparent at each Reynolds number investigated-a ‘formation region’ in which the vortex street is developed and large dissipation of vorticity occurs, a ‘stable region’ in which the vortices display a stable periodic laminar regularity, and an ‘unstable region’ in which the street disappears and turbulence develops. Geometry and velocities were determined.

Beschreibung: During the last few years, many experimental devices have been built in which strong shock waves are generated in gases by electromagnetic forces on currentcarrying gas particles. The general theory of these devices is discussed, taking external circuit inductance into account. It is shown that a shock wave of constant speed is finally attained. This shock wave is travelling at 90% of its final speed when the circuit inductance has increased to 3·0 times its initial value.

Beschreibung: The rise of a gas bubble in a viscous liquid at high Reynolds number is investigated, it being shown that in this case the irrotational solution for the flow past the bubble gives a uniform approximation to the velocity field. The drag force experienced by the bubble is calculated on this hypothesis and the drag coefficent is found to be 32/R, where R is the Reynolds number (based on diameter) of the bubbles rising motion. This result is shown to be in fair agreement with experiment.The theory is extended to non-spherical bubbles and the relation of the resulting theory, which enables both bubble shape and velocity of rise to be predicted, to experiment is discussed.Finally, an inviscid model of the spherical cap bubble involving separated flow is considered.

Beschreibung: The modulus of decay of standing waves of finite height is derived by assuming that the attenuation of the waves is due to viscous losses in boundary layers close to the solid walls. Dampings are observed in six basins of varying sizes. The basins are duplicated using glass and lucite for the wall materials. With liquids wetting the walls, the losses due to viscosity are slightly increased from causes presumably related to surface tension. With a liquid not wetting the walls (distilled water and lucite), losses from surface activity, of some obscure origin, outweigh many times the losses due to viscosity in the basins of smaller sizes. For moderately large basins, for which surface activity may be neglected, the agreement between the observed and computed rates of decay is found to be satisfactory.

Beschreibung: 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).

Beschreibung: Previous observations of turbulent motion at large wave-numbers have revealed the existence of an uneven distribution of turbulent energy. The spotty distribution of the turbulent motion at high wave-numbers is here studied experimentally for the turbulent boundary layer. The high wave-number intermittency is observed at all locations through and along the boundary layer from near transition to near separation.The flatness factors for the longitudinal turbulent component at different wave-numbers are measured to give a quantitative value for the intermittency at particular wave-numbers. Upstream of the separation region the flatness factors are found to depend on wave-number and longitudinal distance, but not on the distance from the wall. It appears that the intermittency develops in the transition region and does not diminish very rapidly with distance downstream. Near separation the flatness factors change radically in distribution near the wall, and are there no longer independent of distance from the wall.

Beschreibung: This paper presents a three-dimensional small-perturbation approach to the problem of waves produced in a statically stable stratified air stream flowing over a mountain. The fundamental solution for a doublet disturbance in an air stream in which the parameter l2 = gβ/V2 is constant is calculated, and then is extended to that for a disturbance due to a circular mountain in the same air stream. A simple approximation to the known two-dimensional flow over an infinite ridge is also given. The second (’upper’) boundary condition for the solutions is determined in a rigorous analytical manner, assuming the presence of small friction forces, or, alternatively, of time dependence. It is hoped that this will settle the controversy which exists over the choice of this condition.The results show that the behaviour due to a doublet is peculiar and not truly representative of that due to a mountain. The latter shows waves which decay down-stream and are contained in a strip, the width of the strip being determined by the radius of the mountain. An interesting result is that the circular mountain can give rise to waves which have greater amplitude than those produced by the infinite ridge under the same conditions.In some previous papers the waves produced by the infinite ridge have been neglected, but the present paper shows that in many cases this procedure is not justifiable. The detailed solution for the waves behind a circular mountain has a form which emphasizes the importance for lee-wave production of ’resonance’ between the width of the mountain and the characteristic length l-1 of the air stream.

Beschreibung: 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.

Beschreibung: A two-dimensional free-jet water tunnel developed at the St Anthony Falls Hydraulic Laboratory of the University of Minnesota is described briefly. Results of experimental measurements on a two-dimensional cup, symmetrical wedges, inclined flat plates, and a circular cylinder in the tunnel are given.Measured force coefficients at zero cavitation number are in good agreement with theory. Shapes of the cavities were computed for one of the wedges and for one of the plates at zero cavitation number; the observed shapes are also in good agreement with the theory.For non-zero cavitation numbers, theoretical results for force coefficients were available for comparison in only two cases. For one of these, the cup, agreement between theory and experiment was good up to a cavitation number of about 0.5. For the other, a symmetrical wedge, experimental results were compared with a linear theory with good agreement for cavitation numbers between about 0.1 and 0.3. In the case of the wedge, measured cavity lengths were somewhat shorter than predicted by the linear theory. All other comparisons with theory at non-zero cavitation number had to be made with the theory as developed for infinite fluid. The experimental force coefficients were less than predicted by infinite-fluid theory, but tended to approach the theoretical values as the cavitation number increased. A similar tendency marked the comparison between the experimental data and data taken by others in closed tunnels.

Beschreibung: If an electric current of uniform densityj0is passed axially through a stationary fluid between concentric cylinders of radiir1andr2(〉r1), the fluid is stable to axisymmetric disturbances only if the damping provided by viscosity and electrical resistivity is sufficiently large. It is shown herein that the fluid may also be stabilized by passing a line currentJalong the axis, sufficient conditions for stability being$J le -pi j _0(r^2_2 - r^2_1)$, or$ge J; pi j _0r^2_1$The values ofJneeded to stabilize the fluid when the fluid has non-zero viscosity and finite conductivity are calculated for the caser2-r1[Lt ]r1. In this latter case, the ring vortices which exist under conditions of neutral stability are exactly the same as those for flow between rotating cylinders ifJandj0have the same sign, and ifJis not very small compared with πj0r2.

Beschreibung: The steady, two-dimensional flow through an arbitrarily-shaped gauze, of non-uniform properties, placed in a parallel channel is considered for the case in which viscosity can be ignored except in the immediate vicinity of the gauze. The equations are linearized by requiring departures from uniformity both in the flow and in the gauze parameters to be small. Knowledge of any three of the upstream profile, the downstream profile, the shape of the gauze and the gauze parameters, allows the other to be calculated from a linear relation between these four quantities. Particular solutions are given for the production of a uniform shear and the flow through linear and parabolic gauzes. The validity of the solution is verified by experiment. It is shown that the method can also be applied to two-dimensional flow in a diverging channel, axisymmetric flow in a circular pipe and in a circular cone and to flow through multiple gauzes.

Beschreibung: This paper is concerned with the propagation of small initial disturbances in a conducting gas under the influence of a uniform external magnetic field.For a perfect conductor, there are three types of plane waves, each of which depends strongly on the angle at which the magnetic field is crossed. The modifying effects of finite conductivity are determined and, in the case of these waves, this is done uniformly for all angles. A general disturbance may be resolved into two parts, one of which satisfies a fourth-order equation and the other a fifth; for a perfect conductor these reduce to second-and fourth-order equations, respectively.The free oscillations of the gas are examined when it is contained in a rectangular box, and, in particular, when the external field is very weak or very strong. For vanishingly weak fields the idealization of infinite conductivity proves to be inadequate. Finally, the initial-value problem is discussed.

Beschreibung: 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.

Beschreibung: The early exploration of east Greenland between lats. 70° N. and 82° N. was the work of several nations, and Danish, Swedish, German and British expeditions all played their parts in it. In the last three decades, however, although other groups have made valuable contributions, the expeditions under the leadership of Lauge Koch have been of paramount importance by virtue of the large numbers of scientists involved, the range of the studies, and, in particular, the continuity of effort. This continuity has enabled an unusual degree of foresight and planning to be applied to the operations. Even in these more favoured circumstances, however, “greater results might possibly have been obtained if the means had been ensured beforehand, so that the work could have been planned for a longer period of years at a time”. It has been the policy to concentrate on geological survey as the basic scientific inquiry in this uninhabited, almost virgin, territory. This emphasis on geology has, in turn, stressed the need for detailed geographical information, and stimulated topographical survey to produce an adequate coverage of medium-scale maps for a large part of the region. Other fields have not been overlooked, and biologists—studying the fauna and flora of both land and sea—meteorologists, glaciologists, hydrographers, and archaeologists have been included in the parties.

Beschreibung: In 1954 the Geophysics Research Directorate of the Air Force Cambridge Research Center (AFCRC), at the request of Northeast Air Command, United States Air Force, organized a study of the physical properties, growth, and bearing capacity of sea ice. The object of the study was to gain information about the conditions under which various aircraft and vehicles could operate on sea ice, for supply and rescue purposes. The Navy Hydrographic Office (NHO) and the Snow, Ice and Permafrost Research Establishment (SIPRE) of the Army Corps of Engineers also took part in the project. The spheres of interest of each organization were as follows: AFCRC, the application of geophysical and crystallographic methods to the study of sea ice; NHO, the details of the relations between meteorological conditions and the growth rate and general physical properties of sea ice; and SIPRE, the variation of the strength of sea ice as determined by small-scale field tests, and the application of this information toward an analysis of the bearing capacity of sea ice.

Beschreibung: As a result of these operations 1000 miles of a deep-water North West Passage were charted. In addition, five hundred square miles of detailed hydrographic survey were made in the most dangerous areas. About 285 miles of coastline were covered by triangulation and 28 radar reflector towers were built as navigational aids. The results of the surveys were published in a series of 33 charts and in greatly improved sailing directions.

Beschreibung: Although the principles of water supply and sewage disposal in the north of Canada are the same as those for more temperate regions, the physical features of the installations often vary with the influence of low temperature and permafrost. These not only create technical problems of design but, when coupled with the relative isolation of most northern sites, they also introduce serious economic considerations. Operating costs as well as initial construction costs are higher, making facilities of the kind normally provided too expensive for many people.