ALBERT

Description: Both the 2-L counter, described in GSC I, and the 5-L counter (GSC IV) were operated routinely during the past year. Approximately one-half of the determinations reported here were obtained from each counter. The 5-L counter was operated mainly at 1 atm.For more than a year, age calculations have been carried out monthly by an I.B.M. 1620 computer. If the background, standard, and sample counts during a month conform to statistical laws, they are entered on sheets together with their respective counting times and sample identifications and sent to the computing center for processing.

Description: This date list covers age measurements carried out at the Radiocarbon Dating Laboratory of the German Academy of Sciences of Berlin (DAW) since 1963 and is a continuation of our first date list (Berlin I). Procedures and methods of preparing the samples are essentially the same. We completed our laboratory with a second electronic counting apparatus. Two further proportional counters with internal anticoincidence (Houtermann-Oeschger counters) are made from an old railway-car axle. The total volume of these counters is 4 L, the effective volume 2.2 L, the background 2.0 counts/min at 700 Torr (acetylene filling), and the contemporary standard value (0.95 NBS oxalic acid) is 20 counts/min. Each sample is measured twice, first for 48 hr and after 8 days for another 24 hr. Data have been calculated on the basis of a C14 half-life of 5570 yr (Godwin, 1962). Errors listed include the standard deviations (1σ) of the counting rates of the contemporary samples, the background and the unknown samples. Calculated errors less than 100 yr have been increased to that figure as a minimum.Corrections have not been made for C13 content. Mass spectrometrics C13 measurements of some samples indicate that errors resulting from fractionation are minimal.

Description: The list includes age measurements carried out from December 1964 to October 1965. As in the previous list (Rome III) the samples dated are almost all of archaeological interest and are drawn from Italian and some European and Asiatic territories.

Description: This list reports routine measurements made at this laboratory since the preparation of the last list (Texas III). It also includes measurements made on bone samples earlier as part of a study of the suitability of bone for C14 dating (Tamers and Pearson, 1965). In the absence of the laboratory director, M. A. Tamers, who has been on leave at the Caracas (IVIC) laboratory since October, 1963, laboratory operation and the selection and description of geologic samples have been handled by Pearson, and laboratory administration and archaeologic samples by Davis.

Description: The following is a list of dates which has been obtained since the compilation of List I in December 1963. Owing to an irreparable leak in our original counter, it became necessary to replace it with a new counter of similar design using the same shield as before. The new counter has been operated both at 500 mm Hg pressure, where it has a background of 1.7 counts/min and an NBS oxalic count of 11.4 counts/min, and at 1000 mm Hg pressure, where it has a background of 2.5 counts/min and an NBS oxalic count of 22 counts/min.

Description: The C14 dates given below are a continuation of the work presented in our first list (RIKEN I), and have been obtained by counting CO2 at about 2 atm pressure in a 2.7-L stainless steel counter. In this article, results obtained during 1964-65 are described.Shell samples were treated with 1% HCl to remove the outer 10%. Calcareous deposits on the surface, when observed, were removed by mechanical means.

Description: All measurements reported in the previous date lists (Kusumgar et al., 1963a; Agrawal et al., 1964 and 1965a) were based on acetylene counting. Since September 1964 we have changed over to methane counting and all dates presented here are based on this method. Methane counting offers certain advantages over acetylene, e.g., (1) rapid synthesis, (2) the non-explosive nature of gas, (3) the synthesized gas is radon-free. The disadvantage of having only one atom per molecule in methane (CH4), as against two in acetylene (C2H2), is compensated by the fact that methane can be counted at higher pressures with relatively low operating voltages.

Description: Preparations for the development of a laboratory for the determination of absolute age by the radiocarbon method were started at the Geobiochemical Laboratory of the Institute of Zoology and Botany of the Academy of Sciences of the Estonian SSR in 1957. Dating of various carbon-containing specimens has been carried out since 1959.

Description: The following list comprises a selected number of measurements made up to November, 1965. Age calculations are based on a contemporary value equal to 95% of the activity of the NBS oxalic-acid standard, and on a half life for C14 of 5570 yr. Results are reported in years before 1950, and in the A.D./B.C. scale. Errors quoted include the standard deviations of the count rates for the unknown sample, the contemporary value, and the background. Because possible errors arising from isotopic fractionation in the plants, or from the de Vries effect, have not been included, calculated errors smaller than 100 yr have been increased by rounding to that figure as a minimum.

Description: Results of absolute age determination by the radiocarbon method, obtained in the Radiocarbon Laboratory of the Vernadsky Institute are given in this article. The counting of natural C14 activity was realized by measuring the gaseous carbon compounds—CO2 and C2H6—with the aid of a proportional counter. Investigation objects were wood, peat, coal, plant and animal remains and other organic material. All samples were preliminarily treated with hot 2% NaOH and 5% HCl to remove foreign humic acid and carbonate. Carbon dioxide, which was obtained after burning, was freed of electronegative admixtures by purification with the aid of CaO. Ethane was synthesized from the sample carbon through the following stages: natural sample→CO2→CaCO3→CaC2→C2H2→C2H6. The counting gas was let into the counter up to a pressure of 2 atm. Counters of stainless steel or copper of different volumes from 0.5 to 2 litres were used. The screening of the counters was effected by steel (24 cm thick) and mercury (2.5 cm thick) shields; the counter together with the mercury shield was enclosed in a circle of Geiger counters of the GS-60 type arranged in anti-coincidence. A detailed description of the methods, the constructions and the apparatus has been published (Vinogradov, Devirts, Dobkina, Markova, Martishchenko, 1961).

Description: The following list comprises measurements made since those reported in NPL III and is complete to the end of November 1965.Ages are relative to A.D. 1950 and are calculated using a half-life of 5568 yr. The measurements, corrected for fractionation (quoted δC13 values are relative to the P.D.B. standard), are referred to 0.950 times the activity of the NBS oxalic acid as contemporary reference standard. The quoted uncertainty is one standard deviation derived from a proper combination of the parameter variances as described in detail in NPL III. These variances are those of the standard and background measurements over a rolling twenty week period, of the sample δC14 and δC13 measurements and of the de Vries effect (assumed to add an additional uncertainty equivalent to a standard deviation of 80 yr). Any uncertainty in the half-life has been excluded so that relative C14 ages may be correctly compared. Absolute age assessments, however, should be made using the accepted best value for the half-life and the appropriate uncertainty then included. If the net sample count rate is less than 4 times the standard error of the difference between the sample and background count rates, a lower limit to the age is reported corresponding to a net sample count rate of 4 times the standard error of this difference.

Description: This series reports some of the measurements made since publication of the previous list. Chemical preparation of samples is basically the same as described in Monaco I.The counting electronics of the proportional counter has been entirely rebuilt by J. Galliot and P. Albertinoli of C.S.M. The new device is transistorized and battery-operated. At regular intervals of time, usually 10 min, the count (anti-coincidence channel) is printed in tape. Large deviations from the mean are easily visible and can lead to rejection of the measurement if the distribution is not normal, i.e. does not fit a straight line on Gaussian paper.

Description: This list presents dates on samples measured at Isotopes, Inc., during the years 1963 to 1965 and measurements made previously for which sample data has been recently received. The many results which do not appear are withheld pending additional information or at the request of our clients.

Description: The C14 dating laboratories of Saclay (Saclay I, 1964 and Saclay II, 1965) and Gif (Gif-sur-Yvette, 1966) have joined together under the name of Gif C14 Dating Laboratory. The first series of dating results appears here with code designation Gif, Sa now being obsolete.

Description: Laboratory construction was begun in December 1964 and routine dating was in progress by late February 1965. The primary purpose of this facility is to assist in marine geological studies and the archaeological chronologies of the region. Dating is carried out by utilizing the techniques of liquid scintillation described by Noakes et al. (1965), wherein the carbon of the sample to be dated is converted to benzene and the natural radioactivity detected in a liquid scintillation spectrometer.

Description: The following list covers most of the samples measured at the Louvain C14 laboratory since the last list (Louvain III).The method is essentially the same as the one used for the work described in the previous lists. A CH4 proportional counter, 0.6 L volume, operating at 3 atm pressure, is used. Equipment and counting techniques have been described in Louvain I. Dates are computed on the basis of the Libby half-life, 5570 yr, and the zero of the age scale is A.D. 1950. Ages are quoted with 1σ experimental error, which includes the counting variations of the sample as well as that of the background and the contemporary standard. As modern standard we now use NBS oxalic-acid standard or wood taken from A.D. 1870 to A.D. 1900 tree rings. No differences between the two standards have been observed.

Description: The dates reported in this list were measured from December, 1964 to November, 1965. The laboratory continues to employ liquid scintillation techniques with synthesized benzene; however, the chemical yield has been improved to the point where it is now between 80 and 100%. For most of the measurements listed here, a 4 cc counting vial was used with 3 cc benzene and 1 cc commercial toluene containing PPO and dimethyl-POPOP scintillators. The counting efficiency is 72%, which gives a net modern count of 23.5 cpm, and the background is 8.2 cpm. The detection limit (48 hours counting, 2σ statistics) with ordinary size samples is 43,000 yr using the 4 cc vial and 52,000 yr with a 20 cc vial. Errors introduced by the laboratory procedure are less than ½% (Tamers and Pearson, 1965a). A detailed review of the methods being used has been published recently (Tamers, 1965b).

Description: The following list presents dates on a small fraction of the total number of measurements made during 1964 and 1965 as well as data on some samples previously dated but not published. Results not appearing have not been released by our clients.

Description: This list includes about half of the samples measured during the last year. Many studies need further investigation and the results will be published later when additional information will make better interpretations possible.The equipment and the technique is essentially the same as described earlier (Bern IV).Reliable results on CO2 samples extracted out of ice are obtained with the small counter mentioned in Bern IV.Our laboratory is financed by the Schweizerischer Nationalfonds. The authors wish to thank H. Loosli and P. Horisberger for their assistance in the measurements of part of the samples. They also thank M. Welten and H.-G. Bandi for their help in selecting and discussing the samples.

Description: The problem considered is the entry of a thin symmetric wedge impinging normally on the free surface of a compressible inviscid liquid, gravitational effects being neglected. Since the body is thin, the problem is a linear one, and its solution is possible for the whole range of Mach numbers of the body's motion in the liquid. It is shown that the free-surface elevations are lowered considerably as the Mach number increases, and that the presence of the free surface acts so as to lower the pressure differences arising from compressibility. © 1966, Cambridge University Press. All rights reserved.

Description: A laboratory model of a tornado vortex has been produced, incorporating two features which are believed to be important to the understanding of the atmospheric phenomenon, but which have been largely ignored in previous studies. First, it has been shown that a vortex can be driven from above by a mechanism analogous to convection in a cloud, and that density differences within the funnel itself are not essential. Associated with this mechanism of formation is a circulation in the vertical, with an upflow in the centre surrounded by a compensating annular downflow. Secondly, the bottom boundary is seen to have a strong influence on the vortex, since the down and up flows are linked there by a rapid radial inflow in a thin boundary layer. In the present paper an approximate theoretical description of such a vortex is proposed. The interior and boundary layer flows are first examined separately, and then a condition is sought which makes the two solutions consistent. The starting-point of the theory is the assumption of a form of stream function which describes a circulation in the vertical having the essential features of that observed. The result of the matching procedure is to fix both the form of the tangential velocity profile, and the relative magnitudes of the three components of velocity. These deductions are not critically dependent on the assumed form of the motion in the vertical, and are in good agreement with the first measurements in the laboratory vortices, though the quantitative experimental results are not emphasized here. © 1966, Cambridge University Press. All rights reserved.

Description: Liquid-into-liquid jets in short cylindrical vessels have been investigated under conditions of uniform flow by using an aqueous blue tracer solution in conjunction with tránsparent cylindrical tanks. The vessels had diameters D of 3, 6, 12 and 24in., length-to-diameter ratios L/D of 1, 2 and 3 and inlet diameters d between ¼ and 1 in. Reynolds numbers in the inlet tube, Rei, ranged between 100 and 28,000. Four main types of jet were observed: [formula omitted] The laminar length a of sub-turbulent jets was investigated and correlated with Rei and the geometric parameters by the equation [formula omitted]. © 1966, Cambridge University Press. All rights reserved.

Description: A correlation scheme for velocity and temperature profiles is derived for turbulent boundary layers in adverse pressure gradients. The resulting analytical expressions are obtained by what could be referred to as ‘regional similarity’ arguments. This avoids the need to make use of the Reynolds analogy (explicitly, at least) or the usual local gradient-type diffusion expressions for momentum and thermal transport (‘the local similarity’ and Boussinesq concept). The expressions agree well with experimental data for the velocity profiles and encouraging correlation is shown for the temperature profiles. The expressions cover a wider part of the profile than given by the logarithmic law of the wall. Surface roughness and Prandtl-number effects are included in the analysis. © 1966, Cambridge University Press. All rights reserved.

Description: The principle of exchange of stabilities (exchange principle) for the thermal stability problem has been proved by Pellew & Southwell (1940) for fluids bounded by two infinite, horizontal parallel planes. Chandrasekhar (1952) discussed the establishment of the exchange principle for the same geometry when the fluid is an electrical conductor and when an arbitrary oriented, uniform, external magnetic field is applied in the vertical direction. In this paper, the exchange principle is examined for fluids completely confined in an arbitrary region with rigid bounding surfaces that are good electrical conductors with respect to the fluid. The uniform magnetic field is applied in an arbitrary direction. A generalized thermal boundary condition is imposed which includes the fixed temperature and prescribed heat-flux conditions as special cases. If no magnetic field is applied to the fluid, the present work reduces to a generalization (for completely confined fluids) of the Pellew & Southwell proof of the exchange principle. In the magnetohydrodynamic (MHD) thermal stability problem, the exchange principle is found to be valid if the total kinetic energy associated with an arbitrary disturbance is greater than or equal to its total magnetic energy. In a special case it is demonstrated that a sufficient condition which will establish the exchange principle is k ≤ η, where k is the fluid thermal diffusivity and η is the fluid electrical resistivity. © 1966, Cambridge University Press. All rights reserved.

Description: In this paper the viscous, slightly stratified flow towards a sink is investigated. The fluid is assumed incompressible, linearly stratified in density, and the flow steady. The theoretical portion of this paper includes both the two-dimensional and the axisymmetric cases, whereas the experimental portion includes only the two-dimensional case. The solutions obtained indicate that there exists a with-drawal layer symmetrically situated about the horizontal plane of the sink. The flow occurs in this layer while outside this layer there is essentially no motion. This withdrawal layer grows in thickness with the distance x (or r) from the sink at a rate proportional to [formula omitted]). The velocity distributions u(y) (or u(z)) are similar from one station x (or r) to another. © 1966, Cambridge University Press. All rights reserved.

Description: The solution for the flow of a fully ionized gas over a wedge of finite angle is known for the case when the applied magnetic field is aligned with the incident stream. In this flow there are current sheets on the surfaces of the wedge. When the magnetic field is allowed to deviate slightly from the stream, the current sheets may move into the gas and become shock waves. The magnetic fields adjacent to the wedge above and below it have to be matched. A perturbation method is introduced by means of which expressions for the unknown quantities in the different regions may be determined when there are four shocks attached to the wedge. The results give insight into the manner in which the shock-wave pattern develops as the obliquity of the magnetic field to the stream increases. The question of the stability of the shock waves is also examined. © 1966, Cambridge University Press. All rights reserved.

Description: This is a continuation of our previous work (1965) on the Sears–Resler–Stewartson controversy, in the context of axially symmetric flow. A new approach is presented using boundary-layer arguments, which remove much of the old complexity. For resistive bodies of shape R(x) we uncover a similarity with plane airfoils of shape F(x) = R2(x). As before, Stewartson's slug flows develop fore and aft. For bodies of very high conductivity the Sears–Resler (steady-state) solution turns out to be one possibility. It pertains to bodies (of much higher conductivity than the liquid) into which the initial magnetic field has not diffused. © 1966, Cambridge University Press. All rights reserved.

Description: A general numerical method of characteristics applicable to problems in magneto-fluid dynamics as well as ordinary fluid dynamics is described. The method can be applied to unsteady three-dimensional flows of chemically reacting, non-equilibrium, multi-component media. Dissipative phenomena must be neglected in order to make the governing equations of change hyperbolic, because the method can be applied only to quasi-linear, hyperbolic, partial differential equations. Practical restrictions on computation time usually require unsteady problems to be limited to cases with short transient times although theoretically the method applies to all unsteady flows. In steady flow the local velocity must be greater than the largest local wave speed. The characteristic and compatibility equations are derived for the most general case of magnetofluid dynamics. A new finite-difference network and its corresponding equations are developed similarly. Specialization of the general method to consider simpler problems is outlined. Preliminary numerical results of calculations using the method are presented. The practicality and feasibility of utilizing the general numerical method of characteristics on presently available, electronic digital computers is evaluated in the light of recent experience in calculating multi-dimensional flows with the method. © 1966, Cambridge University Press. All rights reserved.

Description: A fluid is contained between rigid horizontal planes which move relative to each other with constant horizontal velocity. A gravitationally unstable temperature difference is maintained at the boundaries, and the heat flux and momentum flux (stress) transmitted by the fluid are measured. The Nusselt number, Nu, and the dimensionless momentum flux, Mo, are obtained for small mean rates of shear. The Rayleigh number, R, and the Prandtl number, σ, are both large in these experiments. The data are consistent with the following relations: [formula omitted] Kraichnan's mixing-length theory of turbulent thermal convection is extended to the present situation, and the above experimental dependence of Nu and Mo on R and σ is obtained. The agreement between mixing-length theory and experiment provides strong support for Kraichnan's concise treatment of turbulent convection. The importance of this result is that heat and momentum fluxes may be calculated in this way for a variety of flows in geophysics. © 1966, Cambridge University Press. All rights reserved.

Description: The assumptions of the shock-expansion method are re-examined. Although the shock-expansion method and Whitham's rule are used to treat two different classes of problems, certain similarities between these two methods are noted. It is suggested that a single procedure leads to solutions for the entire flow field for both classes of problems. © 1966, Cambridge University Press. All rights reserved.

Description: A procedure is introduced to extend the usefulness of some perturbation solutions previously presented by Libby & Fox (1963) and Fox & Libby (1964). The perturbations are now formulated about a Blasius solution with an unknown origin. This origin, an additional degree of freedom, is selected, in the spirit of local similarity, so that it will yield a better approximation to the initial profile. With this modification the basic solution will handle a much wider class of problems successfully. Numerical examples are presented to demonstrate the improved accuracy and applicability of this new scheme. © 1966, Cambridge University Press. All rights reserved.

Description: In a recent study related to transition in the wake flows behind circular cylinders held transversely to an air stream, Bloor (1964) has reported the observation of velocity ‘spikes’ and attributed these to the close proximity to the hot wire of vortex centres on the opposite side of the von Kármán vortex street. Further observations of spikes are reported here, and the characteristics of their distribution indicate that other explanations of their form must be found. Some idealized flows are considered, and it is concluded that observations of spikiness within the hot-wire output may be accountable in terms of large-scale distributions of vorticity within the flow convected past the wire, the distributions being reasonable representations of a separated flow. The observations also provide some evidence that small vortices of Strouhal frequency exist on the inside of the coherent separated shear layer, and this may assist in the understanding of the feed-back mechanism where by the von Kármán street establishes itself as a self-perpetuating phenomenon. © 1966, Cambridge University Press. All rights reserved.

Description: The turbulent flow of a weakly conducting liquid between parallel plates in the presence of a transverse magnetic field is investigated. The form of the mean velocity profile is determined by a series of constraints resulting from the boundary conditions and the Navier–Stokes equations and by the Malkus postulates on the spectrum of the mean vorticity gradient. The width of the transition regions near the walls is derived in terms of the governing dimensionless numbers and this expression is checked, in the asymptotic laminar case, against the well-known Hartmann result. A graphical method, exploiting the relation between the boundary region thickness and the smallest scale of motion defined by the Malkus theory is proposed to determine the scale of the velocity profile, i.e. the flow rate in terms of the pressure gradient and the magnetic field strength. © 1966, Cambridge University Press. All rights reserved.

Description: Numerical methods are used to investigate the steady two-dimensional motion of a viscous incompressible fluid past a flat plate of finite breadth at zero incidence to a uniform stream. Before application of numerical techniques, the governing partial differential equations for the stream function and vorticity are reduced to ordinary differential equations by an adaptation of methods normally used to solve Oseen's linearized equations. The complete range of the Reynolds number R is considered, from indefinitely small to indefinitely large. All the results are intended to represent solutions of the full Navier-Stokes equations of motion, although in practice approximations are inevitable. These are mainly brought about by the necessity of limiting the size of the calculations. At the lower end of the Reynolds-number range, the calculated frictional drag coefficient agrees well with the results of Tomotika & Aoi (1953) based on Oseen's equations. At intermediate and higher Reynolds numbers there is good agreement with the experimental results of Janour (1951) and with the improvement of the Blasius solution given by Kuo (1953). Finally a limiting solution is obtained as R → ∞. This shows that the drag coefficient is proportional to R−½, in accordance with boundary-layer theory. The actual calculated value of the coefficient is about 4% higher than the Blasius value. Although the present results tend generally to confirm the trend of the recently published results at R = 0·1, 1 and 10 of Janssen (1957), there are substantial discrepancies in the detailed results in a number of instances. In particular, the drag values obtained at R = 1 and 10 are some 20% higher than Janssen's although there is reasonable agreement at R = 0·1. It seems possible that Janssen's analogue is a little crude at the higher Reynolds numbers. © 1966, Cambridge University Press. All rights reserved.

Description: A critical scrutiny of the nature of the three-dimensional characteristics of the vortex wake of a circular cylinder serves to suggest lines for further investigation and furnishes some ideas on the nature of the growth and development of these non-uniformities. It is suggested that the basic occurrence in the growth of three-dimensionality is the continuation of vortex lines, oriented more or less parallel to the body, into the direction of the free stream. The causes of this vary, as do the details of the development with the particular situation considered. Experiments were performed in a wind tunnel at Reynolds numbers based on cylinder diameter of 85, 235 and 2 × 104, at which stable, transitional and turbulent vortices were investigated. © 1966, Cambridge University Press. All rights reserved.

Description: Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error. The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail. © 1966, Cambridge University Press. All rights reserved.

Description: An analysis of the exact equations of the inviscid flow of a perfect gas over cusped concave bodies is described. The field is examined in the limit of infinite free-stream Mach number M ∞. The slope of the shock wave in a small region adjacent to the leading edge is strongly dependent on M ∞, while much further downstream the shock-wave slope is controlled primarily by the body slope. Consequently the region near the leading edge introduces into the field downstream a thin layer of gas, adjacent to the body, where the entropy is much lower than that of the gas above it. This layer is so dense that the gas velocity along it is not appreciably slowed by the pressure gradient along the body. However, it is so thin that there is little pressure change across it. The well-known self-similar solutions to the hypersonic small-disturbance equations have previously only been used to study the flow on blunted slender convex surfaces. They are known to behave singularly at the body. It is shown that there is a region on concave power-law shapes where the self-similar solutions are the correct first approximation to the exact inviscid equations in the limit M∞ → ∞; and that, further, they predict the correct first-order surface pressure. Numerical results for surface pressure from the similar solutions are presented, and comparisons are made with certain approximate theories available for more general shapes. Pressure measurements taken on a cubic surface in the Imperial College gun tunnel are presented and compared with the theoretical distributions. © 1966, Cambridge University Press. All rights reserved.

Description: The large-eddy energy equilibrium hypothesis states that the largest eddies of a turbulent shear flow are in approximate energy equilibrium throughout a significant part of their lives. This hypothesis leads to a relationship between the mean rate of shear strain and the Reynolds shear stress which involves the scale of the large eddies. By assuming that the large-eddy scale is proportional to the standard deviation of the free turbulent boundary, or laminar superlayer, the validity of this hypothesis may be checked experimentally. Intermittency and mean velocity measurements made in five different two-dimensional shear flows are presented and these results, together with values calculated from Townsend's measurements in a two-dimensional wake, support the form of relationship suggested by the energy equilibrium hypothesis. © 1966, Cambridge University Press. All rights reserved.

Description: Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).

Description: The flow field in the nose region of a blunt body in hypersonic flow is studied by considering the transport of vorticity and enthalpy. The entire region between body and shock is considered to be viscous, not necessarily thin in comparison with the nose radius of the body and to be of slowly varying density. The (given) post-shock vorticity need not be small and the density ratio ρ∞/ρs may either be small or near unity, the analysis being valid asymptotically at both limits. It is found that the vorticity equation may be uncoupled from the total enthalpy equation if μ√ρ is constant. While the equations are not expected to be necessarily restricted to the immediate vicinity of the stagnation line, only there can the solution be written down explicitly; elsewhere, numerical integration is required. © 1966, Cambridge University Press. All rights reserved.

Description: The effect of uniform rotation on surface-tension-driven convection in an evaporating fluid layer is considered both theoretically and experimentally. The theoretical analysis follows the usual small-disturbance approach of perturbation theory and leads, at the neutral state, to a functional relation between the Marangoni and Taylor numbers which is then computed numerically. In addition, it is shown analytically that, in the limit of rapid rotation, the velocity and temperature fluctuations are confined to a thin Ekman layer near the surface, and that Mc= 4·42T½ and ac= 0·5T¼, where Mc and ac are, respectively, the critical Marangoni number and the critical wave number for neutral stability, and T is the Taylor number. The experimental part deals primarily with the flow pattern of a 50% solution of ethyl ether in n-heptane evaporating into still air. In this case, the convective flow is surface-tension-driven and its structure was observed using schlieren optics. In the absence of rotation, the flow shows a remarkable cellular pattern when the layer is shallow, but when the depth of the layer is increased the pattern quickly becomes highly irregular. In contrast, for T 〉 103, a cellular structure is always observed even for deep layers, a result which is attributable to the stabilizing effect of the Coriolis force. A further increase in T leaves the flow pattern unchanged except that the size of the cells is found to decrease as T−¼ which is in agreement with the results of the linear stability analysis. © 1966, Cambridge University Press. All rights reserved.

Description: A considerable quantity of observations and measurements exists concerning the phenomenon of intermittency which is connected closely with the entrainment process in free turbulent flows. A number of these are described in the first part of the paper and conclusions are drawn about the shape and motion of the bounding surface that separates turbulent and non-turbulent fluid. The salient features are that indentations of the surface grow and decay cyclically, that each cycle leads to substantial entrainment of ambient fluid into the turbulent region, that the indentations move at a considerable speed relative to the free stream, and that the surface has a comparatively simple form. The growth–decay cycle of the indentations suggests that a critical condition for growth exists, but the pressure field consequent on the convection velocity of the indentations makes for a Helmholtz type of instability that is unlikely to be stabilized by purely viscous behaviour of the turbulent fluid. It is known that the initial response of turbulent fluid to distortion is elastic in character, with incremental Reynolds stress proportional to increment of total strain, and sufficient rigidity could stabilize the bounding surface. A simple flow model–an inviscid stream flowing over an elastic jelly—is examined and the condition for marginal stability is compared with the observed properties of the flow. The model leads to the conclusion that indentations of more than a critical wave-number are stable, and provides reasons for the comparatively simple form of the surface and for the occurrence of indentations in groups of about three. The relative values of entrainment constants in different flows of uniform density do not depend critically on the nature of the entrainment process provided that the main turbulent motion remains geometrically similar, but the correlation between entrainment constant and relative depth of the indentations found by Gartshore (1966) appears as a consequence of the ‘elastic’ control of the growth–decay cycle. Lastly, the properties of the engulfment mechanism are used to show that the entrainment constant for a jet is proportional to the square root of the ratio of ambient density to the average density inside the jet. In contrast, the corresponding result for engulfment controlled by an eddy viscosity is variation as the ratio of the mean of the ambient and inside density to the inside density. Observations of high-speed jets of water in air and air in water give some support to the ‘elastic’ hypothesis. © 1966, Cambridge University Press. All rights reserved.

Description: This paper studies the two-dimensional convective motion in a rectangular cavity, the two vertical sides of which are maintained at different temperatures. This system is studied for the special case in which the temperature difference ΔT between the two vertical walls is so large that the transfer of heat from one vertical wall to the other is achieved almost entirely by convection. Heat transfer by conduction is assumed to be of importance only in thin boundary layers adjoining the walls. For a cavity of height H, the boundary layers on the two vertical walls are found to have thickness proportional to l, where l4 = κνH/ΓgΔT, and the condition for the boundary-layer regime to be established is that l be small compared with the width of the cavity. An approximate solution of the problem is obtained for the case of large values of the Prandtl number ν/κ, and found to be in satisfactory agreement with experimental results obtained by Elder (1965). © 1966, Cambridge University Press. All rights reserved.

Description: A solution is offered for the relative phase relationship of bed, depth and surface waves observed in alluvial channels, and is found to be in good agreement with observation in laboratory flumes. The solution does not depend on an assumption of a phase lag between the velocity and sediment movement. The emphasis of the paper is on the mechanics of bed-wave formation. © 1966, Cambridge University Press. All rights reserved.

Description: It has been found that ventilated cavities extending behind hydrofoils, plates, and other two-dimensional bodies, oscillate when the air supply rate is sufficient to reduce the cavitation number to about one-fifth of its natural value. As the rate increases further, higher modes of oscillation occur in which the cavity–water interface supports several waves that are convected downstream towards the wake, which, owing to a pinching-off action replacing the usual entrainment sink, consists of a sequence of large bubbles drifting downstream. A theory of such flows that allows both for the convected velocity fluctuations in the cavity, and for the transport of bubble volume down the wake, is given in this paper. Coupled with a rather simple phenomenological relation between the pressure fluctuations within the cavity and the departure of the pinched-off rear portion of the cavity‒explained in terms of the action of the re-entrant jet‒this theory successfully predicts the resonance frequencies obtained in experiments by Silberman & Song. The theory also provides a solution of the more general problem of determining the fluctuations in the pressure distribution over the whole surface of the body, when it is in a prescribed unsteady motion along its axis of symmetry (the theory is confined to symmetrical bodies and flows). Thus the growth in drag due to a sudden increment in the upstream velocity can be predicted, and also the damping forces acting on the body when it is forced to oscillate at a given frequency. It is shown that in all cases the body is unstable. One important feature of the mathematical model chosen is that it completely avoids the presence of a time-dependent sink at infinity‒with its associated infinite pressures‒by conserving total volume of wake and cavity in just the same way as vorticity is conserved in unsteady aerofoil theory. © 1966, Cambridge University Press. All rights reserved.

Description: The paper deals with an extension of previous work on the radiation properties of turbulent flow formed on compliant surfaces. The effect of simple supports is shown to be acoustically equivalent to an extended dipole system of strength equal to the support stress. The dipole radiation is reduced by a transmission factor below that radiated into a uniform environment. A particular example is worked out in detail. That example deals with the case of a single point support on an otherwise homogeneous surface excited by boundary-layer turbulence. © 1966, Cambridge University Press. All rights reserved.

Description: The paper deals with the refraction of a plane shock wave by an interface between two different gases. It is shown that the equations of motion can be reduced to a single polynomial equation of degree 12. Detailed numerical results are presented for the air-CH4 and the air-CO2 interfaces, which are respectively ʻslowfastʼ and ʻfast–slowʼ combinations. When the results are compared with experiment good agreement is obtained. The numerical data are multi-valued, but it is found that it is always the weakest solution that agrees with the experimental data. The multiple roots of the equation are often found to be associated with the appearance of degenerate and irregular wave systems and some attempt is made to analyse and discuss these systems. © 1966, Cambridge University Press. All rights reserved.

Description: In the presence of an air stream, a uniform liquid film on a horizontal flat plate may be unstable to small disturbances, and waves may arise. In this paper the hydrodynamic stability of thin liquid films is examined both experimentally and theoretically. The experiments concern water films thinner than those which have been examined in the past. It is found that, when the film thickness is sufficiently small, a previously unknown type of instability occurs. The theoretical analysis explains this surprising phenomenon. Due to interaction of the mean airflow and small disturbances of the liquid-air interface, normal and tangential stress perturbations are produced at the liquid surface. It is shown that small wave-like disturbances become unstable when the joint influence of the component of normal stress in phase with the wave elevation and the component of tangential stress in phase with the wave slope is sufficient to overcome the ʻstiffnessʼ of the liquid surface due to gravity and surface tension. It is found that the destabilizing role of the tangential stress component is dominant for very thin films, and that instability may occur whatever the velocity of the air stream, provided the film is made sufficiently thin. © 1966, Cambridge University Press. All rights reserved.

Description: The dynamics of rotating fluids was, in the main, developed by methods special to the field, using the equationsof motion of a fluid inarotatingframe of reference. It is, nevertheless, possible to derive all the leading results from the classical principles of fluid dynamics in non-rotating frames; specifically, from the rules governing rate of change of vorticity. Although writers on the subject have adopted this approach increasingly often in recent years, the author believes that a broad survey of the field, deriving results from those classical rules concerning vorticity, has not previously been given and may be of some interest to fluid dynamicists in general. The present survey was read to the IUTAM Symposium on Rotating Fluid Systems at La Jolla, California, on 28 March 1966. It states briefly (§2) the rules governing rate of change of vorticity, and then applies them, first, to problems of steady relative motion of rotating fluids; in particular, of the atmosphere (§3), of rotating fluids in the laboratory (§4), and of the oceans (§5). Waves and wavy movements are then studied, first (§6) for systems with constant Coriolis parameter, including inertial waves, surface waves, ʻlong wavesʼ and internal waves, and, secondly (§7)) for systems with variable Coriolis parameter, including Rossby-Haurwitz waves with and without the influence of tidal effects, as well as problems of barotropic and baroclinic instability. Vorticity principles are used as the sole theoretical tool throughout the survey. © 1966, Cambridge University Press. All rights reserved.

Description: The experiments described here were designed to illustrate the dynamical behaviour of flexible cylinders in axial flow theoretically examined in Part 1. Rubber cylinders, either clamped or pinned at the upstream end and free at the other, or pinned at both ends, displayed both buckling and oscillatory instabilities when immersed in flowing water of sufficiently high velocity. The conditions of neutral stability were determined in a number of cases and compared with theory. The observations were in substantial agreement with the theory. © 1966, Cambridge University Press. All rights reserved.

Description: The results of a detailed mean velocity survey of a smooth-wall turbulent boundary layer in an adverse pressure gradient are described. Close to the wall, a variety of profiles shapes were observed. Progressing in the streamwise direction, logarithmic, ½-power, linear and [Formula omitted]-power distributions seemed to form, and generally each predominated at a different stage of the boundary-layer development. It is believed that the phenomenon occurred because of the nature of the pressure gradient imposed (an initially high gradient which fell to low values as the boundary layer developed) and attempts are made to describe the flow by an extension of the regional similarity hypothesis proposed by Perry, Bell & Joubert (1966). Data from other sources is limited but comparisons with the author's results are encouraging. © 1966, Cambridge University Press. All rights reserved.

Description: The Navier-Stokes vorticity equation is solved numerically for the circulation induced in a vertical plane, by a constant stress acting on a liquid, enclosed in a basin of uniform depth and vertical sides. Solutions of the linearized vorticity equation are obtained for all Reynolds numbers (τsD2/4ρν2 where νs is the surface stress, ρ is the density, ν is the kinematic viscosity, and D is the depth of the liquid) and solutions of the complete vorticity equation for Reynolds numbers 0–400. The notable feature of the solutions is the totally different end circulations. At the upwind end the flow becomes very slack, and the vorticity equation has a boundary-layer limit, while at the downwind end a damped wave occurs and the equation has an inviscid limit. At Reynolds numbers between 400 and 600, the streamlines at the downwind end lead to a condition of hydrodynamic instability, in approximate agreement with some experimental observations by G. H. Keulegan. © 1966, Cambridge University Press. All rights reserved.

Description: The distance between the separation point and the final approach to a fully developed turbulent mixing layer is found to be of the order of a thousand times the momentum-deficit thickness of the initial boundary layer, whether the latter be laminar or turbulent. There are correspondingly large shifts in the virtual origin of the mixing layer, resulting in spurious Reynolds-number effects which cause considerable difficulties in tests of model jets or blunt-based bodies, and which are probably responsible for the disagreements over the influence of Mach number on the development of free shear layers. These effects are explained. © 1966, Cambridge University Press. All rights reserved.

Description: A theory of finite-amplitude secondary flow between concentric rotating cylinders has been published by Davey (1962). A necessary feature of the theory is the generation of harmonics of the spatial periodicity in the axial direction of the velocity field. A method has been devised to measure the amplitude of each harmonic separately and experimental results for the fundamental and first three harmonics are presented here for Taylor numbers up to 100 times the critical value. The agreement with Davey's theory is excellent, and the agreement extends far beyond the range where the theory is expected to be valid. It is shown that all the harmonics are in phase with the fundamental. This result requires that jets and shock-like structure must be present in the velocity field. © 1966, Cambridge University Press. All rights reserved.

Description: The changes of surface stress in a deep boundary layer passing from a surface of one roughness to another of different roughness are described fairly accurately by theories that assume self-preserving development of the flow modifications. It has been shown that the dynamical conditions for self-preserving flow can be satisfied if the change in friction velocity is small and if log l0/z0 is large (l0 is the depth of the modified flow and z0 is the roughness length of the surface). In this paper it is shown that, if the change of friction velocity is not small, the dynamical conditions can be satisfied to a good approximation over considerable fetches if log l0/z0 is large. The flow modification is then locally self-preserving, that is, the fields of mean velocity and turbulence are in a moving equilibrium but one which changes very slowly with fetch and depends on the ratio of the initial to the current friction velocity. In the limit of a very large increase in friction velocity, the moving equilibrium is essentially that of a boundary layer developing in a non-turbulent free stream. Equations describing the flow development are derived for all changes of friction velocity, and the form of the velocity changes is discussed. For large increases of friction velocity, the depth of the modified layer is substantially less than would be expected from the theories of Elliott and of Panofsky & Townsend. © 1966, Cambridge University Press. All rights reserved.

Description: A symposium on ʻRotating fluid systemsʼ was held at La Jolla, California, from 28 March to 1 April 1966. The meeting was organized under the auspices of the International Union of Theoretical and Applied Mechanics, and took place at the Institute of Geophysics and Planetary Physics of the University of California. There were 75 participants, and attendance was by invitation. The subjects discussed included steady flows, both thermally driven and non-thermal; transient motions and instabilities; planetary waves and gravity waves affected by rotation; inertial oscillations; and hydromagnetic flows relating to the Earth's interior. The following is a brief account of the proceedings as seen by the authors. No formal volume of the papers presented is to be published, but references to published or unpublished work are given at the end of this article. © 1966, Cambridge University Press. All rights reserved.

Description: Expressions are obtained for the jump in vorticity across a discontinuity surface which is not a contact surface. Admitting arbitrary motion of the fluid and the discontinuity, the most general of these is established on a purely kinematical basis. More specific expressions are obtained by successively enforcing the momentum equation of the flow and the conditions of conservation of mass and momentum across the discontinuity. Eventually Hayes's (1957) result for a gasdynamic discontinuity is recovered. © 1966, Cambridge University Press. All rights reserved.

Description: The equilibrium burning of a spherical drop of pure non-gaseous fuel in a slow convective flow of hot oxidant is examined for Lewis number unity. A Stokes or Oseen flow with modified boundary conditions to permit mass transfer at the drop surface describes the velocity field. The method of inner and outer expansions is then adopted to describe the thermal and mass-fraction profiles under the model of a direct one-step irreversible indefinitely fast chemical reaction. The thin-flame position and surface mass-transfer rate, both functions of polar angle as well as radial position when convection is added to the conventional diffusive transport, are furnished in terms of the Peclet number. It is found that the interaction of the perturbational free-streaming with the asymmetric vaporization it induces can lead to drag coefficients in excess of the Stokes value. © 1966, Cambridge University Press. All rights reserved.

Description: A series of experiments is described in which a jet issues from an orifice at the nose of a body in supersonic flow to oppose the mainstream. An analytical model of the flow is developed which suggests that the aerodynamic features of a steady flow depend primarily on a jet flow-force coefficient, and the Mach number of the jet in its exit plane. A sufficient condition for steady flow is developed. The experiments are found to agree well with predictions based on the flow model. A short account is presented of some previous investigations, and some of their conclusions are re-examined in the light of the present study. © 1966, Cambridge University Press. All rights reserved.

Description: The investigation of a separated shear layer was undertaken to clarify the non-linear mechanisms associated with instability and transition to turbulence. Such an investigation is of practical importance since profiles which resemble the separated shear layer are a common occurrence. A two-dimensional free shear layer was formed by separation of a laminar boundary layer from a rearward-facing step. The free-stream speed was approximately 16 ft./sec. Hot-wire measurements were made in the region directly downstream of the plate trailing edge. The measurements included mean velocity profiles, frequency spectra of the longitudinal fluctuation, and root-mean-square amplitude and phase distributions of various spectral components of the longitudinal fluctuation. Several measurements were designed to detect the presence of periodic spanwise structure. The most important findings were: Significant non-linear distortion of the initial unstable wave occurred without periodic spanwise structure. Non-linear distortion was first manifest by the growth of a subharmonic oscillation, which was strongly intermittent. Numerous harmonics of the sub-harmonic oscillation were also present. Strong evidence suggests that secondary instabilities were present, which created still higher frequencies. © 1966, Cambridge University Press. All rights reserved.

Description: The structure and mode of propagation of spinning detonation waves in stoichiometric oxyhydrogen, at initial pressures of 20–30 mm, have been investigated. The waves were generated in a square-section tube and observations have been made by the smoked-film technique, spark schlieren photography and pressure gauges. At the front of the self-sustaining detonation waves obtained at these pressures, two Mach interactions exist, the trajectories of which are derived from the imprints made on the smoked foil. As the triple point traverses the tube section, its direction of motion is found to vary between 50° and 70° with the tube diameter. An analysis of a Mach triple point for these conditions predicts the absence of chemical reaction behind the Mach stem in the immediate neighbourhood of the triple point. Experimentally determined pressures and triple shock angles confirm, to within experimental error, the postulated theoretical configuration. © 1966, Cambridge University Press. All rights reserved.

Description: A method is proposed for obtaining regular solutions of the boundary-layer equations near a point of vanishing skin friction for steady incompressible laminar two-dimensional flow. The boundary-layer equations are integrated numerically in the usual way until the separation point is approached; then the displacement thickness is prescribed as a regular function of the distance along the surface, leaving the pressure gradient to be calculated from the consequent solution. Numerical solutions are obtained with reversed flow and shallow separation bubbles inside the boundary layer without the occurrence of a singularity at the separation point. © 1966, Cambridge University Press. All rights reserved.

Description: Experimental evidence suggests that it may be profitable to separate the discussion of the high-frequency components of jet noise from low-frequency components. Theory then leads one to the recognition that the physical mechanism of noise generation is slightly different for the two components and for this reason one may speak of high-frequency ʻself noiseʼ and low-frequency ʻshear noiseʼ (Lilley 1958; Ribner 1964). Both theory and experiment indicate that mean-flow refraction effects on self noise are appreciable. Using geometrical acoustics a description of the far-field radiation pattern of the high-frequency end of the jet-noise spectrum is obtained, in good qualitative agreement with observations. A conservation law of acoustic energy, applying between the frame of reference in which the sound sources move, and the fixed frame in which the observations are carried out, results in the absence of the convection amplification effect (over and above the U8 law) for total sound power at high frequencies, a result which helps explain the uniform validity of the U8 law. An analysis of the shear-noise source term suggests that this part of the sound radiation is due to a combination of quadrupoles which have at least one axis parallel to the jet. This then explains the observed concentration of low-frequency noise around the jet axis. © 1966, Cambridge University Press. All rights reserved.

Description: Calculations are presented for two-dimensional BÉnard convection between free bounding surfaces for ranges of Rayleigh and Prandtl numbers. The variables are expanded in a series consisting of the eigenfunctions of the stability problem and the system is truncated to take into account only a limited number of terms. The amplitudes of the eigenfunctions are evaluated by numerical integration of the resulting non-linear equations. In all cases considered, the system achieves a steady state with the motion consisting of a single large cell. Results for Nusselt number vs. Rayleigh number are given for a range of Prandtl number varying between 0·01 and 100 and show that heat flux increases slightly with decreasing Prandtl number. The calculations agree with those of Kuo where the ranges of Rayleigh number overlap. A simple heuristic argument based on the assumption that turbulent boundary layers exist is also given and the conclusions of the latter indicate that heat flux should decrease with decreasing Prandtl number. Thus the behaviour is qualitatively different from that of the calculations. The reason appears to be associated with the fact that the single large cell in the computed cases enables the fluid to accelerate through repeated cycles until it achieves a steady state with the amplitude of the motion much larger than could be acquired by a single turbulent blob free-falling in the gravitational field. © 1966, Cambridge University Press. All rights reserved.

Description: The maximum amplitude of the solitary wave of constant form is determined to be 0·83b, where b is the depth far from the crest. In the analysis it is assumed that the crest is pointed and the motion is two-dimensional and irrotational. The complex velocity potential is expressed in terms of known singularities and an infinite power series with unknown coefficients. Approximate solutions are obtained by truncating the power series after N terms, where N = 1, 3, 5, 7, and 9. The amplitude, a measure of the error, and several other pertinent quantities are computed for each value of N. © 1966, Cambridge University Press. All rights reserved.

Description: A technique has been developed to measure the instantaneous shear stress at the boundary over which a liquid is flowing. It is being used to study turbulence in the immediate vicinity of a pipe wall. A reaction is conducted on an electrode mounted flush with a solid wall at high enough voltages to reduce the concentration of the reacting species to zero at the surface. Under these conditions, the rate of reaction is controlled by the rate of mass transfer. The electrode is analogous to a constant-temperature hot-wire anemometer in that the surface concentration is kept constant and the current flowing in the circuit is related to the surface shear stress. For fully developed turbulence the limiting velocity intensity, based on the local average velocity, is 0·32. Some of the velocity fluctuations are as large as the local average velocity and their distribution is nearly symmetric about the average. The ratio of the longitudinal to circumferential scale is about 30 : 1, because the circumferential scale is very small. There is some indication that close to a wall the velocity fluctuations in the circumferential direction are much smaller than the longitudinal fluctuations. © 1966, Cambridge University Press. All rights reserved.

Description: Experimental and theoretical investigations were made of the instability and transition of the wake behind an axisymmetric slender body at high Reynolds number. The sound from a loudspeaker was used as an artificial disturbance. The velocity fluctuations induced by the sound are selectively amplified depending on the frequency. The wavelength, the phase velocity and the amplification rate of the velocity fluctuations were measured. A linearized stability equation of the disturbance superposed on the axisymmetric wake was solved numerically for both neutral and amplified disturbances. Theoretical results on eigenvalues and eigenfunctions of the stability equation show good agreement with experimental results. Measurements on phase distributions in streamwise and azimuthal directions indicate that the line of same phase forms a helix and not a series of discrete closed loops. © 1966, Cambridge University Press. All rights reserved.

Description: The peeling of a flexible strip from a rigid surface to which it is attached by a thin layer of adhesive is discussed, treating the adhesive as a Newtonian viscous fluid. This makes it possible to examine the flow and stress distributions ahead of the point where separation occurs. The conditions at this point are taken to be the same as those observed in other cases where a stream of viscous fluid separates into two. In particular, the effect of surface tension at the separating meniscus on the speed of peeling is predicted. Experiments are described in which a sheet of ʻMelanexʼ 4μm thick was laid on a sheet of fluid covering a piece of plate glass. The apparatus was designed to ensure that this was peeled off at a constant angle, and the speed of the separation meniscus, as well as the load on the sheet, was measured. The experimental results are analysed in the light of the theory and shown to be consistent with it. An interesting feature is the prediction that at low peeling speeds there is a great reduction in the thickness of the adhesive layer immediately ahead of the line of separation. Although the initial thickness of the layer dictates the scale of the shape adopted by the strip ahead of this line, it exerts no effect upon the relation between the external variables. It is noted that, when the adhesive layer remains intact ahead of separation, the physical appearance of commercially available tapes in slow peeling can resemble that of simple viscous adhesives. © 1966, Cambridge University Press. All rights reserved.

Description: The problem solved concerns the disturbance to a stream of shallow water due to an immersed slender body, with special application to the steady motion of ships in shallow water. Formulae valid to first order in slenderness are given for the wave resistance and vertical forces at both sub- and supercritical speeds. The vertical forces are used to predict sinkage and trim of ships and satisfactory comparisons with model experiments are made. © 1966, Cambridge University Press. All rights reserved.

Description: A series of flat-plate laminar boundary layer experiments carried out in an arc-heated supersonic wind tunnel is described. Measurements of the static pressure distribution, the total pressure profiles through the boundary layer, and the heat-transfer rates to catalytic and non-catalytic surfaces at moderately high enthalpies are given and compared with various theoretical predictions. The observations indicate that the dissociation fraction affects the boundary-layer profiles through its influence on the local transport properties. It is confirmed that the atomic recombination at the surface is retarded by using a non-catalytic oxide coating, and hence the heat transfer to the wall is reduced. © 1966, Cambridge University Press. All rights reserved.

Description: In this paper systems of non-linear integral equations are formulated which are equivalent to the Krook kinetic equation for steady problems in two and three space-dimensions. The boundary conditions used are discussed and some of the properties of the equations which are significant in their numerical solution pointed out. This work will then serve as a basis for the consideration of a sequence of particular problems to be presented in subsequent papers. © 1966, Cambridge University Press. All rights reserved.

Description: It is found that when the average kinetic energies of normal velocity components in decaying, grid-generated turbulence are equilibrated by a symmetric contraction of the wind tunnel, this equality can persist downstream. A second result is further confirmation of the fact that the best power-law fit to the inverse turbulent energy during the early part of decay is near (x–x1)1·25, for both rod grids and disk grids. The Kolmogorov decay law [formula omitted] is re-derived by a spectral method which is essentially equivalent to the original. Finally, a crude theoretical estimate of component energies in the straight duct after a weak contraction seems to support the experiments. © 1966, Cambridge University Press. All rights reserved.

Description: An experimental study has been made of the motion of long bubbles in closed tubes. The influence of viscosity and surface tension on the bubble velocity is clarified. A correlation of bubble velocities in vertical tubes is suggested and is shown to be useful for the whole range of parameters investigated. In addition, the effect of tube inclination angle on bubble velocity is presented, and certain features of the flow are described qualitatively. © 1966, Cambridge University Press. All rights reserved.

Description: Taylor's formula for the velocity of an oscillating sheet in a viscous fluid is extended to larger amplitudes of motion and his formula for the velocity of a rotating or oscillating filament is proved to be valid for amplitudes of motion small but greater than the filament radius. A simple formula is derived for the velocity of a sheet or filament in any general oscillatory motion of small amplitude. The forces and energy involved in oscillating tubes are calculated. © 1966, Cambridge University Press. All rights reserved.

Description: This paper deals with the growth of small disturbances in a separated laminar boundary layer for high Reynolds numbers as a function of the dimensionless flow parameters. Using a hot-wire technique, the experiments show that spatially growing disturbances are only affected by the Strouhal number. Thus the basic equations of the process become relatively simple. The experiments show good agreement with theoretical results obtained by means of hydrodynamic stability theory for spatially growing disturbances. © 1966, Cambridge University Press. All rights reserved.

Description: The dynamical properties of a fluid, occupying the space between two concentric rotating spheres, are considered, attention being focused on the case where the angular velocities of the spheres are only slightly different and the Reynolds number R of the flow is large. It is found that the flow properties differ inside and outside a cylinder ℰ, circumscribing the inner sphere and having its generators parallel to the axis of rotation. Outside ℰ the fluid rotates as if rigid with the angular velocity of the outer sphere. Inside ℰ the fluid rotates with an angular velocity intermediate to the angular velocities of the two spheres and determined by the condition that the flux of fluid into the boundary layer of the faster-rotating sphere is equal to the flux out of the boundary layer of the slower-rotating sphere at the same distance from the axis. The return of fluid is effected by a shear layer near ℰ and we show that it has a complicated structure for it can be divided into three separate layers, two outer ones, of thickness [Formula omitted] and ∼R−¼, and an inner layer of thickness [Formula omitted]. © 1966, Cambridge University Press. All rights reserved.

Description: The directional spectrum of wind-driven surface waves has been measured under conditions of limited fetch, in order to check the predictions of the Phillips–Miles theory of wave generation (Miles 1960). The expression obtained for the directional spectrum in this theory involves the spectrum of the atmospheric pressure fluctuations, but it is possible to obtain theoretical estimates of the major features of the directional spectrum without knowledge of the pressures. Specifically, it is possible to predict the frequency at which the power spectrum should peak, and, for the higher frequencies, the range of azimuth over which high spectral values should be observed; for the lower frequencies the theory indicates a bimodal distribution in azimuth (Phillips's resonance waves), and gives the angle of travel relative to the wind as a function of frequency. The results of the measurements are in fairly good agreement with the theoretical predictions for the higher frequencies. The asymmetry of the fetch results in the prediction that the waves will travel at an angle to the wind which varies with frequency, and this was observed. The range of azimuth over which the spectral density is high is also close to the theoretical prediction. For the low frequencies the bimodal distribution was not observed: the waves were found to have a single predominant direction of travel at each frequency. However, this direction conformed closely to that of one of the two wave trains predicted by Phillips, and its variation with frequency was also that given by the theory. There is reason to suppose that the peculiarities of the experimental site may be responsible for the absence of the second wave train, especially as it would be difficult to account for the observed effects on any basis other than that of Phillips's theory. © 1966, Cambridge University Press. All rights reserved.

Description: The incompressible viscous flow along a right-angle corner, formed by the intersection of two semi-infinite flat plates, is considered. The effect of the three-dimensional geometry on the second-order ʻboundary layerʼ flow away from the corner is determined and an interesting secondary flow is deduced. It is observed that this cross-flow prescribes the necessary asymptotic boundary conditions for the equations governing the flow inside the ʻcorner layerʼ. A systematic matching scheme is specified and the corner flow problem is reformulated in terms of the ʻcorner layer-boundary layerʼ matching conditions. © 1966, Cambridge University Press. All rights reserved.

Description: Results of experimental investigations of vibrational relaxation regions of shock waves in nitrous oxide are reported in this paper. The Mach-number range covered was from 1·5 to 7·5 and the photographs of the shocks were made using a Mach-Zehnder interferometer and a spark source. The experimental and calculated values of the over-all density ratio were found to be in good agreement, and the values of the relaxation frequencies were consistent with the data of other workers. © 1966, Cambridge University Press. All rights reserved.

Description: The collapse time of a closed cavity that is initially at rest in an incompressible, inviscid fluid of density ρ and ambient pressure p ∞ has the form[Formula omitted]where pc is the internal pressure, which is assumed to remain constant during collapse, and l is a length that depends only on the geometry of the cavity. A variational formulation of the dynamical problem is constructed from Jacobi's statement of the principle of least action. A single-degree-of-freedom approximation is developed from the similarity hypothesis that the cavity collapses through a family of similar surfaces with volume as the generalized co-ordinate. Two-degree-of-freedom approximations are given for both prolate and oblate spheroidal cavities and are used to obtain error estimates for the similarity approximation (approximately 2% for the limiting case of a needle-like, prolate spheroid and approximately ½ % for a disk-like, oblate spheroid). A perturbation analysis is developed for an approximately spherical cavity, which is found to have the same collapse time as a spherical cavity of equal volume within a factor 1 + O(e4), where e is a representative eccentricity. A first-order correction for surface tension is obtained. © 1966, Cambridge University Press. All rights reserved.

Description: The cavity in which the magnetic field of two arbitrary line currents is confined by a streaming plasma which is assumed cold and perfectly conducting is investigated by using conformal transformations. When the magnetic field at the boundary is always directed in the same sense the finite breadth of the cavity at infinity depends only on the algebraic sum of the inducing currents and not their position. If the two line currents are of opposite sign the boundary magnetic field may change sign at two ʻpseudo-singularitiesʼ. © 1966, Cambridge University Press. All rights reserved.

Description: A study of the unique role of impurities in the initial stages of ionization relaxation in shock-heated argon, using a sampling mass spectrometer to determine the ionic products of the reaction, is described. The ions are extracted from the shock tube through a small orifice in the end wall after they have diffused through the dense thermal layer adjacent to the wall from the ionizing gas behind the reflected shock wave. The ion diffusion is analysed in detail to assess the possibility that the sampling process alters the reaction products. It is shown that this is unlikely because the impurities are in dilute concentration and the reaction is studied in its initial stages. This mode of sampling is compared with others. The experiments were conducted in argon at temperature of 16,600 °K and pressure of 16 mmHg with an estimated impurity level of 300 parts per million. A surprisingly large number of different ions were detected during the initial stages of ionization. O+ and H+ were found in much greater amounts than any of the other products, each being about five times more abundant than A+. The results suggest that H2O is probably quite generally the most important impurity in thermal-ionization experiments, and that ionization ‘incubation’ is due to dissociation of molecular impurities (especially H2O) before ionization commences. Possible explanations of the well-known efficiency of small amounts of impurities in initiating ionization are discussed. © 1966, Cambridge University Press. All rights reserved.

Description: The piston problem for a viscous heat-conducting gas is studied under the assumption that the piston Mach number ε is small. The linearized Navier–Stokes equations are found to be valid up to times of the order of ε−2 mean free times after the piston is set in motion, while at large times the solution is governed by Burgers's equation. Boundary conditions for the large-time solution are supplied by the matching principle of the method of inner and outer expansions, which is also used to construct a composite solution valid both for small and for large times. © 1966, Cambridge University Press. All rights reserved.

Description: An inviscid transonic theory appears to be inadequate to describe the flow near the throat of a converging–diverging nozzle during the transition from the symmetrical Taylor (1930) type of flow to the subsonic–supersonic Meyer (1908) flow. A viscous transonic equation taking account of heat conduction and longitudinal viscosity has been developed previously (Cole 1949; Sichel 1963; Szaniawski 1963). An exact, nozzle-type of similarity solution of the viscous transonic equation, similar to the inviscid solution of Tomotika & Tamada (1950), has been found. This solution does provide a description of the gradual transition from the Taylor to the Meyer flow and shows the initial stages in the development of a shock wave downstream of the nozzle throat. The solution provides a viscous, shock-like transition from an inviscid, supersonic, accelerating flow to an inviscid, subsonic, decelerating flow. © 1966, Cambridge University Press. All rights reserved.

Description: The characteristics of the laminar boundary layer on a continuous moving surface are described and an experiment is performed to demonstrate that such a flow is physically realizable. The hydrodynamic stability of the flow is analysed within the framework of small-perturbation stability theory. A complete stability diagram is mapped out. The critical Reynolds number is found to be substantially higher than that for the Blasius flow and, correspondingly, the critical layer lies closer to the wall. The disturbance amplitude function and its derivative are numerically evaluated, from which are derived the vector flow field of the disturbance, the resultant flow field (main flow plus disturbances), the root-mean-square distributions of the disturbance velocity components, and the distributions of the kinetic energy and the Reynolds stress. The energy criterion for stability is also investigated and is found to be consistent with the solutions of the eigenvalue problem. © 1966, Cambridge University Press. All rights reserved.

Description: Measurements of grid turbulence have been obtained for grid Reynolds numbers ranging from 2·4 ˣ 106 to 1·2 ˣ 105. The decay law and the effect of Reynolds number on the turbulence level are established. The measured power spectra of the turbulence are consistent with Kolmogoroff scaling for kη 〈 0·1 (k is the wave-number and η is the Kolmogoroff length); but for kη 〈 0·1, the spectra of the stream-wise turbulence velocity component and of the cross-stream component do not appear to be isotropically related. However, the stream-wise spectrum does display a [Formula omitted] region, which increases in extent with increasing Reynolds number. © 1966, Cambridge University Press. All rights reserved.

Description: The stability with respect to ʻsupersonicʼ disturbances of the laminar mixing of two parallel streams of a compressible fluid is studied. For locally supersonic disturbances there will be waves propagating outward from the mixing layer. The numerical results show that the flow is generally unstable with respect to supersonic disturbances, although the amplification rate is smaller than that for subsonic disturbances. The flow is more unstable at lower Mach number, and the increase of the angle between the disturbance wave-number vector and the principal flow direction tends to increase the instability. © 1966, Cambridge University Press. All rights reserved.

Description: A theory is developed for an incompressible fluid in a steady three-dimensional rotational flow. Solutions are obtained subject to the restriction of small perturbations and are determinant provided that the vorticity distribution along the axis of rotation is known. Effects of viscosity are included. Closed-form expressions for the zeroth-order circulation and stream function and first-order circulation are given, with other higher-order expressions requiring high-speed computers. Experimental results of radial variation of axial velocity in the core show a distribution more elaborate than Gaussian. © 1966, Cambridge University Press. All rights reserved.