ALBERT

Description: The following list consists of dates for archaeologic samples mostly measured from July 1976 to December 1977. The dates were obtained by liquid scintillation counting of benzene using the laboratory procedures outlined in previous lists (see, eg, BM-VIII, R, 1976, v 18, p 16). Dates are expressed in radiocarbon years relative to ad 1950 based on the Libby half-life for 14C of 5570 yr, and are corrected for isotopic fractionation (δ13C values are relative to PDB). No corrections have been made for natural 14C variations (although in some instances approximate calibrated dates taken from the tables of R M Clark (1975) have been given in the comments where this aids interpretation of results). The modern reference standard is NBS oxalic acid (SRM 4990). Errors quoted with the dates are based on counting statistics alone and are equivalent to ± 1 standard deviation (± 1σ), Dates in this and the next list (BM-XIV) reported to submitters or published elsewhere before the introduction of the new guidelines for rounding of computed figures have deliberately been left unrounded. From BM-XV onwards all BM dates will be rounded before publication in conformity with the recently recommended procedures (R, 1977, v 19, p 362). Descriptions, comments, and references to publications are based on information supplied by submitters.

Description: The radiocarbon laboratory of the Center of Applied Research and Documentation of Udine (CRAD), became operative early in 1977 and uses a benzene liquid scintillation counting method. Benzene is prepared as outlined by Legers and Tamers (1963), Noakes, Kim, and Akers (1967), Belluomini et al (1978). The procedure of chemical synthesis is detailed in CRAD (1977).

Description: The Radiocarbon Dating Laboratory of The Granada University was established to support the work of archaeologists and geologists. The method of dating is benzene synthesis and liquid scintillation counting developed by a number of investigators (Polach and Stipp, 1967; Tamers, 1969; Pietig and Scharpenseel, 1966) with sample combustion in pure oxygen (Switsur, 1974).

Description: This list reports a portion of the analysis completed on archaeologic and paleo-environmental samples measured in the UCR laboratory between August 1974 and August 1976. Results of measurements made during that period on sample suites which are not as yet completed or lack review by submitters will be reported in a subsequent date list.

Description: The following list consists of dates for archaeologic and geologic samples mostly measured over the period from January 1980 to June 1981. The dates were obtained by liquid scintillation counting of benzene using the laboratory procedures outlined in previous lists (see, eg, BM VIII, R, 1976, v 18, p 16).

Description: During the last seven years, there has been a concerted effort in eastern Australia to obtain 14C ages from detrital shell samples of prograded sand barriers composed of beach ridges and chenier deposits (Cook and Polach, 1973; Cook and Mayo, 1977; Thom, Polach, and Bowman, 1978; Thom et al, 1981). These ages were used to establish the age sequence of deposition and rates of progradation. This date list is the result of work in two areas of the Gulf of Carpentaria, Queensland, Australia, where 57 shell samples were collected for 14C dating. For details of this research, see Rhodes et al (1980).

Description: The following list includes 14C measurements of geologic samples, the majority of which pertain to sea-level variations, and of archaeologic samples mainly from France, West Africa, and South America. Most of the dates were measured between 1972 and 1973 when installations were not modified. The technique used is described in Radiocarbon, 1972, v 14, p 280–320. Dates were calculated using the 14C half-life of 5568 years; modern standard is 0.95 of the NBS oxalic acid. Reported errors are one standard deviation for 2000 minutes measurements.

Description: The SFU Archaeology Department has constructed a small radiocarbon dating facility to serve its own needs and, to the extent that time is available, the needs of other archaeologists and earth scientists. All dates reported here were processed by our laboratory from October 1979 to September 1980. The 14C measurements are made using conventional techniques for liquid scintillation counting of benzene. The samples are burned in a Phonon Mark IV combustion bomb and the resultant CO2 is purified and converted to Li2C2 using a reaction vessel based on the design of Polach, Gower, and Fraser (ms). Acetylene is formed by hydrolysis with distilled H2O which has been aged for a minimum of three months. The acetylene is trimerized to benzene with the Mobil Durabead I catalyst. The conversion efficiency of CO2 to C6H6 is typically 95%. Gas chromatographic analysis of typical samples of the synthesized benzene indicates 99.8% purity with toluene produced in trace amounts.

Description: In January 1975 a radiocarbon dating laboratory was established at the Marine Resources Research Institute for geochemical and geologic studies. A liquid scintillation system is employed according to the method of Noakes, Kim, and Akers (1967). A Searle (Nuclear Chicago) Isocap 300 liquid scintillation counter is currently being used for counting. This system is a duplicate of the one formerly used at Texas A & M University except for the counter (Mathews et al, 1972)

Description: The following radiocarbon measurements are a partial list of geologic samples from S Florida dated during the summer of 1975. The technique used is liquid scintillation counting of wholly synthesized benzene as indicated in R, v 16, p 402-408 and R, v 18, p 210-220. Dates are calculated using a 14C half-life of 5568 yr and errors are reported as one standard deviation. Before conversion, shell material was etched with HCl to remove all soft or powdery material. All wood and peat samples were treated with NaOH.

Description: Most of the 14C measurements reported here were made between October 1974 and October 1975. Equipment, measurement, and treatment of samples are the same as reported previously (R, 1968, v 10, p 36-37) except for bone samples (see below).

Description: The Radiocarbon Laboratory under the Chair of Nuclear physics of Tbilisi State University is engaged in studies of radiocarbon variation in the atmosphere and mineral waters and determination of the absolute age of archaeologic, geologic, botanical, and other samples. This list reports dates of archaeologic and geologic specimens only. Gas counting and liquid scintillation methods are used for dating.

Description: The following list of dates is compiled from samples prepared and catalogued since publication of our last date list (R, 1975, v 17, p 99-111). The counting equipment and operating procedures are the same. Ages are quoted with a 1σ counting error which includes statistical variation of the sample count as well as for background and standard, using ad 1950 as the reference year and 95% NBS oxalic acid for 14C dating as the standard. The half-life value used is 5570 years.

Description: This list contains radiocarbon dates of archaeologic samples of wood, charcoal, and peat measured between 1967 and 1973, analyzed by the Laboratory of the Institute of Archaeology, Leningrad Branch, USSR Academy of Sciences. The samples measured include charcoal from cultural strata and hearths, wood from kurgans and cultural strata, peat, etc, coll from various archaeologic sites by Soviet scientists, as well as a series from Dashly site, Afghanistan.

Description: The analytical facilities at Glasgow have been extended to include gas proportional (CO2 and CH4) and liquid scintillation (C6H6) counting laboratories. The results presented here were obtained during 1972-1974 using the CO2 gas counting system only. In brief, organic samples, after pretreatment as described in the text, are burned in a tube combustion unit and the evolved CO2 absorbed in KOH solution. BaCO3 is precipitated and acid-hydrolyzed in vacuo using H3PO4. Evolved CO2 is purified via adsorption/desorption on CaO and is stored prior to counting. The 2.6L proportional counter is surrounded by a gas-flow Geiger anticoincidence guard and 10cm thick Pb shielding to reduce background count rates to ca 4.9 cpm at 1 atm filling and barometric pressures. A barometric sensitivity in background of −0.01cpm/mbar is observed. Constant gas gain is ensured by monitoring the coincidence meson spectrum and normalizing the detector operating voltage. All sample activities are related to the NBS oxalic acid standard count rate which averages 14.71 cpm at 1 atm filling pressure and 15°C. Mass spectrometric assay of CO2 after counting is performed on a VG Micromass 602B instrument to a precision of 0.05% (±1σ). Since uncertainties quoted on all results represent 1σ counting errors alone, they are related to precision of measurement rather than accuracy. The bulk of data quoted here are connected with a long-term study of the medical aspects of artificial 14C from nuclear weapon tests. These results should therefore be assessed in conjunction with those pub previously (Harkness and Walton, 1972; Farmer et al, 1972).

Description: This list comprises age measurements carried out from 1973 to 1974 In dating the samples reported here as well as in calculating their ages, the same equipment and methods were used as previously described (R, 19/3, v 15, p 586–591; 1974, v 16, p 388–394).

Description: The Dalhousie University Radiocarbon Dating Laboratory was established in 1972, utilizing equipment and procedures formerly in use at Ohio Wesleyan University, Delaware, Ohio. The laboratory is located on the third floor of the 8-story Life Sciences Center at Dalhousie University. Sample preparation includes leaching with dilute alkali and acid, followed by pyrolysis in a stream of N2 at 500°C. Operating procedures remain essentially the same, utilizing reduction of acid or combustion generated CO2 to the counting gas, methane, over Ruthenium catalyst at 500°C. The flow reactor formerly used has been replaced by an in-line static reactor. Following gas purification and one month product gas storage to permit decay of Radon, samples are counted at 50 to 152cm pressure in either of 2 500ml detectors, or a 2L detector.

Description: This list describes samples dated in this laboratory between November 1972 and December 1974.

Description: The first natural 14C measurements in Poland were made, using CO2 + CS2 G M counter as early as 1953 (Mościcki, 1953), but continuous operation was not possible until 1971. Following Poznań Toruń (Mościcki, 1958; 1961) and Gdańsk (Mościcki and Zastawny, 1962a), where the first long series of 14C measurements were made (Mościcki et al, 1967), an actively operating radiocarbon dating laboratory was installed at Gliwice in 1971.

Description: The present list includes 35 dates of geologic samples analyzed at the Geobiochemical Laboratory of the Institute of Zoology and Botany, Academy of Sciences, Estonian SSR. Benzene synthesized from wood dating from 1850 ± 10 yr served as a reference standard. All radiocarbon dates have been calculated using 5568 ± 30 yr before ad 1950 as the half-life of 14C.

Description: The following radiocarbon measurements are a partial list of projects and samples dated since the Spring of 1975. The technique used is liquid scintillation counting of wholly synthesized benzene as indicated in R, v 16, p 402-408. The intermediate chemical step of converting CO2 to Li2C2 has been modified so that the CO2 is reacted with the lithium metal at a temperature of 950° to 1000°C instead of the 600°C as formerly done (Tamers, 1975). This modification has had the effect of reducing occasional variable losses in conversion yields in this step, and reducing the reaction time required from 30 min to 10 min for a typical ¼ mole sample. Dates are calculated using a 14C half-life of 5568 yr and errors are reported as one standard deviation. No other correction factors are applied.

Description: The radiocarbon dating laboratory was set up during 1972 and 1973 with financial support of the FKFO (Fonds voor Kollektief Fundamenteel Onderzoek) Belgium, to enable us to place Upper Pleistocene and Holocene sediments in their correct stratigraphic position. Dating of samples began in the middle of 1974.

Description: The radiocarbon dating laboratory of Queens College, CUNY, was established with the joint support of the Research Foundation of the City University of New York and the departments of Anthropology, Biology, Chemistry, and Earth and Environmental Sciences of Queens College. The laboratory has been operational since June, 1975 and is located in the basement of a two-story concrete and brick building.

Description: The following list of dates are selected from geologic and archaeologic samples measured in early 1975. The technique employed is liquid scintillation counting of wholly synthesized benzene as described by Noakes et al (1965) and discussed in R, v 16, p 402–408. Errors are reported as one standard deviation.

Description: This date list includes samples dated from 1968 through 1972. The method of analysis is described in R, 1968, v 10, p 246 and 1970, v 12, p 87. The ages are calculated with the 5568 year half-life without application of any corrections. The NBS oxalic acid standard is used as the modern reference. Errors (± 1 σ) include standard deviations for sample counts, background and modern standard.

Description: The following list consists of dates for archaeologic and some geologic samples, mostly measured from January 1978 to December 1979. The dates were obtained by liquid scintillation counting of benzene using the laboratory procedures outlined in previous lists (see, eg, BM-VIII, R, 1976, v 18, p 16). The dates are expressed in radiocarbon years relative to ad 1950 based on the Libby half-life for 14C of 5570 yr, and are corrected for isotopic fractionation (δ13C values are relative to PDB). No corrections have been made for natural 14C variations. The modern reference standard is NBS oxalic acid (SRM 4990). Errors quoted with the dates are based on counting statistics alone and are equivalent to ± 1 standard deviation (± 1σ). Dates in this list reported to submitters or published elsewhere before the introduction of the new guidelines for rounding of computed figures have deliberately been left unrounded. From BM-XV onwards all BM dates will be rounded before publication in conformity with the recently recommended procedures (R, 1977, v 19, p 362). Descriptions, comments, and references to publications are based on information supplied by submitters.

Description: The following list sums up the results of radiocarbon dating of geologic samples obtained mostly during 1978 and 1979. Measurements have continued with the same proportional counters, pretreatment procedures, carbon dioxide purification, measurement and calculation as described previously (Pazdur et al, 1982). Ages are reported as conventional radiocarbon dates in years before ad 1950. No corrections for 13C/12C ratio were made for samples reported in this date list. Infinite dates are based on a 2-sigma criterion (Pazdur and Walanus, 1979). Sample descriptions and comments are based on information provided by the submitters.

Description: The following list contains the measurements of archaeologic samples made during 1978 and 1979 using carbon-dioxide-filled proportional counters. Most of the samples were dated with counter No. 3 (L3) filled to 1 or 2 atm pressure (Mościcki and Zastawny, 1977). Our counter No. 1 (L1) previously described (Mościcki and Zastawny, 1976) has been remounted and is now operating at 2 atm pressure of carbon dioxide. Samples measured with this counter have date numbers starting with Gd-1000. Parameters of proportional counters are listed in Table 1. Our transistorized electronics is being gradually replaced by more compact integrated-circuit electronics in CAMAC system (Bluszcz and Walanus, 1980). Counts from proportional counter and guard counters are recorded in 5 channels and punched every 100 minutes. Typical measurement of any sample, including background and oxalic acid samples, consists of a series of 20 to 25 partial measurements. Partial results obtained in such series are analyzed on ODRA 1325 computer at the Computing Centre of the Silesian Technical University according to code C14C written in ALGOL (Pazdur and Walanus, 1979). Age calculations are based on contemporary value equal to 0.95 of the activity of NBS oxalic acid standard and on the Libby value for the half-life of radiocarbon. Ages are reported as conventional radiocarbon dates in years before ad 1950. Corrections for isotopic fractionation in nature are made only for some samples with indicated values of δ13C Errors quoted (±1σ) include estimated overall standard deviations of count rates of the unknown sample, contemporary standard, and background (Pazdur and Walanus, 1979).

Description: Most of the 14C measurements reported here were made between October 1980 and October 1981. Equipment, measurement, and treatment of samples are as reported previously (R, 1968, v 10, p 36–37; 1976, v 18, p 290; 1980, v 22, p 1045).

Description: The complete uniform asymptotic expansion of the velocity and pressure fields for Stokes flow past a slender body of revolution is obtained with respect to the slenderness ratio ε of the body. A completely general incident Stokes flow is assumed and hence these results extend the special cases treated by Tillett (1970) and Cox (1970). The part of the flow due to the presence of the body is represented as a superposition of the flows produced by three types of singularity distributed with unknown densities along a portion of the axis of the body and lying entirely inside the body. The no-slip boundary condition on the body then leads to a system of three coupled, linear, integral equations for the densities of the singularities. The complete expansion for these densities is then found as a series in powers of ε and ε log ε. It is found that the extent of these distributions of singularities inside the body is the same for all the singular flows and depends only upon the geometry of the body. The total force, drag and torque experienced by the body are computed. © 1976, Cambridge University Press. All rights reserved.

Description: The parametric instability of a plane internal gravity wave is considered. When the two-dimensional equations of vorticity and mass conservation are linearized in the disturbance quantities, partial differential equations with periodic coefficients result. Substitution of a perturbation of the form dictated by Floquet theory into these equations yields compatibility conditions which, when evaluated numerically, give the curves of neutral stability and constant disturbance growth rate. These results reveal that, for an internal wave of even infinitesimal amplitude, disturbance waves can begin to grow in amplitude. Moreover, these parametric instabilities are shown to reduce to the classical case of the nonlinear resonant interaction in the limit of vanishingly small basic-state amplitude. The fact that these unstable disturbances can exist for an internal wave of any amplitude suggests that this phenomenon may be an important mechanism for extracting energy from an internal gravity wave. © 1976, Cambridge University Press. All rights reserved.

Description: Artificially initiated turbulent spots in a Blasius boundary layer were investi- gated experimentally using hot-wire anemometers. Electrical discharges generated the spots, which grew in all directions rn they were swept downstream by the mean flow. A typical lateral spread angle of the spots is 10° to each side of t.he plane of symmetry. Conditional sampling methods were used to form ensemble-averaged data yielding the average shape of a spot and the mean flow field in its vicinity. Far downstream a spot exhibits conical similarity and all quantities measured seem to be independent of the type of disturbance which generated the spot in the first place. In plan view, the spot has an arrowhead shape whose leading interface is convected downstream somewhat more slowly than the free-stream velocity near the plane of symmetry and at approximately half the free-stream velocity at the extreme spanwise location. The trailing interface is convected at a constant velocity throughout (UTE = 0·5 U∞). In this way the spot entrains laminar fluid through both interfaces, resulting in its elongation it proceeds downstream. The flow near the surface accelerates abruptly as the leading interface passes by, however the acceleration continues within the spot and the velocity attains a maximum near the trailing interface. There is therefore a continuous increase in skin friction towards the trailing interface. Further away from the surface the passage of the spot is marked by deceleration followed by acceleration after the ridge of the spot passes the measuring station. All changes in velocity occur monotonically without causing inflexions or kinks in the ensemble-averaged velocity profiles. Although the displacement and momentum thicknesses change quite rapidly within the spot, the shape factor is practically constant in the interior region (H = 1·5); and the velocity profiles may be very well represented by the universal logarithmic distribution. The spanwise velocity component W is everywhere directed outwards (i.e. away from the plane of symmetry) and increases with increasing z. The component of velocity normal to the surface is directed towards the plate near the leading interface and away from it in the remaining part of the spot. Two-point velocity correlation measurements suggest that the spot may be represented by an arrowhead vortex tube which is convected downstream with a velocity equal to 65 yo of the free-stream velocity. Pluid which is entrained near the plane of symmetry acquires a helical motion towards the extremities of the spot. This motion helps to explain the lateral as well as the longitudinal spread of the spot. © 1976, Cambridge University Press. All rights reserved.

Description: Measurements have been made of the turbulent flow in a rectangular duct of aspect ratio 12:1 at a Reynolds number [formula ommited] (based on duct height h) using conditional-sampling techniques. The lower boundary layer was heated in the entry region, and the fluctuating output of a resistance thermometer was used to distinguish ‘hot’ and ‘cold’ fluid. Thus separate velocity-fluctuation statistics could be obtained for fluid from the upper and lower boundary layers, even after the two layers had merged. The measurements suggest that the interaction region near the centre-line consists of a continuously contorting interface between the ‘hot’ and ‘cold’ layers, shaped by the eruption of large eddies across the centre-line from either side of the duct and surprisingly little affected by the inevitable fine-scale mixing. In the mean, this time-sharing between ‘hot’ and ‘cold’ fluid gives the impression of two superposed turbulence fields whose mean-square intensities add to give the total intensity. Exact superposition (which cannot take place in a nonlinear system) would imply that one layer had the same turbulent intensity profiles as an isolated boundary layer spreading into a non-turbulent free stream with the same mean velocity profile as the duct flow. The centre-line interaction grows in strength with increasing distance downstream until a steady rate of mutual eddy intrusion and fine-scale mixing is achieved, when the flow is commonly called ‘fully developed’. It is concluded that superposition (timesharing) is a physically reasonable first approximation for use in turbulence models for interacting shear layers: it is argued that better approximations could be obtained if necessary by correlating departures from superposition (i.e. changes in turbulence structure) by means of one or more interaction parameters. © 1976, Cambridge University Press. All rights reserved.

Description: A new approximate theory is proposed for treating the flow past smoothly contoured two-dimensional bluff bodies in the intermediate Reynolds number range O(1) 〈 Re 〈 0(102), where the displacement effect of the thick viscous layer near the surface of the body is large and a steady laminar wake is present. The theory is based on a new pressure hypothesis which enables one to take account of the displacement interaction and centrifugal effects in thick viscous layers using conventional first-order boundary-layer equations. The basic question asked is how the wall pressure gradient in ordinary boundary -layer theory must be modified if the pressure gradient along the displacement surface using the Prandtl pressure hypothesis is to be equal to the pressure gradient along this surface using a higher-order approximation to the Navier-Stokes equation in which centrifugal forces are considered. The inclusion of the normal pressure field with displacement interaction is shown to be equivalent to stretching the streamwise body co-ordinate in first-order boundary-layer theory such that the streamwise pressure gradient as a function of distance along the original and displacement body surfaces are equal. While the new theory is of a non-rigorous nature, it yields results for the location of separation and detailed surface pressure and vorticity distribution which are in remarkably good agreement with the large body of available numerical Navier-Stokes solutions. A novel feature of the new boundary-value problem is the development of a simple but accurate approximate method for determining the inviscid flow past an arbitrary two-dimensional displacement body with its wake. © 1976, Cambridge University Press. All rights reserved.

Description: The double-boundary-layer theory of Stuart (1963, 1966) and Riley (1965, 1967) is employed to investigate the mass transport velocity due to two-dimensional standing waves in a system comprising two homogeneous fluids of different densities and viscosities. The most important double-boundary-layer structure occurs in the neighbourhood of the oscillating interface, and the possible existence of jet-like motions is envisaged at nodal positions, owing to the nature of the mean flows in the layers. In practice, the magnitude of the mass transport velocity can be a significant fraction of that of the primary, oscillatory velocity. © 1976, Cambridge University Press. All rights reserved.

Description: The mass, momentum and energy-transfer equations are solved to determine the response of a rectangular enclosure to a fire or other high-temperature heat source. The effects of non-participating radiation, wall heat conduction, and laminar natural convection are examined. The results indicate that radiation dominates the heat transfer in the enclosure and alters the convective flow patterns significantly. At a dimensionless time of 5·0 the surface of the wall opposite a vertical heated wall has achieved over 99% of the hot-wall temperature when radiation is included but has yet to change from the initial temperature for pure convection in the enclosure. At the same time the air at the centre of the enclosure achieves 33% and 13% of the hot-wall temperature with and without radiation, respectively. For a hot upper wall the convection velocities are not only opposite in direction but an order of magnitude larger when radiation transfer between the walls is included. © 1976, Cambridge University Press. All rights reserved.

Description: The Wedemeyer model describing the spin-up of a fluid in a rotating cylinder is generalized to include the case of spin-down. Attention is focused on spin-up and spin-down at a finite (constant) acceleration for small Ekman numbers En. It is found that when the full nonlinear Ekman suction is included for spin-up from rest, the characteristics near the propagating wave front intersect, thus yielding an O(1) velocity discontinuity for the inviscid model. This anomalous behaviour is limited to only a small range of Rossby numbers and does not appear in any of the spin-down solutions. Transient spin-down velocity profiles in the O(E1/4Ω) shear layer at the cylindrical wall are calculated for the quasi-steady flow which occurs for sufficiently small decelerations. Results for impulsive spin-up and spin-down between infinite parallel plates are presented and compared with the asymptotic solutions given by Greenspan & Weinbaum and Benton. Finally, characteristic spin-up and spin-down times are computed for both the contained cylinder and the infinite-parallel-plates geometry.

Description: What transient motions occur as a fluid responds to gravitational forces in a rotating channel, and what equilibrium does the fluid adjust to? This problem is studied to illustrate how boundaries affect the process of adjustment to a geostrophic equilibrium. In particular, linear solutions are found for an infinitely long channel of constant width and constant depth when there is an initial discontinuity in the level of the free surface. The results are summarized in the figures, and can be described in terms of Poinearé waves and Kelvin waves. When the channel is wide compared with the Rossby radius, the final state involves a current of that width which follows the left-hand boundary (for Northern-Hemisphere rotation) to the position of the initial discontinuity, then crosses the channel and continues downstream along the right-hand wall. © 1976, Cambridge University Press. All rights reserved.

Description: Approximations for shallow-water ship waves are sought which are valid near the critical speed U = (gh)1/2. For sufficiently thin bodies (struts or ships) the governing equation is dispersive. Simple analytic solutions are given which are valid for all F2 ≤ O(1). As the thickness increases, nonlinearity also enters. A soliton solution is discussed which applies to a sharp-nosed half-body at slightly supercritical speed.

Description: The time development of two-dimensional fluid motion induced by a line sink in a rectangular, density stratified reservoir with a free surface is given. It is shown that the initiation of such a sink gives birth to a spectrum of internal expanding shear fronts with a progressively decreasing vertical wavelength. These fronts move out from the sink and travel towards the far wall, where they are reflected. This process ceases once the front with a vertical wavelength equal to the steady withdrawal-layer thickness has reached the end wall. The fronts so introduced continue to move back and forth, expanding to standing waves if the viscosity of the fluid is small enough. The evolution and nature of the withdrawal layer are shown to depend critically on the relative magnitude of the convective inertia and viscous forces, the number of reflexions from the rear wall and the Prandtl number. © 1976, Cambridge University Press. All rights reserved.

Description: Axially symmetric motion of a viscous fluid in a cone is considered on the basis of the Stokes assumption. Near the apex of the cone the solution obtained reveals features quite similar to those of that near a sharp corner in two dimensions, which has been discussed already. An infinite sequence of eddies is induced near the apex for values less than about 80·9° of the semi-angle of the cone, which is measured from the symmetry axis lying in the fluid. The solution found by Pell & Payne for a spindle in a uniform stream offers a good illustration of the general discussion. Special attention is paid to the angle 120° for the spindle as well as the cone. The limiting case of zero angle of the cone corresponds to the flow occurring in a circular cylinder. © 1976, Cambridge University Press. All rights reserved.

Description: The two-dimensional motion of a fluid confined between two long horizontal planes, heated and salted from below, is examined. By a combination of perturbation analysis and direct numerical solution of the governing equations, the possible forms of large-amplitude motion are traced out as a function of the four non-dimensional parameters which specify the problem: the thermal Rayleigh number RT, the saline Rayleigh number ES, the Prandtl number σ and the ratio of the diffusivities τ. A branch of time-dependent asymptotic solutions is found which bifurcates from the linear oscillatory instability point. In general, for fixed σ, τ and RS, as RT increases three further abrupt transitions in the form of motion are found to take place independent of the initial conditions. At the first transition, a rather simple oscillatory motion changes into a more complicated one with different structure, at the second, the motion becomes aperiodic and, at the third, the only asymptotic solutions are time independent. Disordered motions are thus suppressed by increasing RT. The time-independent solutions exist on a branch which, it is conjectured, bifurcates from the time-independent linear instability point. They can occur for values of RT less than that at which the third transition point occurs. Hence for some parameter ranges two different solutions exist and a hysteresis effect occurs if solutions obtained by increasing RT and then decreasing RT are followed. The minimum value of RT for which time-independent motion can occur is calculated for fourteen different values of σ, τ and RS. This minimum value is generally much less than the critical value of time-independent linear theory and for the larger values of σ and RS and the smaller values of τ, is less than the critical value of time-dependent linear theory. © 1976, Cambridge University Press. All rights reserved.

Description: For practically uniform entry conditions, the features of the steady laminar flow produced by a particular small distortion of the walls of a channel or pipe are shown to alter first from those of the corresponding external situation when the distortion is in an ‘adjustment zone’, sited a large distance O(R⅗l) from the inlet; R (≫ 1) and l signify respectively a typical Reynolds number and length scale of the incompressible fluid motion. The planar channel flow there develops an extended triple-deck structure, with an unknown inviscid core motion bounded by two-tiered boundary layers near the walls. In three-dimensional pipe flow, where a similar structure occurs, the induced secondary motion has a jet-like nature close to the wall. The size and position of the indentation govern the flow properties within this adjustment regime and both can lead to large-scale effects being propagated. The most substantial effects occur if an indentation, interior blockage or bifurcation is sited just downstream of the adjustment stage in a channel. In a pipe, however, such a siting induces much less upstream influence, and instead the most significant long-scale disturbances are generated when the pipe is constricted asymmetrically over a small length. Vortex motion can then be provoked far beyond the constriction, the sense of rotation changing as the fluid moves further downstream, while upstream source-like secondary flow is found. © 1976, Cambridge University Press. All rights reserved.

Description: The direct-simulation Monte-Carlo method for the full Boltzmann equation is applied to the problem of rarefied hypersonic flow of rotationally excited N2 past the leading edge of a two-dimensional flat plate aligned with the free stream. An approximate collision model representing rotational–translational energy exchanges is developed for use in the calculations. The effects of this and other inelastic collision models and of the single-parameter Maxwell gas–surface interaction law on the flow in the kinetic/transition regime are discussed. © 1976, Cambridge University Press. All rights reserved.

Description: When an interface between two fluids moves in contact with a solid boundary, the Navier-Stokes equations and the no-slip boundary condition provide an unsatisfactory theoretical model, because they predict an undefined velocity at the contact line and a non-integrable stress on the solid boundary. If the surface irregularities are included in the model, the flow on a length scale large compared with their size can be calculated, using a slip coefficient and treating the surface as smooth. A simple type of corrugated surface is examined, and the effective slip coefficient calculated, for grooves of finite and infinite depth. The slip coefficient when the grooves are filled with one fluid and another fluid flows over them is also calculated. It is suggested that, when a fluid displaces another on a rough surface, the displaced fluid remains in the hollows on the surface, thus providing a partly fluid boundary for the displacing fluid and leading to a slip coefficient for the flow. Fluid contained between two vertical plates and rising between them provides a simple example of a flow for which the solution can be found with and without a slip coefficient. With slip present, the force on the plates is finite and its value is calculated. © 1976, Cambridge University Press. All rights reserved.

Description: The unsteady laminar flow due to the penetration of a horizontal jet of constant density into a stratified fluid is considered. A numerical solution of the Navier–Stokes equations under the Boussinesq approximation is obtained by means of an implicit finite-difference method. Results for different values of the Reynolds and internal Froude numbers are given and discussed. © 1976, Cambridge University Press. All rights reserved.

Description: Measurements of the azimuthal velocity inside a cylinder which spins up or spins down at constant acceleration were obtained with a laser-Doppler velocimeter and compared with the theoretical results presented in part 1. Velocity profiles near the wave front in spin-up indicate that the velocity discontinuity given by the inviscid Wedemeyer model is smoothed out in a shear layer whose thickness varies with radius and time but scales with hE1/4Ω. The spin-down profiles are always in excellent agreement with theory when the flow is stable. Visualization studies with aluminium tracers have made possible the determination of the stability boundary for Ekman spiral waves (principally type II waves) observed on the cylinder end walls during spin-up. For spin-down to rest the flow always experienced a centrifugal instability which ultimately disrupted the interior fluid motion.

Description: In this paper, it is shown that if two spheres of equal radii are placed axisymmetrically in a steady Stokes stream, separation of the flow from the spheres occurs if the distance between their centres is less than approximately 3-67 times the sphere radius. For spheres whose spacing is less than this value, wakes form on both spheres and the fluid within the wakes moves in closed eddy type motion. When the distance between the centres of the spheres is less than approximately 3.22 times the sphere radius, a cylinder of fluid links both spheres, and within this cylinder the fluid rotates in one or more ring vortices, the number of vortices increasing as the distance between the spheres is decreased. When the spheres are in contact, the fluid rotates in an infinite set of nested ring vortices.

Description: Experiments were carried out in the turbulent boundary layer on a slightly heated plate in order to establish, mainly for the larger scales of motion, any analogy that may exist between the temperature and velocity fluctuations. With this goal in mind, the spectra and cospectra of the temperature and velocity fluctuations were measured. In particular, the cospectra were obtained by the ‘fluctuation-diagram method’. It soon became evident that the temperature spectrum, except very close to the wall, differs strongly from the spectrum of the longitudinal velocity component. At least for the lower frequency spectral range, which includes about 80% of the total variance, the experimental results support an analogy between the temperature spectrum and a new type of spectrum consisting of the sum of the spectra of the three velocity components weighted by their relative energy. This analogy was established throughout most of the boundary layer. © 1976, Cambridge University Press. All rights reserved.

Description: A new laser device has been used to make direct wave-slope measurements in the capillary-gravity range. Owing to the design principles, the digital nature of the system and the use of a laser beam as a probe, the earlier problems of intensity variations and meniscus effects were avoided. Using this new technique, wave-slope spectra both down and across the channel were obtained for different wind conditions, along with corresponding mean-square slope values. Comparisons are made with existing data. The results indicate that a quasi-equilibrium state may exist for each wind speed and that it increases in intensity with increasing wind, which may imply an asymptotic nature for the equilibrium-range coefficient Caa. From the data, two significant frictional velocities, 17.5 and 31 cm/s respectively, are identified as critical values for different ranges of wave development. © 1976, Cambridge University Press. All rights reserved.

Description: The reported experimental coefficients describing the spreading rate and virtual origin of a plane turbulent jet exhibit substantial scatter. The hypothesis is made that the basic reason for these variations is that the growth of the jet is not linear on a large scale. Existing experimental results are used to support this hypothesis. © 1976, Cambridge University Press. All rights reserved.

Description: Measurements are described of the fluid velocities close to rough beds oscillating in their own plane. The roughness with which most of the results were obtained consisted of smooth spheres closely packed in hexagonal formation. Some results are also given for beds of gravel. The beds were oscillated with simple harmonic motion in still air and the measurements were made with a hot-wire anemometer. The measurements very close to the beds of smooth spheres show two maxima in the velocity profile during each half-cycle. One maximum corresponds to a component of velocity which varies nearly sinusoidally with time. The second forms quite a sharp peak and occurs close to cot 90, 270, where ω is the angular frequency of oscillation and t is time measured from the instant of maximum velocity of the plate. The phase at which this peak occurs shows little variation with distance from the bed. For values of βD 〉 3.0, where β = (ω/2v), v is the kinematic viscosity and D is the sphere diameter, the maximum velocity during each half-cycle is found at this peak over at least a certain range of distances from the bed. The variation with height of the nearly sinusoidal component of velocity is quite close to that given by Stokes’ (1851) solution for a flat plate. The peak at ωt = 90, 270, however, rises from zero at the bed to a maximum at a distance of about one-eighth of a sphere diameter above the crests and then falls off again. The measurements with beds of gravel show a variation in velocity similar to that observed by Kalkanis (1957, 1964) and Sleath (1970). Because of the irregularity of the surface it is difficult to draw definite conclusions about the flow in the immediate vicinity of the bed. A number of tests were carried out, with the beds of spheres, using a wire slanted at 45 to the bed in order to determine the velocity product uw. © 1976, Cambridge University Press. All rights reserved.

Description: Results of hot-wire measurements in a plane incompressible jet are reported. The flow was found to be self-preserving beyond x/d 〉 40 and measurements were made up to x/d = 120. The quantities measured include mean velocities, turbulence intensities and third- and fourth-order terms, as well as two-point correlations and the intermittency factor. Conditional sampling techniques were used to obtain exclusively data within the turbulent zone of the jet. The results are compared with previous investigations. This is the third paper in a sequence providing data on turbulent free shear flows. © 1976, Cambridge University Press. All rights reserved.

Description: Flow control by a wide, deep weir in a rotating fluid is investigated theoretically and experimentally. A strong (vertical) vorticity constraint due to frame rotation is combined with conservation of the Bernoulli function along streamlines and a standard hydraulic control assumption to show that the volume flux over the barrier is [formula-ommited] where H is the depth of the fluid column upstream, bo is the crest height, f is the Coriolis parameter, and l is a length-scale measure of the breadth of the weir. The component of the velocity parallel to the weir crest is computed from conservation of potential vorticity to be v = −fl; perpendicular to the crest, we recover the standard hydraulic relation u = (gh0)½. Experimental investigations of upstream height and streamline deflexion as functions of rotation are described. It is found that agreement with theory is good up to a certain rate of rotation, above which the finite width of the experimental weir becomes important. © 1976, Cambridge University Press. All rights reserved.

Description: Slow, steady, mechanically driven, axisymmetric motion of a stably stratified, electrically conducting, rotating fluid is studied. Attention is focused upon the parameter values for which hydromagnetic effects first become important in a rotating stratified fluid and upon the nature of their influence on the interior flow of that fluid. It is found that hydromagnetic effects are able to alter the flow of a stratified rotating fluid at much weaker magnetic field strengths than the flow of an unstratified fluid. Specifically, the interior azimuthal flow is altered if E/α2 ≪ σS ≪ 1 or if E ≪ α2 and 1 ≪ σS, where E = ν/ΩL2, [formula-ommited]. The hydromagnetic effects act to decrease the vertical shear in the azimuthal flow from the levels which would occur in the absence of magnetic fields. © 1976, Cambridge University Press. All rights reserved.

Description: A simple derivation is given of the parabolic flow first described by John (1953) in semi-Lagrangian form. It is shown that the scale of the flow decreases like t-3, and the free surface contracts about a point which lies one-third of the way from the vertex of the parabola to the focus. The flow is an exact limiting form of either a Dirichlet ellipse or hyperbola, as the time t tends to infinity. Two other self-similar flows, in three dimensions, are derived. In one, the free surface is a paraboloid of revolution, which contracts like t-2 about a point lying one-quarter the distance from the vertex to the focus. In the other, the flow is non-axisymmetric, and the free surface contracts like t-5. The parabolic flow is shown to be one of a general class of self-similar flows in the plane, described by rational functions of degree n. The parabola corresponds to n = 2. When n = 3 there are two new flows. In one of these the scale varies as and the free surface has the appearance of a trough filling up. In the other, the free surface resembles flow round the end of a rigid wall; the scale varies as t-4.17. © 1976, Cambridge University Press. All rights reserved.

Description: A realistic theoretical model of steady Langmuir circulations is constructed. Vorticity in the wind direction is generated by the Stokes drift of the gravity-wave field acting upon spanwise vorticity deriving from the wind-driven current. We believe that the steady Langmuir circulations represent a balance between this generating mechanism and turbulent dissipation. Nonlinear equations governing the motion are derived under fairly general conditions. Analytical and numerical solutions are sought for the case of a directional wave spectrum consisting of a single pair of gravity waves propagating at equal and opposite angles to the wind direction. Also, a statistical analysis, based on linearized equations, is developed for more general directional wave spectra. This yields an estimate of the average spacing of windrows associated with Langmuir circulations. The latter analysis is applied to a particular example with simple properties, and produces an expected windrow spacing of rather more than twice the length of the dominant gravity waves. The relevance of our model is assessed with reference to known observational features, and the evidence supporting its applicability is promising. © 1976, Cambridge University Press. All rights reserved.

Description: Experiments have been performed in a low-speed wind tunnel to determine the detention time of airborne smoke particles that become trapped in the wake vortex (or bubble) region behind flat disks placed perpendicular to the flow. Using a laser transmissometer to detect the smoke, its detention time was obtained from the time-dependent decay of the smoke in the disk bubble during the time immediately following the removal of the source of smoke. The dimensionless group H, the product of the detention time and the mainstream air velocity divided by the disk diameter, is seen to be a constant equal to 7.44 ± 0.52 for Reynolds numbers in the range 2000–40000. This result is compatible with a simple fluid-mechanical model which describes the transport of fluid-borne scalar entities across the bubble boundary by turbulent diffusion. The investigation suggests that H should be unique for the flow about a disk over a wide range of conditions, and further suggests the possibility that similar unique values for H can exist for flow about other obstacles. The number H has potential applications in a number of physical and engineering research areas. © 1976, Cambridge University Press. All rights reserved.

Description: A numerical study is made of the temporal eigenvalue spectrum of the Orr-Sommerfeld equation for the Blasius boundary layer. Unlike channel flows, there is no mathematical proof that this flow has an infinite spectrum of discrete eigenvalues. The Orr-Sommerfeld equation is integrated numerically, and the eigenvalues located by tracing out the contour lines in the complex wave velocity (c = cr + ici) plane on which the real and imaginary parts of the secular determinant are zero. This method gives only a finite and small number of discrete eigenvalues for a wide range of Reynolds numbers and wavenumbers. The spectrum of plane Poiseuille flow is used as a guide to study the spectrum of an artificial two wall flow which consists of two Blasius boundary layers. As the upper boundary of this flow moves to infinity, it is found that the portion of the spectrum with an infinite number of eigenvalues moves towards cr = 1 and the spacing between eigenvalues goes to zero. It is concluded, on the basis of this result and the contour method, that the original few eigenvalues found are the only discrete eigenvalues that exist for Blasius flow over a wide portion of the c plane for cr 〈 1 and cr 〉 1. It is suggested that the discrete spectrum is supplemented by a continuous spectrum which lies along the cr = 1 axis for ci 〈 −α/R. © 1976, Cambridge University Press. All rights reserved.

Description: The present investigation is oriented towards a better understanding of the turbulent structure in the core region of fully developed and completely wall-bounded flows. In view of the already existing results concerning the bursting process in boundary layers (which are semi-bounded flows), an amplitude analysis of the Reynolds shear stress fluctuation u1 u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow. For the wall side of the core region, in which the correlation coefficient u1u2/u’1 u’2 does not change appreciably with the distance from the wall, the structure of the Reynolds stress is found to be similar to that obtained in boundary layers: bursts, i.e. ejections of low speed fluid, make the dominant contribution to the Reynolds stress; the regions of violent Reynolds stress are small fractions of the overall flow; and the mean time interval between bursts is found to be almost constant across the flow. For the core region, the large cross-stream evolution of the correlation coefficient u1 u2/u’1 u’2 is associated with a new structure of the Reynolds stress induced by the completely wall-bounded nature of the flow. Very large amplitudes of u1u2 are still observed, but two distinct burst-like patterns are now identified and related to ejections originating from the two opposite halves of the flow. In addition to this interaction, a focusing effect caused by the circular section of the pipe is observed. As a result of these two effects, the mean time interval between the bursts decreases significantly in the core region and reaches a minimum on the pipe axis. Investigation of specific space-time velocity correlations reveals the possible existence of rotating structures similar to those observed at the outer edge of turbulent boundary layers. These coherent motions are found to have a scale noticeably larger than that of the bursts. © 1976, Cambridge University Press. All rights reserved.

Description: The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient [formula omitted] is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging. © 1976, Cambridge University Press. All rights reserved.

Description: This paper presents a procedure whereby three-dimensional inviscid flow through a highly loaded turbomachinery cascade of lifting lines can be treated by methods corresponding to classical aerodynamic theory. In contrast to earlier linearized (thin airfoil) three-dimensional theory, the present study allows analysis of the flow corresponding to the large turning and/or large pressure ratios induced by practical rotors or stators. For the sake of simplicity, the present paper is limited to incompressible flow through a highly loaded rectilinear cascade and to the design problem, i.e. given blade loading. Formulae are derived for both the mean and the three-dimensional components of the flow; in particular, the velocities at the blades induced by the trailing vorticity associated with nonuniform blade circulation are determined. © 1976, Cambridge University Press. All rights reserved.

Description: The method of Vickery for calculating the drag of plane lattice structures normal to a turbulent stream is extended to cases of increased solidity. The analysis incorporates an extended version of Taylor's theory for the flow through a porous plate, and a simplified version of Hunt's analysis of the distortion of a turbulent flow by the mean flow field of a body. Some comparisons are made with experimental data. © 1976, Cambridge University Press. All rights reserved.

Description: This work is concerned with the dispersion of a buoyant solute in a straight horizontal pipe of circular cross-section where dispersion is affected by molecular diffusion, the laminar flow along the pipe and density currents. Erdogan & Chatwin (1967) have derived an equation for the mean concentration [formula-ommited] of a buoyant solute using a relatively simple asymptotic model, and have predicted that the dispersion induced by buoyancy effects depends on the Péclet number of the flow. In this part of this study an approximate expression is derived for [formula-ommited] from Erdogan & Chatwin's equation, and an asymptotic form is obtained for the second moment of distributions of buoyant solutes. The examination of the second moment leads to a simple, but important, result: the dispersion induced by density currents at large times is small compared with the dispersion induced by density currents at times when transient effects are significant. © 1976, Cambridge University Press. All rights reserved.

Description: The purpose of the present paper is to derive expressions for the pressure fields of various high frequency convected singularities immersed in a unidirectional sheared flow. These expressions include the simultaneous effects of fluid and source convection and refraction. These results are then combined to predict the far-field directivity of cold round jets. It is found that the agreement between experiment and the present theory is quite good at a source Strouhal number of unity but that this agreement deteriorates as the source frequency is increased. Our theoretical results show the explicit form of the ‘refraction integral’ and that convective amplification for the pressure of a quadrupole is increased by a factor of (1 — MJ cos Θ)-1 over the classical results, where MJ is the jet Mach number and Θ is the angle from the jet axis. Thus acoustic/mean-flow interaction not only implies refraction but also additional convective amplification due not to source convection but to fluid motion. © 1976, Cambridge University Press. All rights reserved.

Description: An experimental investigation of the two-dimensional incompressible mixing layer was carried out. The measurements provide new information on the development of the mean and turbulent fields towards a self-preserving state and on the higher-order statistical characteristics of the turbulent field. The relevance of initial conditions to the development of the flow is discussed in the light of both present and previous data. Measurements of spectra, probability densities and moments to eighth order of all three velocity-component fluctuations at various transverse positions across the flow were carried out using an on-line digital data acquisition system. The probability density distributions of the derivative and the squared derivative of the longitudinal and lateral velocity fluctuations were also determined. Direct measurements of moments to eighth order of the velocity derivatives were attempted and are discussed in the light of the simultaneously measured histograms. The problems in obtaining higher-order statistical data are considered in some detail. Estimates of the integral time scale of many of the higher-order statistics are presented. The high wave-number structure was found to be locally anisotropic according to both spectral and turbulent velocity-gradient moment requirements. Higher-order spectra to fourth order of the longitudinal velocity fluctuations were measured and are discussed. Finally the lognormality of the squared longitudinal and lateral velocity-derivative fluctuations was investigated and the universal lognormal constant μ was evaluated. © 1976, Cambridge University Press. All rights reserved.

Description: A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a + (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate. © 1976, Cambridge University Press. All rights reserved.

Description: In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numerical solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container. © 1976, Cambridge University Press. All rights reserved.

Description: An experiment was performed in a 3.5 by 3.5 m variable-height, closed convection box, with conditions ranging from a Rayleigh number of 4 x 104upto 7 x 109, using air as the working fluid. Heat-flux measurements made at Rayleigh numbers up to 7 x 109 yielded a Nusselt number Nu = 0.13Ra0.30. Velocities and temperatures were measured up to Ra = 1.7 x 107, and Fourier spectra calculated to find the predominant horizontal scales of the motion midway between the boundaries. The predominant scale at Ra ˜ 105 was approximately four times the distance between plates, changing to six as Ra increased to 106. With side walls introduced so that the transverse aspect ratio was equal to five, Fourier spectra indicated considerable smaller scale motions, approximately equal to the layer depth. These motions decreased in size as Ra was increased. The results are discussed in relation to previous experimental and theoretical work. © 1976, Cambridge University Press. All rights reserved.

Description: A thermally driven steady axisymmetric flow of gas of small diffusivity in a vertical circular cylinder rotating rapidly about its axis of symmetry is studied. The side wall is a thermal insulator and the horizontal end plates are perfect conductors. The temperature of the top end plate is kept slightly higher than that of the bottom one. The boundary-layer method is applied to solve the linearized basic equations and the following results are obtained. (i) The axial velocity in the inner core is fully controlled by the Ekman suction on the horizontal plates and is the same as that in the case of a perfectly conducting side wall. (ii) The closed circulation in the side-wall Stewartson E½ layer is strongly suppressed compared with the case of a perfectly conducting side wall. (iii) This situation is reflected in the inner temperature field, which deviates from that in the case of a perfectly conducting side wall. The critical parameter governing the solution is found to be (γ − 1) PrG0E−1/3/4γ, where Pr is the Prandtl number, γ the ratio of specific heats, E the Ekman number and G0 the square of the Mach number based on the peripheral speed of the cylinder. © 1976, Cambridge University Press. All rights reserved.

Description: The stability to three-dimensional disturbances of three classical steady vortex configurations in an incompressible inviscid fluid is studied in the limit of small vortex cross-sectional area and long axial disturbance wavelength. The configurations examined are the single infinite vortex row, the Karman vortex street of staggered vortices and the symmetricvortex street. It is shown that the single row is most unstable to a two-dimensional disturbance, while the Karman vortex street is most unstable to a three-dimensional disturbance over a significant range of street spacing ratios. The symmetric vortex street is found to be most unstable to three-dimensional or two-dimensional symmetric disturbances depending on the spacing ratio of the street. Short remarks are made concerning the relevance of the calculations to the observed instabilities in free shear layer, wake and boundary-layer type flows. © 1982, Cambridge University Press. All rights reserved.

Description: A formalism that accounts for inertial and diffusive effects in the dynamics of a dilute gas-particle suspension is introduced. The treatment is purely deterministic away from a very thin Brownian diffusion sublayer, while, within the sublayer, inertial effects are small, permitting a near-equilibrium expansion in powers of the Stokes number (particle relaxation time divided by flow characteristic residence time). This expansion provides phenomenological expressions for theparticle velocity including two terms: the standard Brownian diffusion, and an additional inertial drift velocity which is closely related to the pressure diffusion term of the Chapman-Enskog expansion. As an example, the general formalism is applied in detail to the case of Stokes flow about a sphere, and sketched for the similar case of a cylinder. Two competing mechanisms are seen to affect the total rate of particle capture by the sphere: (i) the stagnation-point region is considerably enriched in particles owing to the high compressibility of the particle phase, which leads to locally enhanced deposition; (ii) centrifugal forces tend to deplete the Brownian diffusion sublayer of particles, reducing diffusion rates away from the stagnation point to the surface. The first effect is seen to dominate over the second except in a very narrow zone of small Stokes numbers. Our method bridges the gap between Levich's solution for the ‘pure-diffusion’ limit and Michael's treatment in the ‘pure-inertia’ limit. © 1982, Cambridge University Press. All rights reserved.

Description: Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale in viscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.† Present address: Dept of Aeronautics, University of Washington, Seattle, WA 98195. © 1982, Cambridge University Press. All rights reserved.

Description: Observations of inertial waves generated by uniform horizontal flow over ridges and truncated axisymmetric obstacles in a homogeneous fluid rotating about a vertical axis are discussed and compared with linear theory. The dependence of the flow on obstacle shape, Ro, H, E and e is investigated. Here Ro = U/2ΩL is the Rossby number, H = Ro(D/L), E = v/2ΩL2 is the Ekman number, and e = h/L is the non-dimensional height of the obstacle, where U is the basic velocity Ω is the angular frequency, L is a streamwise length, D is the depth of the fluid, h is the height of theobstacle, and v is the kinematic viscosity. Previous linear analysis of this problem has been for the limit H fixed, Ro→ 0, referred to here as the small-Ro limit. However, it is shown that certain linear terms neglected in the small-Ro limit can be important for finite Ro, and are included in the analysis given here. The observed flow is then well described by linear theory for H/ e 1, particularly in the case of two-dimensional flow over a ridge. However, for H/e 1 the flow field is dominated by a vertical columnar motion, which is not adequately described by the analysi. © 1982, Cambridge University Press. All rights reserved.

Description: The robustness of localized states that transport energy and mass is assessed by a numerical study of the Euler equation in two space dimensions. The localized states are the translating ‘F-states’ discovered by Deem & Zabusky. These piecewise-constant dipolar (i.e. oppositely-signed or) vorticity regions are steady translating solutions of theEuler equations. A new adaptive contour-dynamical algorithm with curvature-controlled node insertion and removal is used. The evolution of one F-state, subject to a symmetric-plus-asymmetric perturbation is examined and stable (i.e. non-divergent) fluctuations are observed. For scattering interactions, coaxial head-on (or on) and head-tail (or on) arrangements are studied. The temporal variation of contour curvature and perimeter after F-states separate indicate that internal degrees of freedom have been excited. For weak interactions we observe phase shifts and the near recurrence to initial states. When two similar, equal-circulation but unequal-area F-states have a head-on interaction a new asymmetric state is created by contour ‘exchange’. There is strong evidence that this is near to a F-state. For strong interactions we observe phase shifts, ‘breaking’ (filament formation) and, for head-tail interactions, merger of like-signed vorticity regions. © 1982, Cambridge University Press. All rights reserved.

Description: The onset of double-diffusive convection is discussed for a layer of fluid in which the vertical salinity gradient varies with depth and for which the thermal and saline Rayleigh numbers R and Rs are large. These conditions are similar to those that exist in a solar pond prior to the onset of any instability. It is shown that when convection occurs it takes the form of an overstable mode and is essentially confined to a narrow region of vertical extent Rs- 1/4 x depth of the fluid layer, centred at the critical depth where the salt gradient is smallest. The leading terms in asymptotic expansions of the ratio R/Rs, the frequency of oscillation p and the horizontal wavenumber a are determined for Rs 1. The results predicted by the theory are shown to be in good agreement with numerical results and with observations of solar ponds. © 1982, Cambridge University Press. All rights reserved.

Description: Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Here we report on numerical studies dealing with two or three modes with triad interactions. We have found rich time dependence in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favourably. Except at the highest Rayleigh number we have considered (107), the theoretical Nusselt numbers agree well with experiment.† N values from II, table 1.‡ P-estimates from Rossby (1969) and Krishnamurti (1973). © 1982, Cambridge University Press. All rights reserved.

Description: The fluid motion, temperature distribution and the mass-transfer problem of a binary gas mixture in a rapidly rotating centrifuge are investigated. The model centrifuge considered consists of a pair of concentric circular cylinders bounded on the top and bottom by horizontal end plates; the apparatus rotates rapidly about the axis of the cylinders. During steady operation a binary gas mixture containing species A and B is injected into and withdrawn from the centrifuge through axisymmetric slots located on the sidewalls. Solutions for the velocity, temperature and mass-fraction fields within the centrifuge are obtained for mechanically or thermally driven centrifuges. For the mass-transfer problem, a detailed analysis of the fluid-mechanical boundary layers is required, and, in particular, mass fluxes within the boundary layers are obtained for a wide range of source-sink geometries. Solutions to the mass-transfer problem are obtained for moderately and strongly forced flows in the container; the dependence of the separation (or enrichment) factor on centrifuge configuration, rotational speed and fraction of the volumetric flow rate extracted at the product port (the cut) are predicted. © 1982, Cambridge University Press. All rights reserved.

Description: The stability of weakly compressible boundary-layer flow over a spring-mounted piston is examined theoretically by modelling the mean boundary layer at low Strouhal numbers by means of a step-function velocity profile. This constitutes a prototype problem for the treatment of the interaction of unsteady boundary-layer flow with a compliant surface, and the present discussion complements a recent analysis due to Ffowcs Williams and Purshouse by incorporating the influence of flow separation at the edges of the piston. This is effected analytically by application of the unsteady Kutta condition at both the leading and trailing edges of the piston. At high Reynolds numbers and in the case of light fluid loading itis predicted that the separated flow can cause piston flutter. Stability criteria are derived for a rectangular piston of large aspect ratio. © 1982, Cambridge University Press. All rights reserved.

Description: Joint Institute for Laboratory Astrophysics, and Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder, CO 80309.A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed indeendence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. Theconvection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys ofnumerical solutions are presented for a selection of Rayleigh numbers R, stability parameters γ and horizontal wavenumbers a. The solutions yield a buoyancy flux ratio Xthat is insensitive to γ, in accord with laboratory experiments. However X increases with increasing R, in contradiction to laboratory observations. © 1982, Cambridge University Press. All rights reserved.

Description: The central features of linear and nonlinear disturbance growth in the unstable shear layer, mechanisms of impingement of the resultant vortices on the edge, induced force on the wedge, and upstream influence in the form of induced velocity fluctuations at separation are examined by simultaneous visualization, velocity, and force-measurement techniques.The nature of the vortex-wedge interaction, and the associated force on the wedge, are directly related to the induced velocity at the upstream separation edge, thereby providing the essential ‘feedback’ for the self-sustained oscillation. Velocity fluctuations at the upper and lower sides of the separation edge tend to be n out of phase, a condition that is maintained along the outer boundaries of the downstream shear layer. Moreover, the phase between velocity fluctuations at separation and impingement satisfies the relation 2nΠ, where n is an integer.The shear layer downstream of the separation edge initially forms an asymmetric wake, which evolves into large-scale vortices, all of which have a circulation appropriate to the high-speed side. The disturbance amplification associated with the high-speed side dominates from the separation edge onwards, precluding development of instabilities associated with the low-speed side.Regardless of the initial amplitude of the disturbance induced at the separation edge, the same saturation amplitude is attained in the downstream (nonlinear) region of the shear layer, underscoring the fact that variations in force amplitude at the wedge are dominated by the type of vortex-edge interaction mechanism. The sensitivity of this interaction to small offsets between the vortex centre and the leading edge entails that jumps in frequency of oscillation are also associated with jumps in the force amplitude. © 1982, Cambridge University Press. All rights reserved.

Description: Velocity moments have been calculated for the rapid distortion of axisymmetric turbulence in a uniform mean shear. The moments are compared with data on steady pipe flows and two-dimensional channel flows, and the turbulence structure of these flows is summarized in terms of effective distortion strain. The centre-line structure is taken to be characteristic of the undistorted state which from the data is more nearly axisymmetric rather than isotropic. A closer comparison is found than that by Townsend (1970), and in particular the differences in stress ratios T/pu21 T/pq2 found between different experiments can be accounted for with the hypothesis of initially axisymmetric turbulence. Profiles for the effective strain are derived from the experiments and are shown to have the same form and to indicate the existence of a relaxation timescale for the large eddies, comparable to the energy decay timescale. An equation for the effective distortion strain is formulated that can be incorporated into a turbulence model. © 1982, Cambridge University Press. All rights reserved.

Description: This note is to show that in the presence of surface tension small progressive waves can always exist in water having aninertial surface composed of uniformly distributed floating particles, in contrast to the known result in the absence ofsurface tension that precludes propagation under a surface that is too heavy. © 1982, Cambridge University Press. All rights reserved.

Description: An analytical theory is developed for the stability properties of planar fronts of premixed laminar flames freely propagating downwards in a uniform reacting mixture. The coupling between the hydrodynamics and the diffusion process is described for an arbitrary expansion of the gas across the flame. Viscous effects are included with an arbitrary Prandtl number. The flame structure is described for a large value of the reduced activation energy and for a Lewis number close to unity. The flame thickness is assumed to be small compared with the wavelength of the wrinkles of the front, this wavelength being also the characteristic lengthscale of the perturbations of the flow field outside the flame. A two-scale method is then used to solve the problem. The results show that the acceleration of gravity associated with the diffusion mechanisms inside the front can counterbalance the hydrodynamical instability when the laminar-flame velocity is low enough. The theory provides predictions concerning the instability threshold. In particular, the dimensions of the cells are predicted to be large compared with the flame thickness, and thus the basic assumption of the theory is verified. Furthermore, the quantitative predictions are in good agreement with the existing experimental data. © 1982, Cambridge University Press. All rights reserved.

Description: An algorithm is formulated for computing perturbation-series solutions for standing waves on the interface between two semi-infinite fluids of different but uniform densities. Using a computer, the series solutions are computed to fifth order for a general value of r, the ratio of the density of the upper fluid to that of the lower fluid (0 ≤r ≤ 1), and to 21st order for five specific values of this ratio: r = 0, 10-3, 01, 0.5, 1.0. The series for the period, the energy, and the interface profile of the waves are summed using Padé approximants. The maximum wave height for each of the above five density ratios is estimated from the locations of the poles of the Padé approximants for the wave period and the wave energy. At maximum height the interface appears to be vertical at a point on the interface that is very near the crest for r = 10-3 and approaches the midpoint between the crest and the trough as r approaches 1.0. © 1982, Cambridge University Press. All rights reserved.

Description: Steady three-dimensional symmetric wave patterns for finite-amplitude gravity waves on deep water are calculated from the full unapproximated water-wave equations as well as from an approximate equation due to Zakharov. These solutions are obtained as bifurcations from plane Stokes waves. The results are in good agreement with the experimental observations of Su. © 1982, Cambridge University Press. All rights reserved.

Description: The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted. © 1982, Cambridge University Press. All rights reserved.