ALBERT

Beschreibung: The construction and performance of a proportional CO2 counter system is described by which an over-all accuracy is obtained of 1.3‰ after a two-day counting period.

Beschreibung: The following list contains most of the measurements made during 1974, since our last list (R, 1973, v 15, p 241-251). All measurements were performed on a Beckman LS-200 Liquid Scintillation Spectrometer following previously published setting up (Polach, 1974), automatic cycling (Polach, 1969) and benzene synthesis (Polach and Stipp, 1966; Polach et al, 1972) procedures.

Beschreibung: The Geochronology Laboratory has recently changed its name to the Center for Applied Isotope Studies to reflect its steady and diversified expansion since its conception in 1969. Initially the laboratory was set up to offer age dating services to personnel at the University of Georgia. Subsequently, the laboratory expanded its activities so as to enable it to participate in studies of an applied and basic research nature.

Beschreibung: The present list includes 66 dates of geologic samples determined using the liquid-scintillation 14C metod 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.

Beschreibung: All samples described in this date list have been measured since July 1973 to Oct 1975 using carbon dioxide filled proportional counters. Most of samples have been dated with Counter No. 1 (LI) as in our previous list (Mościcki and Zastawny, 1976). Some samples were measured with Counter No. 3 (L3), with a total volume of 1.51 and background and NBS oxalic acid standard counting rate of respectively, 3.50 or 4.00 cpm and 10.05 or 20.40 cpm when filled to 1 or 2 atm pressure (Mościcki and Zastawny, 1977).

Beschreibung: The Radiocarbon Dating Laboratory of the Institute was established in 1974 primarily to assist in the program of research undertaken by the Institute's Department of Quaternary Palynology (Rajagopalan and Vishnu-Mittre, 1977). The measurements carried out by the Laboratory up to December 1977 are presented in this date list.

Beschreibung: The following list comprises age measurements carried out during 1976 and 1977. The activity of 14C was computed by one- and two-channel scintillation devices (Punning et al, 1976; 1977). Ages are calculated using a half-life of 5568 ± 30 years for 14G with NBC oxalic acid as a reference standard. All dates are reported in years before 1950. 12C/13C measurements were not performed and results are not corrected for 13C fractionation.

Beschreibung: The following radiocarbon dates are a partial list of samples measured since Sept 1977. The chemical and counting procedures are the same as indicated previously (R, 1978, v 20, p 134-138).

Beschreibung: Most of the 14C measurements reported here were made between October 1976 and October 1977. Equipment, measurement, and treatment of samples are as reported previously (R, 1968, v 10, p 36-37; 1976, v 18, p 290).

Beschreibung: Samples reported in this date list are primarily geologic specimens collected from coastal locations in South Carolina and Florida. Sample material was predominantly shells, with emphasis on single shell dates rather than multiple shell dates. Archaeologic samples from sites either directly above or adjacent to the geologic sampling location were collected whenever possible to provide an upper time limit on the shell deposits.

Beschreibung: The dates presented in this paper comprise results of determinations made on archaeologic and geologic material from Socialist Republic Vietnam since 1969. Radioactivity was measured twice for 48 hours with gas proportional counters of Houtermans-Oeschger type, using methane at 1000mm Hg pressure as filling gas. Influence of cosmic and local environmental radiation on the counters was reduced with 30 tons of shielding material as described earlier (R, 1970, v 12, p 400-420).

Beschreibung: This list reports certain 14C measurements completed by November 1977; other projects completed by this time will be reported later. Age calculations are based on 14C half-life of 5568yr and modern standard of 95% NBS oxalic acid, supplemented by tree rings of pre-industrial wood from a log cut in the 1850's (Tx-540; R, 1970, v 12, p 249). Deviations reported are based on counting statistics of sample, background, and modern, and are ±1σ, except that when sample count approaches either modern or background, 2σ limits are reported. Unless noted, 12C/13C measurements were not made and results are not corrected for 13C fractionation. Our laboratory uses liquid scintillation counting of benzene, with Li2C2 and vanadium-activated catalyst in preparation; chemical yields range between 95% and 99%. Three counters are employed: a Packard Tri-Carb Model 3002 and 2 Beckman LS320 spectrometers obtained through a grant from the National Science Foundation.

Beschreibung: Most dates in this list were obtained between 1972 and 1976. Treatment of samples has remained essentially the same as described previously (R, 1975, p 364).

Beschreibung: The following dates are a partial list of geologic samples dated since December 1976. The method used is described by (Stipp et al, 1976). Ages were calculated using a half-life of 5568 years. Errors reported are one standard deviation and include only the counting errors on the unknown sample, background and modern standard. There have been no corrections made on these dates. Sample descriptions and comments were written, based on information supplied by the submitters.

Beschreibung: Procedures and equipment of the laboratory have been described in previous date lists. Except as otherwise indicated, wood, charcoal, and peat samples are pretreated with dilute NaOH and dilute H3PO4 before conversion to the counting gas methane, marls and lake cores are treated with acid only. Very calcareous materials are treated with HCl instead of H3PO4.

Beschreibung: This list includes ages measured from August 1974 to May 1976 using the benzene scintillation method. All archaeologic and geologic samples except Sahara Libico series, come from Italian territory. These datings were carried out partly with the liquid scintillation counter previously described (Alessio et al, 1973) and partly with a new liquid scintillation counter (Alessio et al, 1976b). Vials, 4.5ml in volume, described in Alessio et al, 1973. Mixture consists of 3.5ml of benzene from sample and 1ml of commercial liquid scintillator NE 216. The characteristics of new counter are: background 2.90 cpm and figure of merit

Beschreibung: This list contains the results of some measurements made between 1965 and 1973. Samples are counted in the form of acetylene gas, as previously, and ages computed on the basis of the Libby half-life, 5568 ± 30 years. The dates have not been corrected for fractionation by a δ13C measurement. The error listed, always larger than the one-sigma statistical counting error commonly used, takes into account possible fractionation in the laboratory and in nature and the variability experienced with replicate samples. We wish to thank Charles Oman for his technical assistance.

Beschreibung: The following list covers all bone sample measurements finished since the last list (R, 1972, v 14, p 247-271) until the end of 1977; the Egyptian samples were measured as an interlaboratory project and all shells were closely related to some of the bone samples.

Beschreibung: The present list contains dates of geologic samples from the southern part of the Karelian ASSR and partly from the northwest Leningrad Region, USSR, made in 1969-1975.

Beschreibung: The following list contains most of the measurements made during 1977, since our last list (R, 1977, v 19, p 383-388). The laboratory procedures used were those outlined in the previous date lists (R, 1976, v 18, p 151-160; R, 1977, op cit). Dates are calculated using 14C half-life of 5568 yr and errors are reported as one-standard deviation. The collagen extraction follows Longin (1970).

Beschreibung: In this date list we have included most of the archaeologic samples dated in this laboratory since publication of our last date list (R, 1977, v 19, p 188-228).

Beschreibung: This list includes results of measurements made during 1973-1974 and 1975 in the Natural Radiocarbon Laboratory of the Centre de Recherches Radiogéologiques de Nancy (CRR).

Beschreibung: The following radiocarbon dates are a partial list of samples measured since March 1977. The techniques used are the same as reported in R, v 16, p 402-408, and modified in R, v 18, p 210-220, with the following exception. A third liquid scintillation counter (Beckman LS-100) has been added and the shortened, low-K glass-counting vials have been replaced with teflon vials of Noakes (1975) design. Backgrounds on the counters were thus reduced from 9.1 cpm, 8.8 cpm and 4.9 cpm to 3.8 cpm, 3.5 cpm and 2.8 cpm, respectively, with an attendant small increase in efficiency.

Beschreibung: A simple procedure for the conversion of 14C NBS oxalic acid standard to benzene without direct combustion or wet oxidation is reported. Fractionation in the synthesized benzene was not detected.

Beschreibung: The carbon isotope analyses reported here include all radiocarbon dates run on packrat middens in the United States and Mexico by the Arizona radiocarbon laboratory through October 1977. All samples described below report dates by CO2 (0.5 or 2.0L) counting. Age calculations are based on a 14C half-life of 5568 years, using 0.949 NBS oxalic acid as the modern value. Errors, based on counting statistics, are quoted to ± 1δ; infinite ages quoted to — 2δ.

Beschreibung: In 1969, at the Nobel Symposium on “Radiocarbon Variations and Absolute Chronology” in Uppsala, a curve was presented that illustrated the functional dependence of measured conventional radiocarbon dates on true historical ages of wood samples (Suess, 1971). The curve was derived from the results of La Jolla measurements of radiocarbon in bristlecone pine wood dendrochronologically dated by and obtained from Professor C W Ferguson of the University of Arizona (Ferguson, 1968). The curve was intended to be adequate for deriving calibrated radiocarbon dates and also for allowing fairly reliable estimates of the accuracy of the absolute dates obtained in this manner. The basis for the validity of this calibration is the well known fact that, for all practical purposes, wood samples that had grown at the same time show the same radiocarbon content. However, the reverse is not always true: Wood samples showing the same radiocarbon content do not necessarily have the same age because of the windings and steps of the curve (Stuiver and Suess, 1966).

Beschreibung: Presented below are dates from some important archaeologic and Quaternary sites. All dates are based on τ ½ = 5568 yr; to convert the radiocarbon dates for archaeologic samples into ad/bc scale, 1950 has been used as base as per the resolution passed at the Ninth International Radiocarbon Conference, San Diego, 1976. The dates are not corrected for 13C fractionation. All the dates older than 10,000 yr have been given with 2σ errors. Due to uncertainty about the contribution of the biogenic carbon in caliche (CaCO3) samples, the dates represent apparent and not true ages.

Beschreibung: This list includes all measurements made between 1969 and 1973 that represent natural samples. Physical and chemical treatment of samples and counting technique remain as previously reported (R, 1973, v 15, p 469-478). Calculations of dates are made with the radiocarbon half-life of 5568 ± 30 years; plus or minus numbers quoted herein are the standard errors for the counting of radioactive disintegrations.

Beschreibung: The persistence of the large vortices formed at the origin of wakes and mixing layers constitutes a kind of memory of initial conditions by the turbulence. In order to study the fading of this turbulence memory, and its effect on the rate of approach to the fully developed state, two wakes with different initial conditions have been examined experimentally. The wake of a sphere was compared with the wake of a porous disk which had the same drag, but did not exhibit vortex shedding. Measurements were made of the mean and fluctuating velocities, the anisotropy of the turbulence, and the intermittency. It was found that the wake of the sphere developed self-preserving behaviour more rapidly than the wake of the disk, and that even after both wakes became self-preserving there were differences between them in the structure of the turbulence and the scale of the mean flow. From this it is concluded that the behaviour of self-preserving wakes does not depend on the drag alone, but also on the structure of the dominant eddies. Generalizing these results, it is suggested that reported differences in the value of the entrainment constant of jets, wakes, and mixing layers are due to differences in the structure of the dominant eddies, rather than differences in the type of flow. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The spectral method of Orszag & Patterson (1972a, b) is used here to study pressure and velocity fluctuations in axisymmetric, homogeneous, incompressible, decaying turbulence at Reynolds numbers Reλ ≲ 40. In real space 323 points are treated. The return to isotropy is simulated for several different sets of anisotropic Gaussian initial conditions. All contributions to the spectral energy balance for the different velocity components are shown as a function of time and wavenumber. The return to isotropy is effected by the pressure-strain correlation. The rate of return is larger at high than at low wavenumbers. The inertial energy transfer tends to create anisotropy at high wavenumbers. This explains the overrelaxation found by Herring (1974). The pressure and the inertial energy transfer are zero initially as the triple correlations are zero for the Gaussian initial values. The two transfer terms are independent of each other but vary with the same characteristic time scale. The pressure-strain correlation becomes small for extremely large anisotropies. This can be explained kinematically. Rotta's (1951) model is approximately valid if the anisotropy is small and if the time scale of the mean flow is much larger than 0·2 Lf/v, which is the time scale of the triple correlations (Lf = integral length scale, v = root-mean-square velocity). The value of Rotta's constant is less dependent upon the Reynolds number if the pressure-strain correlation is scaled by v3/Lf rather than by the dissipation. Lumley & Khajeh-Nouri's (1974) model can be used to account for the influence of large anisotropies. The effect of strain is studied by splitting the total flow field into large- and fine-scale motion. The empirical model of Naot, Shavit & Wolfshtein (1970) has been confirmed in this respect. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Faulted regions associated with geothermal areas are assumed to be composed of rock which has been heavily fractured within the fault zone by continuous tectonic activity. The fractured zone is modelled as a vertical, slender, two-dimensional channel of saturated porous material with impermeable walls on which the temperature increases linearly with depth. The development of an isothermal slug flow entering the fault at a large depth is examined. An entry solution and the subsequent approach to the fully developed configuration are obtained for large Rayleigh number flow. The former is characterized by growing thermal boundary layers adjacent to the walls and a slightly accelerated isothermal core flow. Further downstream the development is described by a parabolic system. It is shown that a class of fully developed solutions is not spatially stable. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Dimensional analysis is applied to the velocity profile U(y) of turbulent boundary layers subjected to adverse pressure gradients. It is assumed that the boundary layer is in moving or local equilibrium in the sense that the free-stream velocity U∞ and kinematic pressure gradient α = ρ−1dP/dx vary only slowly with the co-ordinate x. This assumption implies a rather complicated general equation for the velocity gradient dU/dy which may be considerably simplified for several specific regions of the flow. A general family of velocity profiles is derived from the simplified equations supplemented by some experimental information. This family agrees well with almost all existing data on velocity profiles in adverse-pressure-gradient turbulent boundary layers. It may be used for the derivation of a skin-friction law which predicts satisfactorily the values of the wall shear stress at any non-negative value of the pressure gradient. The variation of the boundary-layer thickness with x is also predicted by dimensional considerations. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Experimental measurements of the frequencies of discrete tones induced by flow over rectangular cavities were carried out over a range of low subsonic Mach numbers to provide a reliable data base for (aircraft wheel well) cavity noise consideration. A mathematical model of the cavity tones and pressure oscillation phenomenon based on the coupling between shear layer instabilities and acoustic feedback is developed to help in understanding the tone generation mechanism. Good agreement is found between discrete tone frequencies predicted by the model and experimental measurements over a wide range of Mach numbers. Evidence of tones generated by the cavity normal mode resonance mechanism at very low subsonic Mach numbers is also presented. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: In the present investigation we consider hydromagnetic Stokes flow past a rotating sphere. The magnetic field is produced by a magnetic pole placed at the centre of the sphere. The problem is analysed by a combination of perturbation and numerical methods. It is seen that the flow reversal (due to rotation) at the rear portion of the sphere is enhanced as the strength of the magnetic field increases. In addition, we obtain the simultaneous effects of rotation and a magnetic field on the streamlines. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The Faxén relations for a rigid particle in an arbitrary Stokes flow are generalized to give expressions for the stresslet (and higher stress moments) exerted by the particle on the fluid, and also to viscous drops immersed in a viscous fluid. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The paper describes correlation measurements in both broad and narrow frequency bands of the longitudinal velocity fluctuations in fully developed pipe flow at four positions for a reference probe whilst a second probe was traversed radially from deep in the sublayer to a position near the axis with both longitudinal and transverse separations zero (Δx = Δz = 0). Such measurements require that both the Covariant (Co) and Quadrature (Quad) correlations be determined for each of the 15 frequencies used to constrain the wave component λx. The new data demonstrate that low frequency, large scale turbulence fluctuations extend over the majority of the radial region and that these components are highly correlated. By using a similarity variable kxy, along with a normalized wall distance y/y REF, both correlation functions, i.e. the Co and the Quad components, are shown to collapse. The physical significance of this is discussed. The broad-band data do not collapse because of the large range of wave sizes. However, the present experiment does show that strong radial correlations exist even when one probe is at y+ = 1. This conflicts with the earlier data of Favre, but agrees with the more recent work of Comte-Bellot. There is a significant amount of turbulent energy in frequencies less than 16 Hz (ω+ = 0·008) for turbulent flows of about 105 Reynolds number. The spectral function ωΦ(ω) is also presented for a range of y+ values. Using this form for the power spectral density, along with the stochastic wave modelling and similarity arguments of this paper, it is shown how a consistent explanation for the behaviour of these spectra is obtained. In addition some preliminary results from cross-spectral analyses are presented and suggestions made as to their physical significance. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The classical power laws describing the similarity solutions for turbulent jets, wakes and shearing layers are found to determine a fixed turbulent Reynolds number for each flow. The power laws are then derived from the principle of marginal instability without the usual assumptions. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The force on a small sphere translating relative to a slow viscous flow is found to O(Re½) for two different fluid flows far from the sphere, namely pure rotation and pure shear. For pure rotation, the O(Re½) correction to the Stokes drag consists of an increase in the drag. For pure shear, the O(Re½) force contains a component perpendicular to the Stokes drag force. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The boundary-layer equations are solved numerically for mainstreams formula omitted which are both O((1 − x)−α) near x = 1. Series expansions are derived near x = 1. For α 〉 1, where, for the similarity solution at x = 1, the outer boundary condition is approached through exponentially small terms, a straightforward expansion in powers of 1 − x is possible. For 0 〈 α 〈 1, where the decay is only algebraic (Brown & Stewartson 1965), the outer boundary condition cannot be satisfied even with algebraic decay by the higher-order terms in the series and this must be regarded as only an inner expansion. An outer expansion is required which matches with this inner expansion and which approaches the outer boundary condition with exponential decay. For α = 1, the decay is exponential, but not of the same form as for α 〉 1, and again the outer boundary condition cannot be attained by the higher-order terms in the series. An outer expansion for this case is also derived. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The developing flow in the entry region of a heated horizontal pipe is analysed. The asymptotic solution of the developing flow near the entrance of the heated straight pipe, distance O(a), is obtained by perturbing the solution of the developing flow in an unheated straight pipe. Two vortices result from the combination of the radial-directional and the downward motions of the fluid particles which are induced by the displacement of the boundary layer and develop along the pipe. The axial velocity has a concave profile in the inviscid core with its maximum off the centre-line near the entrance and it grows toward a uniformly distributed profile downstream. The downward stream caused by the displacement of the secondary boundary layer forces the axial velocity profile to turn anticlockwise continuously along the pipe if the flow is from left to right. The core flow induced by the axial boundary-layer displacement generates a favourable pressure gradient. Simultaneously, the secondary boundary-layer displacement affects the core flow to induce a favourable pressure gradient on the bottom of the pipe and an unfavourable pressure gradient on the top wall. The effect of the axial boundary-layer displacement is stronger than that of the secondary boundary layer near to the entrance. Downstream the growth of the boundary-layer thickness is suppressed by the inviscid secondary flow. It is expected that the displacement effect of the secondary boundary layer becomes dominant downstream from the region of O(d) when Gr is large. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The fully developed laminar flow in a heated curved pipe under the influence of both centrifugal and buoyancy forces is studied analytically. The pipe is assumed to be heated so as to maintain a constant axial temperature gradient. Both horizontal and vertical pipes are considered. Solutions for these two cases are obtained by regular perturbations in the Dean number and the product of the Reynolds and Rayleigh numbers; the solutions are therefore limited to small values of these parameters. Predictions of the axial and secondary flow velocities, streamlines, shear stress, temperature distribution and heat transfer are given for a representative case. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Solutions have been obtained for a family of unsteady three-dimensional boundary-layer flows which approach separation as a result of the imposed pressure gradient. These solutions have been obtained in a co-ordinate system which is moving with a constant velocity relative to the body-fixed co-ordinate system. The flows studied are those which are steady in the moving co-ordinate system. The boundary-layer solutions have been obtained in the moving co-ordinate system using the technique of semi-similar solutions. The behaviour of the solutions as separation is approached has been used to infer the physical characteristics of unsteady three-dimensional separation. In the numerical solutions of the three-dimensional unsteady laminar boundary-layer equations, subject to an imposed pressure distribution, the approach to separation is characterized by a rapid increase in the number of iterations required to obtain converged solutions at each station and a corresponding rapid increase in the component of velocity normal to the body surface. The solutions obtained indicate that separation is best observed in a co-ordinate system moving with separation where streamlines turn to form an envelope which is the separation line, as in steady three-dimensional flow, and that this process occurs within the boundary layer (away from the wall) as in the unsteady two-dimensional case. This description of three-dimensional unsteady separation is a generalization of the two-dimensional (Moore-Rott-Sears) model for unsteady separation. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Some of the dense fluid at the front of an advancing gravity current is observed to be mixed with the ambient fluid. This process continues when the cross-stream non-uniformities at the head of the current are suppressed by advancing the floor beneath the head. In the resulting two-dimensional flow regular billows are visible. This paper considers experimentally and analytically the inviscid gravity current head and specifically includes the observed mixing at the head. Experimental results were obtained with an apparatus in which the head of the gravity current was brought to rest by an opposing uniform flow. The mixing appears to occur through Kelvin-Helmholtz billows generated on the front of the head and controls the dynamics of the head. A momentum balance is used to analyse the flow and the problem is closed by quantitatively introducing the billow structure. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: We consider the problem of mass injection from a flat plate into uniform supersonic flow when the boundary layer is blown off at the leading edge to form a thin free shear layer separating the inviscid injectant layer from the external flow. The injection is moderate, i.e. of the same order of magnitude as the velocity of entrainment into the base of the shear layer. For simplicity, we consider similarity blowing, proportional to x*−½, where x* is measured along the plate from the leading edge. We find that the solution in the injectant region, based on initial conditions at the leading edge, is non-unique unless fixed by downstream conditions. When injection is cut off at a finite distance along the plate, this enables us to find a solution to the problem in which the shear layer eventually reattaches to the plate and for which the pressure and the height of the injectant layer are continuous at cut-off. The study provides a partial connexion between the earlier studies of weak blowing in which the boundary layer is not blown off and of strong blowing for which the boundary layer is blown off and the entrainment into the shear layer is negligible. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: A model of the diffusive interface in double-diffusive convection at high Rayleigh number is proposed. The interface is assumed to have a double structure: Two marginally stable boundary layers from which blobs or thermals arise on the outer edges of the interface, separated by a diffusive core across which all transport takes place by molecular diffusion. The model is time-independent and comparison is made with unsteady ‘run-down’ experiments on the assumption that the experiments run down through a sequence of equilibrium states each of which can be considered separately. The model predicts a constant ratio of the buoyancy fluxes of the two components at a value equal to the square root of the ratio of their molecular diffusivities, and individual fluxes in reasonable agreement with the available experimental data. Some time-dependent features of the model are also examined. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Free shear layer stability measurements with a hot wire revealed that the probe itself can trigger and sustain upstream instability modes like the slit jet-wedge edge tones. The flow fields associated with the free shear layer tones induced in axisym-metric and plane air shear layers by a hot-wire probe and by a plane wedge were then explored experimentally, and found to be different in many ways from the widely investigated jet edge tone phenomenon. As many as four frequency stages have been identified, there being a fifth stage associated with the subharmonic attributed to vortex pairing in the free shear layer. No evidence of hysteresis could be found in the shear layer tone. In the interstage jump (i.e. bimodal) regions, the tone occurred in only one mode at a time while intermittently switching from one to the other. Frequency variations in each stage are shown to collapse on a single curve when non-dimensionalized with the initial momentum thickness θe or with the lip-wedge distance h, and plotted as a function of h/θe. Phase average measurements locked onto the tone fundamental show that the phase velocity and wavelength of the tone-induced velocity fluctuation are essentially independent of the stage of tone generation; in each stage, both phase velocity and wavelength decrease with increasing frequency but undergo jumps at starts of new stages. The measured amplitude and phase profiles, as well as the variations of the shear tone wavenumber and phase velocity with the Strouhal number, show reasonable agreement with the predictions of the spatial stability theory. The wavelength λ bears a unique relation to h, this h, δ relation being different from the Brown-Curle equation for the jet edge tone. Shear layer tones would be typically induced in near-field shear layer measurements involving invasive probes, and can produce misleading results. A method for determining the true free shear layer natural instability frequency is recommended. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: On the basis of a stability analysis of finite amplitude, two-dimensional convection, we have determined the dimensions of boxes containing fluid-saturated porous material in which convection is necessarily unsteady or steady and three-dimensional. For certain box sizes, convective rolls are unstable at Rayleigh numbers Ra lower than 380, the value below which rolls are stable forms of convection between infinite parallel planes. For Ra = 100 and 200, it appears unlikely that there are any box dimensions for which there is not a stable (possibly multicellular) two-dimensional steady motion. At Ra = 340 and 400, boxes in which rolls are unstable have heights which range from one to five times their horizontal dimensions. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Large-scale atmospheric flow shares certain attributes with two-dimensional turbulence. In this paper, we study the effect of spherical geometry on two-dimensional turbulence. Energy transfer is multi-component in spherical geometry in contrast to energy transfer among triads of wave vectors in Cartesian geometry. It follows that energy transfer is more local in spherical than in Cartesian geometry. Enstrophy transfer to higher wavenumbers in spherical geometry is less than enstrophy transfer to higher wavenumbers in Cartesian geometry. Since both energy and enstrophy are inviscid constants of motion, the back transfer of energy is also less in spherical than in Cartesian geometry. Therefore, with a finite viscosity, enstrophy decays more slowly in spherical geometry than in Cartesian geometry. Here these conjectures are tested numerically by spectral methods. The numerical results agree well with the conjectures. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Two-dimensional time-periodic water waves on a gently sloping bottom are investigated under the classical long-wave assumptions that ∊ = h′0/λ′ and δ = H′/h′0 are small parameters (H′ being the wave height, h′0 a characteristic water depth and δ′ the horizontal scale for the oscillatory motion) and the assumption that δ/∊2 = O(1) as δ and ∊ tend to zero. It is shown that for a bottom slope hx for which hx = o(∊3) the governing KdV equation with slowly varying coefficients (derived by Johnson 1973a) has a time-periodic solution which in the first approximation is a slowly varying cnoidal wave. The second-order approximation in an asymptotic expansion with respect to the bottom slope represents the deformation of this wave due to the sloping bottom. For hx ≫ ∊5 this deformation is larger than the second-order contribution from the basic expansion with respect to wave amplitude which underlies the KdV equation itself; the calculation is then a consistent approximation to physical reality. Numerical results for the deformation are given. Also, the wave profiles are compared with experiments on a plane of slope formula omitted and show good agreement even for the large values of H’/h’ appropriate to waves rather close to breaking. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The equations for the earthquake forces on a rigid dam with an inclined upstream face of constant slope are solved exactly by two-dimensional potential-flow theory. The distribution of the hydrodynamic pressure along the upstream face and the total horizontal, vertical and normal loads on the dam are computed from the integral solutions. The results obtained from the exact theory are compared with those derived from the momentum-balance method and there is reasonable agreement. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The structure of the Stewartson E ¼-layer (E being the Ekman number) in a compressible gas contained in a rapidly rotating cylinder is investigated for the case in which the end plates of the cylinder are thermally insulated. It was found by Matsuda & Hashimoto (1976) that the E ¼-layer could not have a relevant structure in the ordinary configuration in which the E ¼-layer meets the end plates through its Ekman extension of thickness E ½. In this paper the E ¼ × E ¼ square region, in addition to the Ekman extension, is considered. The heat generation due to the radial fluid motions in the Ekman extension causes the temperature fields in the E ¼ × E ¼ square region through which heat is conducted to the side wall of the cylinder. Numerical calculations were made to obtain the temperature fields, which are shown in several figures. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: An experimental investigation was conducted at selected locations in the wall region of a three-dimensional turbulent boundary layer relaxing in a nominally zero external pressure gradient behind a transverse hump (in the form of a 30° swept, 5 ft chord, wing-type model) faired into the side wall of a low-speed wind tunnel. The boundary layer (approximately 3·5 in. thick near the first survey station, where the length Reynolds number was 5·5 × 106) had a maximum cross-flow velocity ratio of 0·145 and a maximum cross-flow angle of 21·9° close to the wall. The hot-wire data indicated that the apparent dimensionless velocity profiles in the viscous sublayer are universal and that the wall influence on the hot wire is negligible beyond y+ = 5. The existence of wall similarity in the relaxing flow field was confirmed in the form of a log law based on the resultant mean velocity and resultant friction velocity (obtained from the measured skin friction). The smallest collateral region extended from the point nearest to the wall (y+ ≈ 1) up to y+ = 9·7, corresponding to a resultant mean velocity ratio (local to free-stream) of 0·187. The unusual feature of these profiles was the presence of a narrow region of slightly decreasing cross-flow angle (1° or less) that extended from the point of maximum cross-flow angle down to the outer limit of the collateral region. A sublayer analysis of the flow field using the measured local transverse pressure gradient slightly overestimated the decrease in cross-flow angle. It is concluded that, in the absence of these gradients, the skewing of the flow could have been much more pronounced practically down to the wall (limited only by the resolution of the sensor), implying a near-wall non-collateral flow field consistent with the equations of motion in the neighbourhood of the wall. The streamwise relaxation of the mean flow field based on the decay of the cross-flow angle was much faster in the inner layer than in the outer layer. Over the stream-wise distance covered, the mean flow in the inner layer and the wall shear-stress vector relaxed to a two-dimensional state in approximately 10 boundary-layer thicknesses whereas the relaxation of the turbulence was slower and was not complete over the same distance. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: This paper deals with a two-dimensional turbulent boundary layer disturbed by a circular cylinder. The cylinder was placed inside or outside the boundary layer with its axis parallel to the wall and normal to the flow direction. The mean velocity, wall shear stress, longitudinal turbulent intensity, autocorrelations and turbulent length scale were measured and here the relaxation features of the disturbed boundary layer are discussed. The measurements were made for a ratio of the cylinder diameter d to the undisturbed boundary-layer thickness δ0 equal to 0·30 and for three values of the ratio of the height h of the cylinder axis to δ0 equal to 0·222, 0·556 and 1·24. The results show that the near-wall region of the disturbed boundary layer recovers much more quickly than the outer region and that in the case h/δ0 = 0·222 the recovery is faster than in other cases, as reported by Clauser (1956). Moreover, it is found that the fluctuating velocity field recovers more slowly than the mean velocity field, and that the characteristics of the turbulence in the outer region are still close to those in the wake of an isolated cylinder at the last measurement station, although the mean velocity profile has almost completely returned to its natural shape. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: It is shown that the Orr-Sommerfeld equation, which governs the stability of any mean shear flow in an unbounded domain which approaches a constant velocity in the far field, has a continuous spectrum. This result applies to both the temporal and the spatial stability problem. Formulae for the location of this continuum in the complex wave-speed plane are given. The temporal continuum eigenfunctions are calculated for two sample problems: The Blasius boundary layer and the two-dimensional laminar jet. The nature of the eigenfunctions, which are very different from the Tollmien-Schlichting waves, is discussed. Three mechanisms are proposed by which these continuum modes could cause transition in a shear flow while bypassing the usual linear Tollmien-Schlichting stage. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Experimental visualization of natural convective flow was carried out by using several kinds of fluid contained in a narrow vertical rectangular cavity with one vertical wall heated, the opposing vertical wall cooled and the upper and lower walls insulated. The effects of the Prandtl number Pr of the working fluid and the width of the cavity W on the flow pattern are discussed qualitatively in the present paper. The occurrence of flow patterns consisting of unicellular flow, steady secondary flow, tertiary flow and transition (from laminar to turbulent) flow is categorically demonstrated by the photographs taken. Moreover, experimental measurements of the net heat transfer through the vertical fluid layer are given for aspect ratios of 6-30 and Prandtl numbers of 4-12 500. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: This paper describes part of a detailed study of the initial region of three annular jets. The configurations are the basic one, without any bullet in the centre, and those with a conical and an elliptical bullet. From the mean velocity and turbulence intensity measurements the initial region can be divided into the initial merging, the intermediate and the fully merged zones. Within these three zones similarity of both the mean velocity and the turbulence intensity profiles has been found. The similarity curves are compared with those for a single jet. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The origin of meandering and braiding of alluvial rivers is re-analysed in terms of stability theory. The flow is described by a two-dimensional model, and the transportation of sediment is separated into bed-load transport and transport of suspended sediment, by use of the improved knowledge of sediment transport mechanisms achieved in recent years. The paper explains why it is important to distinguish between the sediment transported as bed load and that in suspension. The analysis is able to predict whether a river remains stable or tends to meander or braid. The results of the stability analysis are compared with laboratory experiments and data from natural rivers, and the agreement is satisfactory. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: In the absence of molecular diffusion there exists a space-independent transformation which transforms the probability density of dynamically passive scalars undergoing chemical reaction and advection into the probability density of scalar fields undergoing advection alone. In two well-known limits the equation for the probability density of non-reacting scalars is linear and parabolic in physical space. In such cases it is shown that the equation for the probability density of reacting scalars is likewise linear and parabolic in physical space, although hyperbolic in concentration space. The general solution of such an equation is obtained and the particular case of a second-order, decaying, single-species reaction is displayed. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: In two recent papers Itoh has developed a finite amplitude stability theory which indicates that nonlinearity increases the damping rate of a small but finite amplitude disturbance to flow in a circular pipe when the disturbance is concentrated near the axis of the pipe. For such a centre mode, which is the only mode considered by Itoh, Davey & Nguyen found, in an earlier paper, the opposite result that nonlinearity decreases the damping rate. We examine the reasons for this discrepancy and we explain the subtle difference between Itoh's method and the method of Reynolds & Potter, which was used by Davey & Nguyen. We suggest that for the centre mode of pipe flow neither Itoh's result nor Davey & Nguyen's result is a reliable guide to the true situation. However, for the wall mode of pipe flow, and especially for plane Couette flow, both methods give very similar results and we suggest that this similarity indicates that in these cases the damping rate is decreased by nonlinearity. For a particular problem we believe that it is only when the results of the two methods are very similar that either method is likely to be useful. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The two-dimensional steady flow of a non-Newtonian fluid (a dilute polymer solution) is examined. The flow domain is composed of a parallel-walled inflow region, a contraction region in which the walls are rectangular hyperbolae, and a parallel-walled outflow region. The problem is formulated in terms of the vorticity, stream function and appropriate rheological equation of state, i.e. an Oldroyd-type constitutive equation (with no shear-thinning) for the total shear and normal-stress components. Computational results from the numerical solution of the equations are presented. In particular, the molecular extension and pressure distribution along the centre-line are presented as well as contour plots of the different flow variables. The alignment of the molecules with the principal axes of strain rate is shown by a qualitative comparison of the streamwise normal-stress contours with contours of the eigenvalues of the strain-rate matrix. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Using a two-layer fluid model, equations are developed which describe long internal waves propagating along a channel of arbitrary cross-section. Expressions for the phase speed of these waves are derived in terms of geometric properties of the cross-section. When weakly nonlinear effects are balanced by weak dispersion, a Korteweg-de Vries equation is derived to describe the waves. The effects of a slowly varying cross-section are included. Applications of the theory are made to recent observations of internal surges in lakes. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The rate at which a particle in suspension can capture diffusing solute molecules can be increased by stirring the fluid. It is shown that the increase is closely related to the total power expended, per unit volume of fluid, by the stirring device. The increase in diffusion current to a particle is related to the local rate of deformation of the fluid Ω (which, in turn, determines the dissipation) by a function F(Ωa2/D), where a is the particle radius and D the diffusion constant for the molecule in question. The function F has been determined experimentally by investigating the corresponding problem in heat transfer. In a fluid of viscosity η, stirring which is vigorous enough to double the mean diffusion current to a particle must entail a power dissipation, per unit volume, not less than 500ηD2/a4. For particles a few microns in size, or smaller, in water, effective stirring is not feasible. The results can be used also to predict the effect of stirring on the coagulation of similar particles. To double, by stirring, the rate at which particles of radius b form dimers requires a stirring power proportional to b−6, and is not feasible in water if b is less than 10−5 cm.

Beschreibung: Flows of incompressible, electrically conducting liquids along ducts with electrically insulating or weakly conducting walls situated in a strong magnetic field are analysed. Except over a short length along the duct where the magnetic field strength and/or the duct cross-sectional area vary, the duct is assumed to be straight and the field to be uniform and aligned at right angles to the duct. Magnitudes of the field strength B0 and the mean velocity V are taken to be such that the Hartmann number M [Gt ] 1, the interaction parameter N (= M2/Re) [Gt ] 1 (Re being the Reynolds number of the flow) and the magnetic Reynolds number Rm [Lt ] 1.For an O(1) change in the product VB0 along the duct across the non-uniform region, it is shown that:(i) In the non-uniform region the streamlines and current flow lines follow surfaces containing the field lines satisfying $int B^{-1}ds = { m constant}$, the integration being carried out along the field line within the duct; these surfaces are equipotentials and isobarics. This leads to(ii) a tube of stagnant, but not current-free fluid at the centre of the duct parallel to the field lines around which the flow divides to bypass it. To accommodate this flow,(iii) the usual uniform field/straight duct flow is disturbed over very large distances upstream and downstream of this region, the maximum length O(duct radius × M½) occurring in a non-conducting duct;(iv) a large pressure drop is introduced into the pressure distribution regardless of the direction of the flow, the effect being most severe in a non-conducting duct, where the drop is O(duct radius × (uniform field/straight duct pressure gradient) × M½);(v) in the part of the duct with the lower value of VB0 a region of reverse flow occurs near the centre of the duct and the stagnant fluid.

Beschreibung: The behaviour of the interface between two immiscible fluids of different density and viscosity in a centrifuge is investigated both analytically and experimentally. The study includes the interfacial shape and behaviour during both steady and transient operation of the centrifuge. The interface shape is investigated for rigid-body rotation and during slow steady acceleration or deceleration of the centrifuge. The dependence of the interface shape on time is investigated during a rapid spin-up to a slightly different value of the angular velocity, which then remains constant. Some aspects of interface stability are also reported. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: A semi-analytical numerical study was performed to simulate the development of a vortex ring in a stratified and/or shearing environment. Practical applications of results of this study can be found in turbulence modelling and in studies of plumes and wakes. The objective is to follow exactly the evolution of a vortex ring so that the three-dimensional vortex-stretching mechanisms due to stratification and the shear effects, respectively, can be understood.The basic formulation consists of the solution of the vorticity equation in a stratified medium. The approach adopted is unique in that discrete vortex elements are used and arbitrary nonlinear interactions are allowed (therefore three-dimensional effects) among various vorticity generators. One of the two fundamental assumptions in this approach is that the vorticity is allowed to be generated only along the density discontinuity. The second assumption is that, while the vorticity carried by the vortex ring is modelled by vortex elements tangential to the vortex loop (which was a vortex ring initially), the vorticity generated by stratification effects is modelled by long vortex lines parallel to the axis of the vortex ring. This limits the validity of the present calculation to high Froude number flow.Numerical stability is guaranteed by the finite core radius for each discrete vortex element and uniform spacing between them; the former is determined by consideration of the momentum integral over the vortex-ring plane. The latter is determined by a cubic spline interpolation method which conserves the circulation and centroids of the vorticity. The velocity of each vortex element is determined by the discretized Biot-Savart law, and motion of the vortex loop is calculated by a predicator-corrector time integration method.Calculations were carried out for both momentum-carrying and momentumless vortex rings. A particular two-dimensional case gives good agreement with Kármán's theory. The evolution of the vortex loop reveals a process in which only the vorticity normal to the stratification is conserved; the remaining vorticity is dissipated through a simulated viscous dissipation. Evolution of a vortex loop on a shear layer reveals a vortex-loop rotation rate equal to the velocity shear, and a twisting motion due to the Magnus force which can lead to the turbulence energy cascade phenomenon. Numerical results demonstrate effects of each individual vorticity source and observed phenomena can be explained.

Beschreibung: Integral-transform theory is used to solve the problem of sinusoidal initial perturbations in a planar stagnation counterflow, with extension to the axisymmetric case. The two incompressible fluids are assumed to be inviscid, so that across the initially plane interface the velocity shear is a velocity slip which grows linearly with the distance from the stagnation point. The solution for the interface displacement shows a competition between an amplification produced by the shear instability and a decay produced by the stretching effect of the accelerating unperturbed flow. At early times the interface perturbation grows exponentially with time, but eventually the stretching process reduces the interface displacement to a magnitude comparable to the initial perturbation. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: Measurements of the statistical property called the ‘rescaled range’ in grid-generated turbulence exhibit a Hurst coefficient H = 0·5 for 43 〈 UT/M 〈 1850, where M/U is a characteristic time scale associated with the grid size M and mean velocity U. Theory predicts that H = 0·5 for independence of two observations separated by a time interval T, and the deviation from H = 0·5 is referred to as the ‘Hurst phenomenon’. The rescaled range obtained for grid turbulence contains an initial region UT/M 〈 43 of large H, approaching 1·0, corresponding approximately to the usual region of a finite non-zero autocorrelation of turbulent velocity fluctuations. For UT/M 〉 1850 the rescaled range breaks from H = 0·5 and rises at a significantly faster rate, H = 0·7-0·8, implying a long-term dependence or possibly non-stationarity at long times. The measured autocorrelations remain indistinguishable from zero for UT/M 〉 20. The break in the trend H = 0·5 is probably caused by motions on scales comparable to characteristic time scales of the wind-tunnel circulation. Rescaled-range analysis is a powerful statistical tool for determining the time scale separating the grid turbulence from the background wind-tunnel motions. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The equations for the viscous flow between two coaxial infinite disks, one stationary and the other rotating, are solved numerically. The effects of applying a uniform suction through the rotating disk are determined. Initially, the fluid and disks are at rest. The angular velocity of one disk and the amount of suction through it are gradually increased to specific values and then held constant. At large Reynolds numbers R, the equilibrium flow approaches an asymptotic state in which thin boundary layers exist near both disks and an interior core rotates with nearly constant angular velocity. We present graphs of the equilibrium flow functions for R = 104 and various values of the suction parameter a (0 ≤ a ≤ 2). When a = 0, the core rotation rate ωc is 0·3131 times that of the disk. Fluid near the rotating disk is thrown centrifugally outwards. As a increases, ωc increases and the centrifugal outflow decreases. When a 〉 1·3494, the core rotation rate exceeds that of the disk and the radial flow near the rotating disk is directed inwards. We also present accurate tabular results for two flows of special interest: (i) the flow between a stationary and a rotating disk with no suction (a = 0) and (ii) Bödewadt flow. The latter can be obtained by suitable scaling of the boundary-layer solution near the stationary disk for any a ≥ 0. Since several solutions to the steady-state equations of motion have been reported, the question arises as to whether other solutions to the time-dependent equations of motion with zero initial conditions can be found. We exhibit a rotational start-up scheme which leads to an equilibrium solution in which the interior fluid rotates in a direction opposite to that of the disk. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The stability of two-dimensional convection rolls has been studied as a function of the Rayleigh number, wavenumber and variation in viscosity. The experiments used controlled initial conditions for the wavenumber, Rayleigh numbers up to 25 000 and variations in viscosity up to a factor of about 20. The parameter range of stable rolls is bounded by a hexagonal-cell regime at small Rayleigh numbers and large variations in viscosity. Otherwise, the rolls are subject to the same transitions as have already been studied in fluids of uniform viscosity. The bimodal instability leading to a stable three-dimensional pattern occurs at smaller values of the average Rayleigh number as the variations in viscosity increase. This appears to be a consequence of the low viscosity of the warm thermal boundary layer associated with the original rolls. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The geometry of large-scale structures in the turbulent mixing layer of a moderate Reynolds number jet is deduced from measurements of the fluctuating pressure in the hydrodynamic near field. The structures are rings of concentrated vorticity that distort with downstream distance until statistical axisymmetry disappears. The rings are spaced quasi-periodically and coalesce with each other, producing larger spacings. Statistical and flow-visualization techniques are applied to free and forced jets over a range of Reynolds numbers from 5000 to 50000 to demonstrate that rings of a given spacing do not coalesce with each other until they are far enough downstream that the local mixing layer has attained some critical thickness which scales with the wavelength of the vortex pair. Wave dispersion is evaluated as a plausible mechanism for localizing the coalescences. The central feature of the model is the observation that a shear layer is dispersive to wavelengths much longer than its thickness and non-dispersive to shorter waves. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: This paper is concerned with small amplitude vortical and entropic unsteady motions imposed on steady potential flows. Its main purpose is to show that, even in this unsteady compressible and vortical flow, the perturbations in pressure p’ and velocity u can be written as p’ = ρ0D0ϕ/Dt and u = ϕ + u(I) respectively, where D0/Dt is the convective derivative relative to the mean potential flow, u(I) is a known function of the imposed upstream disturbance and ϕ is a solution to the linear inhomogeneous wave equation formula omitted with a dipole source term ρ0−1 ▽ρ0u(I) whose strength ρ0u(I) is a known function of the imposed upstream distortion field. (Here c0 and ρ0 denote the speed of sound and density of the background potential flow.) This equation is used to extend Hunt's (1973) generalization of the ‘rapid-distortion’ theory of turbulence developed by Batchelor & Proudman (1954) and Ribner & Tucker (1953). These theories predict changes occurring in weakly turbulent flows that are distorted (by solid obstacles and other external influences) in a time short relative to the Lagrangian integral scale. The theory is applied to the unsteady supersonic flow around a corner and a closed-form analytical solution is obtained. Detailed calculations are carried out to show how the expansion at the corner affects a turbulent incident stream. © 1978, Cambridge University Press. All rights reserved.

Beschreibung: An exact and very general Lagrangian-mean description of the back effect of oscillatory disturbances upon the mean state is given. The basic formalism applies to any problem whose governing equations are given in the usual Eulerian form, and irrespective of whether spatial, temporal, ensemble, or ‘two-timing’ averages are appropriate. The generalized Lagrangian-mean velocity cannot be defined exactly as the ‘mean following a single fluid particle’, but in cases where spatial averages are taken can easily be visualized, for instance, as the motion of the centre of mass of a tube of fluid particles which lay along the direction of averaging in a hypothetical initial state of no disturbance. The equations for the Lagrangian-mean flow are more useful than their Eulerian-mean counterparts in significant respects, for instance in explicitly representing the effect upon mean-flow evolution of wave dissipation or forcing. Applications to irrotational acoustic or water waves, and to astrogeophysical problems of waves on axisymmetric mean flows are discussed. In the latter context the equations embody generalizations of the Eliassen-Palm and Charney-Drazin theorems showing the effects on the mean flow of departures from steady, conservative waves, for arbitrary, finite-amplitude disturbances to a stratified, rotating fluid, with allowance for self-gravitation as well as for an external gravitational field. The equations show generally how the pseudomomentum (or wave ‘momentum’) enters problems of mean-flow evolution. They also indicate the extent to which the net effect of the waves on the mean flow can be described by a ‘radiation stress’, and provide a general framework for explaining the asymmetry of radiation-stress tensors along the lines proposed by Jones (1973). © 1978, Cambridge University Press. All rights reserved.

Beschreibung: The theory presented here describes the motion of a large gas bubble rising through upward-flowing liquid in a tube. The basis of the theory is that the liquid motion round the bubble is inviscid, with an initial distribution of vorticity which depends on the velocity profile in the liquid above the bubble. Approximate solutions are given for both laminar and turbulent velocity profiles and have the form formula omitted Us being the bubble velocity, Uc the liquid velocity at the tube axis, g the acceleration due to gravity, and D the tube diameter; ϕ indicates a functional relationship the form of which depends upon the shape of the velocity profile. With a turbulent velocity profile, a good approximation to (1) which is suitable for many practical purposes is formula omitted Us0 being the bubble velocity in stagnant liquid. Published data for turbulent flow are known to agree with (2), so that in this case the theory supports a well-known empirical result. Our laminar flow experiments confirm the validity of (1) for low liquid velocities. © 1978, Cambridge University Press. All rights reserved.