Perforated screens are often deployed to attenuate aerodynamic sound in heat-exchanger cavities and other ducts conveying mean flow. The dissipation is caused by vorticity production in the perforations. This mechanism is investigated theoretically for the case of a thin rigid plate lying along the centreline of a duct and having a single transverse slot, a configuration that is to be studied experimentally at the Institute of Sound and Vibration Research of Southampton University. Time-harmonic acoustic waves are incident on the slot in the presence of equal parallel mean flows on either side of the plate. A linearized theory of unsteady shearing flow over a slot, which incorporates the influence of vorticity ejection into the flow, is used to examine mean-flow/acoustic energy exchanges. According to this theory acoustic energy is absorbed provided that the Strouhal number based on slot width and mean-flow velocity is sufficiently small. At higher frequencies there exists an infinite set of discrete frequency intervals within which there is a net production of acoustic energy at the slot at the expense of the kinetic energy of the mean flow.

A systematic study of two-dimensional, turbulent, small-deficit wakes was carried out to determine their structure and the universality of their self-preserving states. Various wake generators, including circular cylinders, a symmetrical airfoil, a flat plate, and an assortment of screens of varying solidity, were studied for a wide range of downstream distances. Most of the generators were tailored so that their drag coefficients, and therefore their momentum thicknesses, were identical, permitting comparison at identical Reynolds numbers and aspect ratios. The flat plate and airfoil had a small, trailing-edge flap which could be externally driven to introduce forced sinuous oscillations into the wake. The results indicate that the normalized characteristic velocity and length scales depend on the initial conditions, while the shape of the normalized mean velocity profile is independent of these conditions or the nature of the generator. The normalized distributions of the longitudinal turbulence intensity, however, are dependent on the initial conditions.

Linear inviscid stability theory, in which the divergence of the mean flow is taken into account, predicts quite well the amplification and the transverse distributions of amplitudes and phases of externally imposed sinuous waves on a fully developed turbulent wake generated by a flat plate. There is a strong indication that the large structures observed in the unforced wake are related to the two-dimensional instability modes and therefore can be modelled by linear stability theory. Furthermore, the interaction of the two possible modes of instability may be responsible for the vortex street-type pattern observed visually in the small-deficit, turbulent wake.

It is shown that a consideration of the magnetic field in a highly conducting turbulent medium, using Lagrange variables, involves deriving kinetic equations of fluid-particle transition probability densities. A derivation of such equations is performed for joint probability densities of n particles up to n = 4. By assuming normality of one particle distribution function it was found that these kinetic equations are the generalized Kolmogorov–Fokker–Planck (KFP) equations. The dynamics of mean and fluctuating magnetic fields is described by means of these equations. The eddy diffusivity of a mean field for processes described by generalized KFP equations coincides with that of a scalar field (depending in general on helicity in implicit form). It is shown that at sufficiently large magnetic Reynolds number, a turbulence with any spectrum generates fluctuating magnetic fields.

Composite vertical shear spectra of Gargett et al. (1981) and composite vertical temperature-gradient spectra of Gregg (1977) are compared with the fossil-turbulence model of Gibson (1980–6). Both the shear and temperature-gradient spectra show high-wavenumber microstructure bumps which are identified by Gargett et al. (1981) and Gregg (1980) as due to turbulence in the fluid at the time of measurement. However, using γ [ges ] 5N as the criterion for turbulence to exist in a stratified fluid, where γ is the rate of strain and N is the Brunt-Väisälä frequency, the largest-scale fluctuations of the microstructure bumps may actually be remnants of previous turbulence persisting in fluid that is no longer turbulent at these scales: such fluctuations are termed fossil vorticity turbulence (a class of internal waves) and fossil temperature turbulence respectively. Both composite spectra exhibit k−1 subranges which are identified by their low amplitudes as subsaturated (two-three)-dimensional internal waves and resulting temperature fine structure by comparison with saturated three-dimensional internal-wave subranges proposed by Gibson (1980):7N2k−1 for the saturated vertical shear spectrum and $0.7 (\partial \overline{T}/\partial z)^2 k^{-1}$ for the saturated temperature gradient spectrum. Both composite spectra exhibit a transition between k−1 and k0 subranges at wavelengths of 6–14 metres: possibly a fossil remnant of previous overturning turbulence which produced 3–7 m thick partially mixed layers. Dissipation rates ε and χ and Cox numbers $C \equiv (\overline{{\boldmath \nabla}T})^2/(\overline{{\boldmath \nabla}T})^2$ of the turbulence required by this assumption are much larger than the measured values, suggesting that the turbulence process has been undersampled. Fossil overturning scales up to about 10 m are indicated by the Gregg (1977) data. Average (150 m) C values $\overline{C}$ are distributed as a very intermittent lognormal, with variance $\sigma^2_{\ln \overline{C}} = 5.4$, also indicating extreme undersampling of the turbulence and mixing.

The orientation state of a dilute suspension of rigid, axisymmetric particles subjected to the sudden inception of simple shearing flow in the presence of small Brownian couples is investigated experimentally. In contrast to mechanical rheometric methods, the experimental technique, a recently developed optical method based on conservative linear dichroism (Frattini & Fuller 1984), provides a direct probe of the constituent particle dynamics. The average particle orientation direction projected into the shear plane and the average degree of alignment about that direction are measured as functions of time for Péclet numbers, $\dot{\gamma}/D_{\rm r}$, ranging from 20 to 200. Data are presented for dilute glycerol/water suspensions of two types of particles: disk-like bentonite clay and rod-like synthetic akaganeite (βFeOOH). The data provide, for the first time, an experimental basis with which the closure approximation required for solution of the evolution equation for 〈u,u〉, the second moment of the particle orientation distribution, may be critically evaluated in shearing flows. Two closures are examined: the ad hoc but often-used pre-averaging closure, and the first-order closure suggested by Hinch & Leal (1976). The latter results in a more accurate fit of the data. Finally, new experimental observations of the effect of particle size polydispersity are reported for the orientation relaxation following sudden cessation of steady simple shear at moderately high Péclet number.

Matched asymptotic expansion methods are used to solve the title problem. First-order Taylor number corrections to both the Stokes-law drag and Kirchhoff's-law couple on the sphere are obtained for Rossby numbers of order unity. This calculation fills a gap between the Proudman-Pearson (1957) rectilinear trajectory analysis, which includes Reynolds-number effects but does not address Taylor-number effects arising from the curvilinear trajectory, and the Herron, Davis & Bretherton (1975) curvilinear-trajectory analysis, which incorporates Taylor-number effects but ignores those arising from the Reynolds number. At the same Reynolds number, the drag on the sphere is found to be greater or less than the classical Oseen (1927)-Proudman & Pearson (1957) value, depending upon the magnitude of a certain dimensionless length parameter B measuring the tether radius to the sphere radius. This drag difference is attributed, in part, to the fact that the sphere runs into the disturbance created by its own wake.

An investigation is made into the dynamics involved in the movement of the contact line when one liquid displaces an immiscible second liquid where both are in contact with a smooth solid surface. In order to remove the stress singularity at the contact line, it has been postulated that slip between the liquid and the solid or some other mechanism must occur very close to the contact line. The general procedure for solution is described for a general model for such slip and also for a general geometry of the system. Using matched asymptotic expansions, it is shown that for small capillary number and for small values of the length over which slip occurs, there are either 2 or 3 regions of expansion necessary depending on the limiting process being considered. For the very important situation where 3 regions occur, solutions are obtained from which it is observed that in general there is a maximum value of the capillary number for which the solutions exist. The results obtained are compared with existing theories and experiments.

A theoretical study is made of the effect of the presence of a surfactant on the dynamics involved in the movement of the contact line when one liquid displaces an immiscible second liquid where both are in contact with a smooth solid surface. The general procedure of solution is described for a general model for slip between solid and liquid near the contact line and also for a general macroscopic geometry. For small capillary number and for small values of the length over which slip occurs, it is shown, using singular perturbation analysis, that either 2 or 3 regions of expansion are necessary depending on the type of limiting process being considered. Solutions are obtained for both situations but for the more important three-region expansion case (where there can be large dynamic effects), a detailed discussion is given of the manner in which the observable macroscopic contact angle is shown to depend on the contact line velocity and on surfactant concentration. The conditions of validity for the theory are also discussed.

A multiple-scale analysis of the Kuramoto-Sivashinsky one-dimensional model of a flame front with 2π-periodic boundary conditions is presented. For arbitrary large values of the number M of linearly unstable modes there exist stable steady solutions of period 2π/N where N = O(M). These ‘cellular solutions’ exhibit elastic behaviour under perturbations of wavelength much larger than 2π/N. The results are illustrated by numerical experiments. Elasticity has its origin in the translation and Galilean invariances. Similar invariance properties are likely to be at the root of the viscoelastic behaviour of turbulent flows conjectured by many authors.

The problem of small-aspect-ratio thermohaline convection is discussed in conditions appropriate to the salt-finger regime. Two-scale methods are employed to produce nonlinear coupled evolution equations for an arbitrary number of interacting roll solutions. These are solved in simple cases and it is shown that roll-type planforms are preferred over square cells throughout the range of validity of the analysis. The methods can be generalized to other double-diffusive convection problems.

A boundary-layer scale analysis is presented for steady, zonally symmetric flow in a Cartesian channel of rectangular cross-section, subject to uniform internal heating, and cooling at the lateral boundaries, using an approach based on that of Hignett, Ibbetson & Killworth for a related system. Six main flow regimes are identified, depending chiefly upon the magnitude of the parameter ℙ defined as the square of the ratio of the (non-rotating) thermal-boundary-layer thickness scale to that of the Ekman layers adjacent to the horizontal boundaries. For ${\mathbb P} \ll {\mathbb A}^{\frac{1}{6}}\epsilon^{\frac{1}{2}}(\gg 1$, where [Aopf ] is the Rayleigh number and ε the channel aspect ratio), the flow consists of an advectively dominated interior, characterized by a balance between vertical advection and internal heat generation, diffusively dominated thermal boundary layers adjacent to the sidewalls, and horizontal, viscously dominated Ekman layers (for non-zero rotation rate). If ℙ [Lt ] 1, the flow is only weakly modified by rotation, but as ℙ increases through unity, rotation tends to inhibit heat transfer and thickens the thermal boundary layers. Provided ℙ [Gt ] ε2σ −2, (where σ is the Prandtl number), the zonal flow is predominantly geostrophic, though not given by the conventional thermal-wind scale (based on the total thermal contrast ΔT) unless ℙ [Gt ] 1.

The results of the scale analysis are compared with laboratory measurements and numerical simulations of steady flow in a rotating, cylindrical annulus subject to (radially non-uniform) internal heating and sidewall cooling. Over the range of parameters accessible in the laboratory, the azimuthal velocity scale and thermal contrast were found to vary with rotation and heating rates in the way predicted from the scale analysis for the Cartesian system. Above a certain critical value of ℙ (for the geometry used here ℙt ≈ 1), the baroclinic wave regime was found to occur, corresponding to where rotational constraints first begin to influence significantly the heat transfer of the axisymmetric flow. The numerical simulations are compared with the laboratory measurements, and used to extend the ranges of rotation rate and aspect ratio over which the scale analysis could be verified. Good agreement was found for the dependence of globally averaged flow parameters on ℙ, and the dynamical characteristics of each regime were further verified using explicit calculations of the balance of terms in the basic equations from the numerical model.

Further applications of the scaling technique to other, related systems are also discussed, together with a consideration of its generalization to systems of geophysical interest.

Fundamental properties of standing edge waves are investigated experimentally in a physical model with a uniformly and mildly sloping beach with a straight shoreline. Using a unique experimental set-up, quantitative measurements for the detailed nonlinear effects of edge waves are obtained. The experimental results are generally in good agreement with the theoretical predictions (Guza & Bowen 1976a and Rockliff 1978) including the offshore profile, dispersion relation, and the outgoing radiated waves generated by the nonlinear interaction of edge waves. The observed behaviour of the excitation process of ‘forced’ edge waves by the wavemaker can be predicted qualitatively by the inviscid theory, whereas the damping process of ‘free’ edge waves is governed by the viscous effects, i.e. the theoretical (inviscid) prediction totally underestimates the actual damping phenomenon in the laboratory.

The paper reports on measurements of the flow generated by a plane buoyant jet discharging vertically into shallow water. The study comprises visualization experiments, mean-velocity and turbulence measurements with a two-channel laser-Doppler anemometer and temperature measurements with thermistor probes. According to the previous investigation of Jirka & Harleman (1979) (JH) the flow may be either stable with the heated discharge water leaving the near field in a warm water layer adjacent to the surface, or unstable with flow recirculation and re-entrainment of heated water into the jet. The stable situation usually involves an internal hydraulic jump associated with a roller. Both stable and unstable situations were investigated, the limiting case of a non-buoyant jet representing the unstable one. In order that a roller representing an internal hydraulic jump developed in the relatively short test channel in the buoyant situations, a strong downstream control had to be imposed by inserting a slightly submerged weir. Most experiments were carried out at a depth-to-discharge-width ratio of 100, and in this case the strong upstream control caused the hydraulic jump to be flooded for both of the densimetric Froude numbers studied (F = 9.9 and 21). In each case, a thick upper layer of nearly uniform temperature developed, with a larger layer thickness for F = 21. Below this layer was a relatively thin interface with temperature gradients and below this a counterflow of cold ambient water. For both Froude numbers, the flow was stable in the sense of JH, but only marginally so in the higher-Froude-number case. The observed trends of the flow behaviour follow the stability analysis of JH, but the dilution of the heated water, which was determined from the temperature measurements, is different from that predicted by the JH mixing analysis. The dilution is much lower in the present case with the flooded jump than in the JH analysis and experiments without specific downstream control and with a much longer test channel and thus no flooded jump.

The nonlinear instability of Hill's spherical vortex, subject to axisymmetric perturbations is considered. The problem is formulated as a nonlinear integrodifferential equation for the motion of the vortex boundary. This equation is solved employing a numerical procedure which involves a piecewise representation of the vortex contour with discrete elements. This formulation offers an efficient method for studying a variety of vortex flows in axisymmetric geometry.

Our results indicate that if Hill's vortex becomes a prolate spheroid, a certain amount of rotational fluid is detrained from the rear stagnation point of the vortex, leaving behind a reduced vortex of approximately spherical shape. The amount of detrained fluid is a function of the initial deformation. If the vortex becomes an oblate spheroid, irrotational fluid is entrained into the vortex from the rear stagnation point, reaches the front vortex boundary, and circulates along the vortex boundary in a spiral pattern. In this fashion, the vortex reduces to a nearly steady vortex ring whose asymptotic structure is a function of the initial deformation. The structure of the asymptotic rings arising from oblate vortices is similar to that of steady rings described by Norbury (1973). The vortex speed is shown to tend to a constant value for prolate perturbations, and to fluctuate around a mean value for oblate perturbations.

The suitability of an Euler-level two-fluid theory to describe the behaviour of gas mixtures with disparate masses is explored for the problem of sound propagation at frequencies high enough that dispersion effects are important. The determination of the speed of propagation is reduced to solving a quadratic equation in the complex plane. The model leads to small errors of the order of the molecular mass ratio M when the molar fraction xp of the heavy gas is small (xp = O(M)), becoming increasingly inaccurate at larger values of xp. Yet agreement with He-Xe experiments is excellent for the whole range of frequencies tested, up to values of xp = 0.4. For values of xp above 0.5 our quantitative results become poorer but they still agree qualitatively with experiments, predicting small and negative dispersion coefficients and the presence of a bifurcation at critical values of the frequency and the composition. It is concluded that this generalized Euler theory provides an excellent framework within which to develop a two-fluid boundary-layer description of the peculiar dynamics of disparate-mass mixtures in the region of parameters of greatest industrial interest.

The development of two-dimensional vortex patterns in accelerating flow starting from rest has been investigated by streakline visualization and documented in photographic sequences. We considered flow over spoilers, double steps and cavities. A limited parametric analysis is provided for some of the photographic results.

We present numerical solutions of the fully three-dimensional flow of a round, turbulent jet emitted normal to a uniform free stream. Comparisons with available laboratory data and comparison between different numerical grid resolutions are used to demonstrate the quality of the simulation. Examination of the detailed flow pattern within a computational domain, which extends 15 jet diameters from the source allows us to follow the vorticity dynamics in the transition from an initially vertical jet to a wake with a vortex pair essentially aligned with the free stream. The transition is presented as a function of the ratio of the jet exit velocity to free stream velocity. For large velocity ratios, the source of the streamwise vorticity in the vortex pair can be readily traced back to the original streamwise vorticity in the sides of the vertical jet.

The static equilibrium of a journal rotating within a circular bush in the presence of a complete oil film is considered. Fluid inertia, though having negligible effect on load capacity and attitude angle, is shown to provide an important stabilizing mechanism. For any bearing (with specified geometry and lubricant) there is both a characteristic neutral stability curve and a characteristic operating curve which may intersect in two positions. Analysis of the weakly nonlinear motion, in the vicinity of the neutral curve, reveals the existence of stable, small-amplitude limit cycles which may be either subcritical or supercritical according to where the operating and neutral curves intersect.

By means of a high-frequency analysis it is shown that a Rayleigh instability is possible within the interactive boundary-layer formulation. This instability reflects the tendency of large-Reynolds-number flows to be unstable. For most, but not all, pressure-displacement relations both Rayleigh's and Fjørtoft's theorems hold, although Fjørtoft's criterion is not a sufficient condition for instability. However, for two pressure-displacement relations neither theorem could be proved, and for one of these, unstable flows exist which are free of inflexion points. Analytically, the existence of this instability may result in a finite-time singularity, while numerically the presence of Rayleigh modes often leads to accuracy problems which cannot be overcome by simple grid refinement. A test integration resulted in the generation of small grid-dependent eddies. It is suggested that the instability may be a possible cause of the eddy splitting observed in experiments on unsteady flows through distorted channels. This Rayleigh instability is also possible within the ‘inverse’ boundary-layer formulation, but is absent from classical boundary-layer problems.

The radial dynamics of a spherical bubble in a compressible liquid is studied by means of a simplified singular-perturbation method to first order in the bubble-wall Mach number. It is shown that, at this order, a one-parameter family of approximate equations for the bubble radius exists, which includes those previously derived by Herring and Keller as special cases. The relative merits of these and other equations of the family are judged by comparison with numerical results obtained from the complete partial-differential-equation formulation by the method of characteristics. It is concluded that an equation close to the Keller form, but written in terms of the enthalpy of the liquid at the bubble wall, rather than the pressure, is most accurate, at least for the cases considered of collapse in a constant-pressure field and collapse driven by a Gaussian pressure pulse. A physical discussion of the magnitude and nature of compressibility effects is also given.