A numerical technique is presented which allows one to estimate hydrodynamic forces and torques or translational and angular velocities of particles in a general flow field. Particle–solid wall interactions can be readily included. The base functions used in the technique presented are singular fundamental solutions of the Stokes equation for a point force and a point force and a point source. The least-square approach is used preferentially in order to find the intensities of these singularities. Test calculations show that the results are self-consistent and in fairly good agreement with the exact solutions in a wide range of conditions. For example, for a spherical particle moving with no slip towards the solid wall, it has been shown that the method can provide good estimates of the resistance coefficient up to separations of the order of 5% of the particle radius. We believe that better agreement, for smaller separations, is within reach at the expense of increased computer costs. For spheroidal particles good results were obtained for aspect ratio in the range 0.5–2.0.

This paper presents a model for film-condensation heat transfer on a general cylindrical surface in the presence of a non-uniform electrostatic field. The steady-state liquid-film flow is assumed to be fully developed and smooth. The liquid is electrically non-conducting. The vapour in contact with the film is pure and saturated. We also describe two experiments in which R113 is condensed in a tube. In one case condensation occurs in an asymmetric electric field as described by the model. In the other case, done for comparison, it occurs in an axisymmetric one. We report average heat-transfer measurements and visual observations in both cases. Comparison of the theory with the first experiment is good, despite the model not accounting for the film's waviness.

Known similarity solutions of the shallow-water equations representing the motion of constant-volume gravity currents are studied in both plane and axisymmetric geometries. It is found that these solutions are linearly stable to small correspondingly symmetric perturbations and that they constitute the large-time limits of the solutions of the initial-value problem. Furthermore, the analysis reveals that the similarity solution is approached in an oscillatory manner. Two initial-value problems are solved numerically using finite differences and in each case the approach to the similarity solution is compared with the analytic predictions.

The modelling of the subgrid-scale stresses in the large-eddy simulation of turbulence is examined from a theoretical standpoint. While there are a variety of approaches that have been proposed, it is demonstrated that one of the more recent models gives rise to equations of motion for the large eddies of turbulence which are not Galilean-invariant. Consequently, this model cannot be of any general applicability, since it is inconsistent with the basic physics of the problem, which requires that the description of the turbulence be the same in all inertial frames of reference. Alternative models that have been proposed which are properly invariant are discussed and compared.

A numerical and analytical study is described for the divided flow field produced when the flows in two equal parallel channels, separated upstream by an aligned splitter plate, join together to form a single channel beyond the enclosed trailing edge of the plate. On the numerical side the second-order-accurate finite-difference scheme is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers R. Account is taken also of the influence of the boundedness of the computational domain and of the irregular behaviour of the flow solution at the trailing edge. The numerical solutions are presented for values of R up to 1000. On the analytical side the asymptotic structure of the solution for large R is governed mainly by a long $O(R^{\frac{1}{7}})$ relative lengthscale upstream and beyond the trailing edge. This is followed by a longer O(R) scale far downstream, but effects of practical significance also arise on the nominally tiny scale of O(R−½). Comparisons between the numerical and the asymptotic results for the wall shear stresses and the wake centreline velocity are made, and overall the agreement seems reasonable. The use of comparisons is believed to strengthen the value of both the numerical and the analytical approaches for these flows.

The linear and weakly nonlinear stability of Poiseuille–Couette flow is considered for various values of the relative wall velocity 2uw, An account is given first of the asymptotic upper and lower branches of the linear neutral curve (s), followed by their disappearance, as uw is increased. Two main (and one minor) neutral curves are found to exist for smaller O(1) (or lesser) values of uw, then one for moderate O(1) values of uw, and none for larger O(1) values of uw. The cut-off velocity at which each main neutral curve disappears is determined, and in each case the whole neutral curve for uw just below the cut-off value is determined in closed form. Secondly, weakly nonlinear solutions are found to bifurcate subcritically from the neutral curve for uw just below cut-off, but to ‘bifurcate from infinity’ just above cut-off. This identifies a minimum threshold amplitude at the entry to the regime where no linear neutral curve exists.

The main effects on the dynamics of a liquid bridge due to the presence of an outer liquid, as occur in experiments using the Plateau-tank technique, are considered. The one-dimensional nonlinear model developed here allows us to perform the computation of both breaking processes and oscillatory motions of slender liquid bridges, although in this paper only the results concerning breaking processes are reported. Additionally, the oscillatory motions are studied both experimentally and by using a new linear model. Results from both sources show good agreement.

We present here a new type of generalization of the conservation law of circulation, in two dimensions, and of the helicity-conservation law in three dimensions assuming zero potential vorticity. The conserved quantities keep their usual expressions ∫∫k· rot vd2 r, ∫∫∫v· rot vd3 r, respectively, as in the barotropic case.

These generalizations are based upon the general formulation of conservation laws in terms of potentials (here the Clebsch potentials). The conserved currents that we derive are expressible in terms of the ordinary physical variables (r, t, v, P, ρ) only, as they should.

The response of regular arrays of two-dimensional Helmholtz resonators mounted in a rigid baffle and subject to external excitation by a plane acoustic wave is studied. The inviscid. The inviscid linearized problem is solved by the matched-asymptotic-expansion technique in the low-frequency limit, i.e. when the characteristic neck dimension is small compared with the acoustic wavelength. Different spacings between resonators, from comparable with down to much smaller than the wavelength, as well as variable neck length and different cavity shapes, are studied without assumptions about the velocity distribution in the neck. The results yield predictions of resonance for the different geometries and compare favourably with measurements. Besides showing analytically the dependence, of, say, the acoustic impedance on all geometric parameters and forcing frequency, the analysis also reveals that for deep narrow cavities the basic Helmholtz model with uniform cavity pressure is inappropriate at resonance.

This paper describes an experimental investigation of the shielding effects of various disks placed coaxially upstream of an axisymmetric, flat-faced cylinder. Remarkable decrease of the drag of such a system was observed for certain combinations of the basic geometric parameters, namely the diameter and gap ratios. For such optimum shielding the stream surface which separates from the disk reattaches smoothly onto the front edge of the cylinder, in what is close to a ‘free-streamline’ flow; alternatively, the flow may be viewed as a cavity flow. For the optimum as well as other geometries, flow pictures, pressure distributions and some LDV measurements were also obtained. From these, several flow regimes depending on the gap/diameter parameters were identified. Variations on the axisymmetric disk–cylinder configuration included a hemispherical frontbody, rounding of the front edge of the cylinder and a change from circular to square cross-section.

The flow past a cylinder in a rapidly rotating frame is described when the Rossby number Ro is O(E½), where E is the Ekman number. Previous studies of the configuration have noticed the development of a singularity within the E¼ layer at the rear stagnation point once the ratio Ro/E½ is larger than a critical value, and concluded that the boundary-layer flow is unsteady. In this paper a description of a steady boundary-layer flow for this parameter range is presented, showing the development of flow separation as Ro/E½ approaches a larger critical value. Details of the flow once the E½ layer has separated from the cylinder are also described.

This paper attempts to explain MHD instabilities observed in aluminium reduction cells. The model analysed is a plane horizontal poorly conducting fluid layer, sandwiched between two highly conducting semi-infinite layers, the lower one a fluid and the upper solid. A uniform normal current passes through all three layers, and the stability of small perturbations to the fluid–fluid interface is analysed. Plane waves are described which can be of either constant or exponentially growing amplitude, depending on the form of the magnetic field due to distant current sources. A model of an electric are furnace in which the upper layer too is fluid is considered, and in this case MHD effects can also be destabilizing.

Local skin-friction reductions have been measured using an array of flush-mounted hot-film probes in a microbubble-modified, zero-pressure-gradient, turbulent bounddary layer. The results of earlier integrated skin-friction measurements, that showed the reduction to be a function of plate orientation, gas-flow rate and free-stream velocity, have been confirmed both qualitatively and quantitatively. With the measurement plate oriented so that buoyancy keeps the bubbles in boundary layer, it is shown that skin friction is reduced monotonically for all air-flow rates at each of three free-stream velocities between 4 and 17 m/s. For the opposite plate orientation it is possible for increasing gas injection to lead to smaller local skin-friction reduction at the lowest speeds. Drag reduction appears to persist for as much as 60–70 boundary-layer thicknesses downstream of the injection region. It is further shown, using a probe flush-mounted just upstream of the injection section, that there is no apparent upstream interference due to the gas injection. Spectral measurements indicate that microbubbles can cause a reduction of high-frequency shear-stress fluctuations. This suggests a destruction of some of the turbulence in the near-wall region.

The presence and behaviour of vaporous cavities are of major importance in many modern industrial applications where heat transfer, boiling or cavitation are involved. Following a sudden depressurization of a superheated fluid, the bubble growth rate controls the generated transients and heat transfer. Most existing computer modelling and prediction codes are based on individual spherical-bubble-growth studies and neglect possible interactions and collective phenomena. This paper addresses this collective behaviour using a singular-perturbation approach. The method of matched asymptotic expansions is used to describe the bubble growth, taking into account its interaction with a finite number of surrounding bubbles. A computer program is developed and the influence of the various parameters is studied numerically for the particular case of a symmetrical equal-size-bubble configuration and a thermal-boundary-layer approximation. A significant influence of these interactions on bubble growth and heat transfer is observed: compared to an isolated-bubble case, the growth rate of a bubble is reduced in the presence of other bubbles, and the temperature drop at its wall is smaller. As a result the heat loss due to bubble growth is smaller. These effects increase with the number of interacting bubbles.

In the previous work (Tanaka 1983), the linear stability problem of surface gravity waves on deep water to ‘superharmonic’ disturbances was investigated. The result obtained there suggested that the waves lose stability at the steepness which corresponds to the maximum total energy and the impulse. This result, however, apparently contradicts other work and thus the validity of it has been regarded as questionable. In the present paper, the validity of our previous result is first confirmed by two independent methods. Then, it is also shown that the contradictions with other works will disappear in a natural way when the explicit form of the unstable disturbance around the critical steepness is appropriately taken into account.

The hydrodynamics of enhanced longitudinal heat transfer through a sinusoidally oscillating viscous fluid in an array of parallel-plate channels with conducting sidewalls is examined analytically. Results show that for fixed frequency the corresponding effective thermal diffusivity reaches a maximum when the product of the Prandtl number and the square of the Womersley number is approximately equal to α2 Pr = π Under such tuned conditions the axial heat transfer achievable is considerable and can exceed that possible with heat pipes by several orders of magnitude. The heat flux between different temperature reservoirs connecting the parallel-plate-channel configuration is shown, under tuned conditions, to be proportional to the first power of both the axial temperature gradient and the flow oscillation frequency and to the square of the tidal displacements. A large value for the fluid density and specific heat is also found to be beneficial when large heat-transfer rates are desired. The process discussed involves no net convection and hence achieves large heat-transfer rates (in excess of 106 W/cm2) without a corresponding net convective mass transfer. A discussion of the physical origin for this new heat-transfer process is given and suggestions for applications are presented.

We investigate the development of density stratification in a confined fluid due to a buoyancy source which gives rise to a vertical convective boundary layer. We find that the stratification is significantly different when the boundary layer is laminar rather than turbulent. In particular, the magnitude of the density gradient in the fluid interior increases rather than decreases in the direction of flow of the boundary layer, and this density gradient varies smoothly so that there is no density front between the stratified fluid and the unmodified homogeneous fluid. Laboratory experiments are described in which homogeneous fluid in a rectangular container was heated at a vertical sidewall. Vertical temperature profiles and streak photographs were taken which show the dominant features of the stratification mechanism under laminar flow conditions. We review similarity theory for a vertical, laminar, free-convection boundary layer in a homogeneous environment, and develop new similarity solutions for convective boundary layers in stratified environments. We use these analytic results to interpret qualitative features of the experimentally observed flow fields and to develop an expression for the depth of the stratified layer as a function of time.

It seems that no treatment of pulsating flow in deformable tubes is complete without a reference to the work of Womersley (1955) which for an infinitely long tube deals with the waves of axismmetric transverse motion and of longitudinal motion of the walls. This theory has so far been subjected to experimental test only for tethered tubes in which longitudinal wall motion is absent.

A series of measurements of the longitudinal motion has been made on horizontal water-filled latex tubes suspended by an array of strings so that there is minimal longitudinal constraint except at the ends, which are fixed. One end of the tube is driven by oscillating flow produced by a piston; the other end is closed. Theory and experiment agree when the tube is long provided an entrance length greater than a wavelength is included. Tubes which are short enough for reflection from the closed end to be significant present a more complicated problem. It is found that in the entrance length the theory of Womersley cannot be applied. A more refined theory is required which takes into account a distributed end constraint more completely than as a simple boundary condition.

Experiments on tethered tubes in which longitudinal wall motion is absent are also presented. These serve to demonstrate that the theory for such tubes agrees with measurements without any appreciable end effect and also shows that the small viscoelasticity of the latex rubber is correctly included.

The diffraction problem for a slender ship held fixed in short regular incident waves is solved by a matched-asymptotic-expansion method which is uniform with respect to all incident wave directions including head seas. Special inner solutions are employed which satisfy the Helmholtz equation in cross-sectional planes of the ship and are non-singular in head seas. The inner expansion of the outer solution is derived directly for all wave directions rather than as a composite. The case of a ship with a long parallel middle body is studied by means of a mixed numerical and analytical solution which explicitly exhibits the transition between the distinctive behaviours of head and oblique seas and distinguishes effects generated at the bow from those of the parallel middle body. Calculations of the pressure distributions and wave elevations along a ship are reported and compared with experimental measurements. The agreement between theory and experiment is generally good, especially at the upwave end of the ship and along the upwave side.

The inviscid near-neutral stability of a trailing-vortex flow is investigated by using a normal-mode analysis in which all perturbation quantities exhibit a factor exp[i(nβz−nθ−ω)]. The problem is treated as a timewise-stability problem. The dependence of the eigenvalues ω on the axial wavenumber β, which has been normalized with respect to the azimuthal wavenumber n, is found both numerically and analytically for large values of n in the upper range of values of β near 1/q, where near-neutral modes are anticipated to occur. Here q, the swirl parameter of the flow, effectively compares the 'strengths’ of the swirl and axial components of motion in the undisturbed flow. Previous normal-mode analyses based on the same form of perturbation quantities have shown that for columnar vortices the unstable modes for large values of n are ring modes, and this feature is shown to persist near the upper neutral points. In fact this work on near-neutral ring modes supplements the earlier asymptotic theory for large n, which is known to fail near β= 1/q. Our numerical and asymptotic results are in excellent agreement and are also shown to be consistent with the earlier asymptotic theory through matching. It is found that ω→0 as β→(1/q)−.