Uniform flow in curved, wide, erodible-bed channels is formulated on the basis of the conservation of flux of moment-of-momentum, to obtain relations for the vertical distributions of radial-plane velocity and radial shear stress. The expression for the radial stress exerted on the bed is utilized in a force-equilibrium analysis of the moving bed layer to obtain relations for the average transverse slope of the bed and for the radial bed profile. The reduction of primary bed shear stress due to the net radial transport of streamwise momentum toward the outer (concave) bank is then calculated, by introducing the derived expressions for the velocity components into the momentum equation for the primary-flow direction. It is found that the stress reductions in deep, narrow channels can exceed 50%. Bed profiles and velocity distributions measured in natural and laboratory streams are found to be in good conformity with those calculated from this moment-based theory.

The effect of a small amount of Brownian diffusion on shear-induced coagulation of spherical particles has been calculated. This has been accomplished by considering the binary collision process between a test sphere and identical spheres interacting with the test sphere through induced-dipole attraction, electrostatic repulsion and hydrodynamically induced forces. The effect of diffusion is found by means of an expansion in inverse Péclet number. Specific calculations were performed for uniaxial extension and for laminar shear flow. It is found that Brownian diffusion, the effect of which is nonlinearly coupled with flow type and strength, can act to increase or decrease the coagulation rate.

A mathematical representation has been developed for the electromagnetic force field and the fluid-flow field in a coreless induction furnace. The fluid flow field was represented by writing the axisymmetric turbulent Navier–Stokes equations, containing the electromagnetic body-force term. The electromagnetic body force field was calculated by using a technique of mutual inductances. The k-ε model was employed for evaluating the turbulent viscosity, and the resultant differential equations were solved numerically.

The theoretically predicted velocity fields were in reasonably good agreement with the experimental measurements reported by Hunt & Moore; furthermore, the agreement regarding the turbulence intensities was essentially quantitative. These results indicate the k-ε model does provide a good engineering representation of the turbulent recirculating flows occurring in induction furnaces. At this stage it is not clear whether the discrepancies between measurements and the predictions, which were not very great in any case, are attributable either to the model or to the measurement techniques employed.

The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave region exceeds the wavenumber for freely propagating waves in the trench are investigated and are found to result in large reductions in wave transmission; however, reflection is not total owing to the finiteness of the obstacle.

Results for one case are compared with data obtained from a small-scale wave-tank experiment. An approximate solution based on plane-wave modes is derived and compared with the numerical solution and, in the long-wave limit, with a previous analytic solution.

In this analysis, the translation of a liquid drop experiencing a strong non-uniform radial velocity has been investigated. The situation arises when a moving liquid drop experiences condensation, evaporation or material decomposition at the surface. By simultaneously treating the flow fields inside and outside the drop, we have obtained physical results relevant to the problem. The magnitude of the radial velocity is allowed to be very large, but the drop motion is restricted to slow translation. The solution to the problem has been developed by considering a uniform radial flow with the translatory motion introduced as a perturbation. The role played by the inertial terms due to the strong radial field has been clearly delineated. The study has revealed several interesting features. An inward normal velocity on a slowly moving drop increases the drag. An increasing outward normal velocity decreases the drag up to a minimum beyond which it increases. The total drag force not only consists of contributions from the viscous and the form drags but also from the momentum transport at the interface. Since the liquid drop admits a non-zero tangential velocity, the tangential momentum convected by the radial velocity forms a part of this drag force. The circulation inside the drop decreases (increases) with an outward (inward) normal velocity. A sufficiently large non-uniform outward velocity causes the circulation to reverse.

In the limit of the internal viscosity becoming infinite, our analysis collapses to the simple case of a translating rigid sphere experiencing a large non-uniform radial velocity. By letting the radial velocity become vanishingly small the Stokes-flow solution is recovered.

An important contribution of the present study is the identification of a new singularity in the flow description. It accounts for both the inertial and the viscous forces and displays Stokeslet-like characteristics at infinity.

A novel, digital, hot-wire anemometer technique for the simultaneous measurement of the instantaneous streamwise and lateral velocity fields in high-intensity turbulent flows is discussed. It involves the use of a three-wire probe comprising two 45° slanted hot wires and a normal hot wire. A comprehensive and systematic examination of several factors that can affect the fidelity of the streamwise and lateral velocity waveforms is developed to assess the performance of the new technique as well as hot-wire systems generally. These factors are: (i) rectification, which stems from the inherent insensitivity of hot wires to the direction of the instantaneous (total) velocity vector in a turbulent flow; (ii) spanwise velocity fluctuations; (iii) axial cooling of hot wires; (iv) unpredictable variations in one of four hot-wire calibration parameters; (v) random hot-wire calibration errors; (vi) spanwise separation of the hot wires. Relevant hot-wire anemometer-response equations relating instantaneous anemometer output voltages to instantaneous flow velocities were established on the basis of extensive voltage-velocity calibration data pertaining to hot wires orientated with respect to the calibration flow velocity at various yaw and pitch angles ranging from 0° to 90°. Simulated Gaussian (streamwise, lateral and spanwise) velocity fields appropriate to flows with turbulence intensity levels varying between 5 and 80% and Reynolds shear-stress coefficients varying between 0.1 and 0.5 were generated by means of a digital computer, and the associated anemometer-voltage signals computed in accordance with the response equations subject to different combinations of the first four of the aforementioned factors. In order to take into account the effects of the last two factors, viz calibration errors and spanwise wire separation, uncorrelated Gaussian ‘noise’ fluctuations were superimposed on the above voltage signals. Estimates of the known (simulated) streamwise and lateral velocity signals were then determined by simultaneous solution of (a) the actual instantaneous response equations, (b) approximate versions of them, and (c) linearized versions of them. The results indicate that reasonably accurate estimates of velocity signals from a turbulent flow can be obtained by means of conventional hot-wire anemometer techniques – which assume that anemometer voltage fluctuations are linear functions of corresponding velocity fluctuations – only if the turbulent intensity level of the flow does not exceed about 20%. In marked contrast, the 3-wire anemometer technique introduced here can be used to measure streamwise and lateral velocity signals simultaneously with a high degree of accuracy for turbulence-intensity levels of up to 40%. In addition, this technique is capable of yielding high-fidelity streamwise velocity waveforms for levels in excess of 70%.

In this paper we investigate nonlinear interactions of narrowband, Gaussian-random, inhomogeneous wavetrains. Alber studied the stability of a homogeneous wave spectrum as a function of the width σ of the spectrum. For vanishing bandwidth the deterministic results of Benjamin & Feir on the instability of a uniform wavetrain were rediscovered whereas a homogeneous wave spectrum was found to be stable if the bandwidth is sufficiently large. Clearly, a threshold for instability is present, and in this paper we intend to study the long-time behaviour of a slightly unstable modulation by means of a multiple-timescale technique. Two interesting cases are found. For small but finite bandwidth – the amplitude of the unstable modulation shows initially an overshoot, followed by an oscillation around the time-asymptotic value of the amplitude. This oscillation damps owing to phase mixing except for vanishing bandwidth because then the well-known Fermi–Pasta–Ulam recurrence is found. For large bandwidth, however, no overshoot is found since the damping is overwhelming. In both cases the instability is quenched because of a broadening of the spectrum.

The homogenization of a passive ‘tracer’ in a flow with closed mean streamlines occurs in two stages: first, a rapid phase dominated by shear-augmented diffusion over a time ≈P1/3(L/U), where the Péclet number P=LU/κ (L,U and κ are lengthscale, velocity scale and diffusivity), in which initial values of the tracer are replaced by their (generalized) average about a streamline; second, a slow phase requiring the full diffusion time ≈ L2/κ. The diffusion problem for the second phase, where tracer isopleths are held to streamlines by shear diffusion, involves a generalized diffusivity which is proportional to κ, but exceeds it if the streamlines are not circular. Expressions are also given for flow fields that are oscillatory rather than steady.

When a tsunami is incident on a plane shelf, the waveform and amplitude of the reflected wave differ significantly from those of the incident wave, and, when the shelf has the extremely irregular character of real continental shelves, the contrast between the two amplitudes is even greater. Here we quantify these statements and we also give an account of the manner in which the run-up depends on the obliquity and on other parameters characterizing the incident wave.

An experimental study of the influence of liquid viscosity and viscoelasticity on flow-generated waves on a compliant surface has been conducted in a rotating-disk geometry. Over the entire range of liquid properties studied, each test gave a well-defined critical onset flow velocity above which waves were present and below which no waves were observed. This onset velocity increased with increasing fluid viscosity, and for sufficiently high viscosities the onset occurred when the flow on the disk was laminar rather than turbulent. The effects of liquid viscoelasticity were examined in the turbulent flow using dilute solutions of high-molecular-weight polymers. This type of viscoelasticity had little influence on the onset flow velocity in these circumstances, but did make the wave structure on the surface more regular in appearance than when the liquid was Newtonian. In all cases the wave structure produced a dramatic increase in drag similar to that expected for a rough surface. For the viscoelastic fluid, however, the increase in drag was much less than for a viscous fluid of the same viscosity.

In this work a study has been made of the Stuart (1960)–Watson (1960) formalism as applied to plane Poiseuille flow. In particular, the higher-order Landau coefficients have been calculated for the Reynolds & Potter (1967) method and for the Watson (1960) method. The results have been used to study the convergence of the Stuart–Landau series. A convergence curve in the (α, R)-plane has been obtained by using suitable Domb–Sykes plots. In the region of poor convergence of the series, and also in a part of the divergent region of the series, it has been found that the Shanks (1955) method, using the em1 transformation, serves as a very effective way of finding the proper sum of the series, or of finding the proper antilimit of the series. The results for the velocity calculations at R = 5000 are in very good agreement with Herbert's (1977) Fourier-truncation method using N = 4. The Watson method and the Reynolds & Potter method have also been compared inthe subcritical and supercritical regions. It is found in the supercritical region that there is not much difference in the results by the ‘true problem’ of Watson and the ‘false problem’ of Reynolds & Potter when the respective series in both methods are summed by the Shanks method. This fact could possibly be capitalized upon in the subcritical region, where the Watson method is difficult to apply.

The evolution of a weakly nonlinear, weakly dispersive gravity wave in water of depth d over a bottom of gradual slope δ and Chezy friction coefficient Cf is studied. It is found that an initially sinusoidal wave evolves into a periodic sequence of solitary waves with relative amplitude a/d = α1 = 15δ/4Cf if α1 < αb, where αb is the relative amplitude above which breaking occurs. This prediction is supported by observations (Wells 1978) of the evolution of swell over mudflats.

Detailed measurements of the velocity profiles in a laminar axisymmetric submerged jet of water were taken using a laser-Doppler anemometer. A non-intrusive measurement technique is particularly advantageous in this application owing to the unstable nature of the laminar jet and the destabilizing effect which objects submerged in the jet have. Flow visualization was employed to ensure that all of the measuring points were located within the laminar region of the jet.

The variation of centreline velocity, jet half-radius and velocity-profile shape are investigated for various Reynolds numbers and axial distances. Emphasis is placed on the jet-development region; however, data from the fully developed region are also presented. Particular attention is given to determine the proper non-dimensional groups which are required to collapse the data. The predictions of a simple boundary-layer analysis are used as a guide in this regard and found to give an accurate representation of the flow field.

Velocity-profile data were taken at sufficiently small radial increments to allow a determination of the jet kinematic momentum using the basic integral definition. Although approximately constant, a slight variation with axial distance is indicated. The momentum initially decreases, and then increases gradually to a value greater than that at the tube exit. An attempt to explain the trend of the variation is made using certain hypotheses regarding the velocity and pressure conditions at the tube exit.

The rate of mass transfer of a diffusing substance along a pipe is augmented by an oscillatory motion of the ambient fluid in the pipe. The increase of the flux is evaluated for the cases of a circular pipe and of a two-dimensional channel. Results are given for a general cross-section in the limiting cases of slow and fast oscillations of the flow.

Experiments were conducted to determine the effective diffusivity for axial transport through a tube of circular cross-section of a contaminant gas in oscillatory flow. Results were compared with the theoretical predictions of Watson (1983) and found to be in excellent agreement. The experiments differ from the theoretical situation in that the oscillations are superimposed upon a steady flow due to a constant infusion of tracer gas, and a buoyancy-induced flow associated with spatial variations in gas density. The influence of both artifacts is found to be negligible.

The problem of cavitating flow past a two-dimensional curved obstacle is considered. Surface tension is included in the dynamic boundary condition. A perturbation solution for small values of the surface tension is presented. It is found that the position of the separation points is uniquely determined by specifying the value of the Weber number and the contact angle at the separation points. In addition, for a given value of the Weber number there exists a particular position of the separation points for which the slope is continuous. This solution tends to the classical solution satisfying the Brillouin–Villat condition as the surface tension tends to zero. Graphs of the results for the cavitating flow past a circular cylinder are presented.

Force measurements were conducted in a pressurized wind tunnel from subcritical up to transcritical Reynolds numbers 2.3 × 104 [les ] Re [les ] 7.1 × 106 without changing the experimental arrangement. The steady and unsteady forces were measured by means of a piezobalance, which features a high natural frequency, low interferences and a large dynamic range. In the critical Reynolds-number range, two discontinuous transitions were observed, which can be interpreted as bifurcations at two critical Reynolds numbers. In both cases, these transitions are accompanied by critical fluctuations, symmetry breaking (the occurrence of a steady lift) and hysteresis. In addition, both transitions were coupled with a drop of the CD value and a jump of the Strouhal number. Similar phenomena were observed in the upper transitional region between the super- and the transcritical Reynolds-number ranges. The transcritical range begins at about Re ≈ 5 × 106, where a narrow-band spectrum is formed with Sr(Re = 7.1 × 106) = 0.29.

The interactive boundary-layer equations for a flat plate are solved numerically when the external velocity field is piecewise linear and would provoke separation if the response of the boundary layer were neglected. A comparable problem had already been solved by Briley using the full Navier–Stokes equations. The equations are solved for various values of the Reynolds number and x0, a parameter defining the corner point of the external velocity. It is found that flows with a limited region of separation can be computed, but that, if x0 is too large, the numerical procedure breaks down. Furthermore, this maximum value is a decreasing function of R and seems to approach the value 0.12 predicted by classical theory as R → ∞. Comparison with Briley's results indicate a reasonable agreement except that different values of x0 are appropriate. It is conjectured that, once x0 increases above the acceptable maximum, rapid changes occur in the flow properties when R is large.

A linear stability analysis of a doubly diffusive system, with rotation and shear, shows that overstable oscillations can occur in stratifications typical of the equatorial ocean, that internal waves encountering an equatorial current can exchange energy with the current, and that the wave-induced fluxes of salt and heat can lead to layer formation in the salinity, temperature and velocity fields.

We address two aspects of the influence of double diffusion on convection from point buoyancy sources (plumes). First we consider double-diffusive convection acting in conjunction with buoyancy from an isolated source in an unconfined environment, and we study the problem of when fluxes of properties occur in the opposite direction to that of the initial buoyancy. A simple dimensional analysis is in good agreement with the experimental data for these ‘counterbuoyant’ fluxes of properties. Secondly, we consider a double-diffusive plume discharging into a confined environment. The plume now does not always reach the bottom (or top) of the confined environment, but can spread out into the environment at intermediate depths. Double-diffusive interfaces form, and we describe their development and the evolution of the density profile in the confined environment. A quantitative measure of the importance of double-diffusive convection in relation to the normal filling-box mechanism is obtained in the experiments by using the measured density profile, and this correlates well with a theoretically derived parameter Bρ.