Experimental and theoretical studies were undertaken to investigate the particulatefree secondary flow interaction in the wire-type electrostatic precipitator. The secondary flow generated by the corona discharge is not negligible, and strong flow interactions take place owing to the induced circulatory cells. The calculated numerical results demonstrate close agreement with experiment.

The linear stability of an extensively modulated cylindrical Couette flow is investigated in the finite-gap range. A closed form analytic solution is obtained for the basic unsteady flow after modulation is introduced through the boundary conditions. The general linear perturbation equations for three-dimensional disturbances are then derived and subsequently solved using the Galerkin method with the stability analysed by the Floquet theory. Modulation is found to destabilize the flow in most cases and results compare very favourably with the ones obtained experimentally. Stabilization is possible only for some cases of outer cylinder modulation.

Far downstream of a sudden contaminant release in a narrow channel the concentration depends on the cloud size. This is largely determined by the longitudinal shear dispersion and the time of travel of the cloud. Near the source the efficiency of the shear dispersion and the velocity of the cloud are strongly dependent upon the source location across the flow. The shear dispersion is greatest when there is both strong shear and strong turbulent mixing (i.e. away from either the centre-line or the banks), while the velocity is least and the time-lag maximized for a source on the banks. The quantitative influence far downstream can be characterized in terms of a deficit variance and a centroid displacement. In this paper exact results are derived for these quantities. It is shown that, except when the banks are extremely steep, the time-lag has the strongest effect and the concentration far downstream of a point discharge is minimized when the discharge is sited at the bank.

The order of magnitude of the flow velocity due to the entrainment into an axisymmetric, laminar or turbulent jet and an axisymmetric laminar plume, respectively, indicates that viscosity and non-slip of the fluid at solid walls are essential effects even for large Reynolds numbers of the jet or plume. An exact similarity solution of the Navier-Stokes equations is determined such that both the non-slip condition at circular-conical walls (including a plane wall) and the entrainment condition at the jet (or plume) axis are satisfied. A uniformly valid solution for large Reynolds numbers, describing the flow in the laminar jet region as well as in the outer region, is also given. Comparisons show that neither potential flow theory (Taylor 1958) nor viscous flow theories that disregard the non-slip condition (Squire 1952; Morgan 1956) provide correct results if the flow is bounded by solid walls.

The behaviour of a single linear array of five equally spaced semi-immersed spheres, absorbing energy in a single mode from a regular wave train, is studied both for optimal tuning and for constrained body displacement amplitudes. This is extended to consideration of two parallel rows of such devices. Finally, the spheres are replaced by identical bodies of a particular geometry, containing a strong angular variation, which are studied using a thin-ship approximation.

The deformation of an axisymmetric bubble or drop in a uniform flow of constant velocity U is computed numerically. The flow is assumed to be inviscid and incompressible. The problem is formulated as a nonlinear integrodifferential system of equations for the bubble surface and for the potential function on the surface. These equations are discretized and the resulting algebraic system is solved by Newton's method. For U = 0 the bubble is a sphere. The results show that as U increases the bubble becomes oblate, spreading out in the direction normal to the flow and contracting in the direction of the flow. Then the poles get pushed in and ultimately they touch each other. The results also show that there is a maximum value of the Weber number above which there is no steady axially symmetric bubble. This value is somewhat smaller than the approximate value obtained by Moore (1965) but close to that found by El Sawi (1974). We also compute the added mass, the drag on the bubble, and its terminal velocity in a gravitational field, for large Reynolds numbers.

Linear stability of rotating Hagen-Poiseuille flow has been investigated by an orthonormal expansion technique, confirming results by Pedley and Mackrodt and extending those results to higher values of the wavenumber |α|, the Reynolds number R, and the azimuthal index n. For |α| [gsim ] 2, the unstable region is pushed to considerably higher values of R and the angular velocity, Ω. In this region, the neutral stability curves obey a simple scaling, consistent with the unstable modes being centre modes. For n = 1, individual neutral stability curves have been calculated for several of the low-lying eigenmodes, revealing a complicated coupling between modes which manifests itself in kinks, cusps and loops in the neutral stability curves; points of degeneracy in the R, Ω plane; and branching behaviour on curves which circle a point of degeneracy.

Measurements are reported on the wavelength of small-amplitude water waves in a parallel-sided channel, covering the frequency range 2 to 10 Hz. Clean-surface techniques were employed in the experiments, and the results show good agreement with the predictions of linearized hydrodynamic theory.

Detailed experimental results are presented for the initial impact force on a sphere striking a horizontal liquid surface vertically at speeds in the range 1-3 m s−1. Results are discussed in terms of an impact drag coefficient. Liquids having viscosities in the range 10−3−102 Pa s have been studied. For low viscosities the results have been compared with the theoretical calculations of Shiffman & Spencer. Good agreement has been found in most respects; in particular the impact force varies as the square root of the depth for depths less than a tenth of the radius. The impact drag coefficient has also been studied through the transition from inertia to viscosity-dominated conditions. The variation of the impact drag coefficient is presented as a function of Reynolds number, and its variation in the range 5 × 10−2 < Re < 5 × 103 is shown to resemble that of a fully immersed sphere moving steadily in a homogeneous fluid.

Hypersonic small-disturbance theory is extended to consider the problem of dusty-gas flow past thin two-dimensional bodies. The mass fraction of suspended particles is assumed to be sufficiently large that the two-way interaction between particle phase and gas phase must be considered. The system of eight governing equations is further reduced by considering the Newtonian approximation γ → 1 and M∞ → ∞. The Newtonian theory up to second order is studied and the equations are solved for the case of a thin wedge at zero angle of attack. Expressions for the streamlines, dust-particle paths, shock-wave location and all flow variables are obtained. It is seen that the presence of the dust increases the pressure along the wedge surface and tends to bend the shock wave towards the body surface. Other effects of the interaction of the two phases are also discussed.

The initial-value problem for the evolution of the interface η(x, t) separating two unbounded, inviscid streams is considered in the framework of linearized analysis. Given the initial shape y = εη0(x) of the interface at t = 0 the objective is to calculate the interface shape η(x,t) for later times. First, it is shown that, if the vortex sheet is of infinite extent, if surface tension is absent and if the two streams are of the same density, the evolution is given by \[ \eta(x,t) = \epsilon(1-\alpha)^{-1}{\rm Re}[\{(1-\alpha)+(1+\alpha)i\}\eta_0\{x-{\textstyle\frac{1}{2}}((1+\alpha)+(1-\alpha)i)t\}], \] where α (≠ 1) is the ratio of the speeds of the streams, provided the initial interface shape εη0(x) is analytic and its Fourier transform decays sufficiently rapidly. An interesting consequence is that it is possible, under certain circumstances, for the interface to develop singularities after a finite time. Next it is shown that when the two streams move at the same speed (α = 1) the growth of η is given by \[ \eta(x,t) = \epsilon\eta_0(x-t)+\epsilon t\,d\eta_0(x-t)/dx \] with mild restrictions on η0(x). The major effect of surface tension, it is found, is to prevent the occurrence of singularities after a finite time, a distinct possibility in its absence. Finally the vortex sheet shed by a semi-infinite flat plate is considered. The unsteady mixed boundary-value problem is formally solved by using parabolic coordinates and Fourier-Laplace transforms.

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of small amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. It is shown that if the frequency parameter is of any order less than R¼ the viscous correction to the Kutta condition and hence to the lift and moment may be determined from the results for the steady case. Justification of this correlation requires discussion of the flow in an additional region not encountered in previous studies.

A non-orthogonal helical co-ordinate system is introduced to study the effect of curvature and torsion on the flow in a helical pipe. It is found that both curvature and torsion induce non-negligible effects when the Reynolds number is less than about 40. When the Reynolds number is of order unity, torsion induces a secondary flow consisting of one single recirculating cell while curvature causes an increased flow rate. These effects are quite different from the two recirculating cells and decreased flow rate at high Reynolds numbers.

An analytical steady-state theory of the detonation ‘diameter effect’ is presented. This theory, which includes the off-axis flow, is a generalization of the Wood-Kirkwood analysis. When the state dependence of the reaction rate is stronger than that of the product of the sound speed squared and the flow divergence, detonation failure can occur. The leading term in the extrapolation of the detonation velocity to infinite charge size is quadratic in the inverse charge size and not linear as popularly believed. When calibrated to the detonation velocity vs. charge-size data, the theory reproduces the limited amount of experimental shock loci to a high degree of accuracy.

A numerical investigation of the problem of rotating disks is made using the Newton-Raphson and continuation methods. The numerical analysis of the problem was performed for a sequence of values of the Reynolds number R and the ratio of angular velocities of both disks s. It was shown that for higher values of the Reynolds number it is necessary to use a large number of grid points. Continuation of the solution with respect to the parameter s indicated that a number of branches may exist. A detailed discussion for three selected values of s (s = -1, s = 0, s = 1) is presented together with a detailed comparison of our calculations with results already published in the literature.

Steady flows of an incompressible, inviscid, and non-diffusive fluid of variable density in a gravitational field are first considered. By a transformation it is shown conclusively that there are infinitely many flows with the same flow pattern, provided the density gradients of these flows at any section (e.g. far upstream) differ only by a multiplicative constant. These flows have identical local internal Froude numbers at all corresponding points of the flows and, hence, identical local Richardson numbers. They are therefore dynamically similar. Every time a solution for one stratification is obtained, one has in fact obtained the solutions for infinitely many stratifications.

The creation of vorticity in steady stratified flows is then examined, and it is shown that this creation can be divided into two parts, one part being entirely due to the inertial effect and the other originating from the gravity effect of density variation.

Finally, compressibility is considered and the results on similarity of stratified flows and on vorticity and circulation are extended to apply to steady flows of gases stratified in entropy.

Nonlinear two-dimensional magnetoconvection in a Boussinesq fluid has been studied in a series of numerical experiments with values of the Chandrasekhar number Q ≤ 4000 and the ratio ζ of the magnetic to the thermal diffusivity in the range 1 ≥ ζ ≥ 0·025. If the imposed field is strong enough, convection sets in as overstable oscillations which give way to steady convection as the Rayleigh number R is increased. In the dynamical regime that follows, magnetic flux is concentrated into sheets at the sides of the cells, from which the motion is excluded.

Nonlinear, two-dimensional magnetoconvection has been investigated numerically for a fixed Rayleigh number of 104, with the ratio ζ of the magnetic to the thermal diffusivity in the range 0·4 ≥ ζ ≥ 0·05. As the Chandrasekhar number Q is decreased, convection first sets in as overstable oscillations, which are succeeded by steady convection with dynamically active flux sheets and, eventually, with kinematically concentrated fields. In the dynamical regime spatially asymmetrical convection, with most of the flux on one side of the cell, is preferred. As Q increases, these asymmetrical solutions become time-dependent, with oscillations about the steady state which develop into large-scale oscillations with reversals of the flow. Although linear theory predicts that narrow cells should be most unstable, the nonlinear results show that steady convection occurs most easily in cells that are roughly twice as wide as they are deep.

We study two examples of two-dimensional nonlinear double-diffusive convection (thermohaline convection, and convection in an imposed vertical magnetic field) in the limit where the onset of marginal overstability just precedes the exchange of stabilities. In this limit nonlinear solutions can be found analytically. The branch of oscillatory solutions always terminates on the steady solution branch. If the steady solution branch is subcritical this occurs when the period of the oscillation becomes infinite, while if it is supercritical, it occurs via a Hopf bifurcation. A detailed discussion of the stability of the oscillations is given. The results are in broad agreement with the largeramplitude results obtained previously by numerical techniques.

Simultaneous measurements of the longitudinal velocity U, normal velocity V, and temperature T have been made in turbulent spots generated in a slightly heated laminar boundary layer. The measurements were made in the plane of symmetry of the spot at several streamwise stations downstream of the spot-producing spark. Ensemble averages of U, V and T, obtained relative to the leading edge of the spot, are presented in terms of disturbances relative to the unperturbed values in the laminar flow. Ensemble-averaged disturbances of U, V and T in the outer part of the spot are consistent with a picture of a relatively large vortical structure with a spanwise vorticity in the same sense as that of the laminar flow. A rather dominant feature of these distributions is the large negative disturbance in V and U near the leading edge in the outer part of the spot; associated with this disturbance is a positive perturbation in T. The terms contributing to the ensemble-averaged values of UV, UT and VT are obtained and discussed. In the case of UV, contributions by the disturbance are found to be of the same order as those by the random turbulence superposed on the disturbance. For VT, the disturbance appears to play a more dominant role in the transfer of heat. The conical property of the spot is tested for disturbance temperature and velocity fields by comparing contours, at three streamwise stations, of the velocity and temperature disturbances using the co-ordinates introduced by Cantwell, Coles & Dimotakis (1978). The results show that the conical transformation, which was found to be a good approximation for the full velocity field, is not an accurate representation for the disturbance fields of velocity and temperature measured relative to laminar values. An alternative viscous transformation represents more accurately the disturbance fields. Features of the turbulence within the spot are compared with those obtained in a fully turbulent boundary layer.