David Crighton was struck down by cancer in his fifty-eighth year. He was then at the height of his career and was one of the most admired personalities in fluid mechanics. He had specialized in wave theory, helping to understand and solve problems of practical importance using the full power of mathematical method. Efforts to control the sound and vibration caused by unsteady flow were never far from his thinking, and Crighton's contribution to those efforts has changed significantly the way the subject is viewed. Having first attracted him into the field and never losing my interest in the way he was influencing it, it is natural that I should comment on the technical developments while looking back on Crighton's professional life. The subject has changed a great deal and there are now many more researchers involved in its study, many of whom rely on techniques that Crighton pioneered – really powerful mathematical methods. But the basic problems remain: powerful flows are noisy.

Rotating fluids support waves. These inertial waves propagate obliquely through the fluid, with an angle that is fixed with respect to the rotation axis. Upon reflection, their wavelength is unchanged only when the wall obeys the local reflectional symmetry, that is, when it is either parallel or perpendicular to the rotation axis. For internal gravity waves in a density-stratified fluid, sloping boundaries thus break the symmetry of ray paths, in a two-dimensional container, predicting their focusing upon attractors: particular paths onto which the wave rays, and hence the energy, converge, and to which the wave energy returns after a small number of refections. Laboratory observations, presented here, show that, despite the intrinsic three-dimensionality of inertial waves, attractors still occur. The intensified wave energy on the attractor encourages centrifugal instabilities, leading to a mean flow. Evidence of this comes from dye spreading, observed to develop most rapidly over the location where the attractor reflects from the sloping wall, being the place where focusing and instabilities occur. This mean flow, resulting from the mixing of angular momentum, accompanying the intensification of the wave field at that location, has geophysical implications, because the ocean, atmosphere and Earth's liquid outer core can be regarded as asymmetrically contained. The relevance of wave focusing in a rotating, spherical shell, the modifications due to the addition of radial stratification, and its implications for observed equatorial current patterns and inertial oscillations are discussed. The well-known universality of oceanic, gravito-inertial wave spectra might reflect complementary, divergent (chaotic) wave-ray behaviour, which occurs in containers obeying the reflectional symmetry, but in which symmetry is broken in the horizontal plane. Periodic orbits still exist, but now repell.

High-precision experimental results are reported showing the tangential momentum accommodation coefficient (TMAC) for several gases in contact with single-crystal silicon to be less than unity. A precise and robust experimental platform is demonstrated for measurement of mass flows through silicon micromachined channels due to an imposed pressure gradient. Analytic expressions for isothermal Maxwellian slip flows through long channels are used to determine the TMAC at a variety of Knudsen numbers. Results from experiments using nitrogen, argon and carbon dioxide are presented. For all three gases the TMAC is found to be lower than one, ranging from 0.75 to 0.85.

Because the three-dimensional large-scale vortex structures dominate the dispersion of particles at intermediate Stokes numbers in shear layers, there is interest in understanding the two-way thermal coupling effect in droplet–gas flows for practical combustion applications. Using pseudo-spectral and Lagrangian approaches, three-dimensional two-way thermally coupled droplet-laden mixing layers are studied with hot air and cool water droplets. Higher air density is observed around the region of the interface of the two streams and, thus, thermal contraction occurs in this region. This thermal contraction results in an increase of the magnitude of the vorticity field, a more unstable flow, a higher droplet concentration and a lower droplet dispersion across the mixing layer.

Simulations of low-aspect-ratio, rectangular free jets are presented. The investigations focus on the entrainment and transitional vortex dynamics in compressible (subsonic) jets initialized with laminar conditions, a thin vortex sheet with slightly rounded-off corner regions, and uniform initial momentum thickness. A monotonically integrated large-eddy simulation approach based on the solution of the unsteady flow equations with high-resolution monotone algorithms is used. Inherent uncertainties in the jet entrainment measurement process are addressed using the database from laboratory experiments and simulations. Vorticity geometries characterizing the near flow field of low aspect-ratio (A) rectangular jets are demonstrated, involving: (i) self-deforming and (ii) splitting vortex rings; interacting ring and braid (rib) vortices including (iii) single ribs aligned with corner regions (A [ges ] 2) and (iv) rib pairs aligned with the corners (A = 1); (v) a more disorganized flow regime in the far jet downstream, where the rotational-fluid volume is occupied by a relatively weak vorticity background with strong, slender tube-like filament vortices filling a small fraction of the domain – as observed in fully developed turbulent flows. The near field entrainment properties of low-A rectangular jets are shown to be largely determined by the characteristic A-dependent coupling geometry of interacting rib and ring vortices and by vortex-ring axis-switching times.

Several new results are obtained for the classical problem of inertial waves in a rotating fluid sphere which was formulated by Poincaré more than a century ago. Explicit general analytical expressions for solutions of the problem are found in a rotating sphere for the first time. It is also discovered that there exists a special class of three-dimensional inertial waves that are nearly geostrophic and always travel slowly in the prograde direction. On the basis of the explicit general expression we are able to show that the internal viscous dissipation of all the inertial waves vanishes identically for a rotating fluid sphere. The result contrasts with the finite values obtained for the internal viscous dissipation for all other cases in which inertial waves have been studied.

The theory of solitary topographic Rossby waves (modons) in a uniformly rotating two-layer ocean over a constant slope is developed. The modon is described by an exact, form-preserving, uniformly translating, horizontally localized, nonlinear solution to the inviscid quasi-geostrophic equations. Baroclinic topographic modons are found to translate steadily along contours of constant depth in both directions: either with negative speed (within the range of the phase velocities of linear topographic waves) or with positive speed (outside the range of the phase velocities of linear topographic waves). The lack of resonant wave radiation in the first case is due to the orthogonality of the flow field in the modon exterior to the linear topographic wave field propagating with the modon translation speed, that is impossible for barotropic modons. Another important property of a baroclinic topographic modon is that its integral angular momentum must be zero only in the bottom layer; the total angular momentum can be non-zero unlike for the beta-plane modons over flat bottom. This feature allows modon solutions superimposed by intense monopolar vortices in the surface layer to exist. Explicit analytical solutions for the baroclinic topographic modons with piecewise linear dependence of the potential vorticity on the streamfunction are presented and analysed.

An experimental and numerical study has been performed to improve the understanding of the air/liquid interaction in an air-blasted breaking water sheet. This research is focused in the near field close to the exit slit, because it is in this region where instabilities develop and grow, leading to the sheet breakup. In the experiments, several relevant parameters were measured including the sheet oscillation frequency and wavelength, as well as the droplet size distribution and the amplification growth rate. The flow was also investigated using linear instability theory. In the context of existing papers on instability analysis, the numerical part of this work presents two unique features. First, the air boundary layer is taken into account, and the effects of air and liquid viscosity are revealed. Second, the equations are solved for the same parameter values as those in the experiments, enabling a direct comparison between calculations and measurements; although qualitatively the behaviour of the measured variables is properly described, quantitative agreement is not satisfactory. Limitations of the instability analysis in describing this problem are discussed. From all the collected data, it is confirmed that the oscillation frequency strongly depends on the air speed due to the near-nozzle air/water interaction. The wave propagates with accelerating interface velocity which in our study ranges between the velocity of the water and twice that value, depending on the air velocity. For a fixed water velocity, the oscillation frequency varies linearly with the air velocity. This behaviour can only be explained if the air boundary layer is considered.

We investigate the application of linear-quadratic-Gaussian (LQG) feedback control, or, in modern terms, [Hscr ]2 control, to the stabilization of the no-motion state against the onset of Rayleigh–Bénard convection in an infinite layer of Boussinesq fluid. We use two sensing and actuating methods: the planar sensor model (Tang & Bau 1993, 1994), and the shadowgraph model (Howle 1997a). By extending the planar sensor model to the multi-sensor case, it is shown that a LQG controller is capable of stabilizing the no-motion state up to 14.5 times the critical Rayleigh number. We characterize the robustness of the controller with respect to parameter uncertainties, unmodelled dynamics. Results indicate that the LQG controller provides robust performances even at high Rayleigh numbers.

The hydrodynamical similarities between the bubbly flow in a bubble column and in a pipe with vertical upward liquid flow are investigated. The system concerns air/water bubbly flow in a vertical cylinder of 14.9 cm inner diameter. Measurements of the radial distribution of the liquid velocity, gas fraction and the bubble velocity and size are performed using laser Doppler anemometry for the liquid velocity and a four-point optical fibre probe for the gas fraction, bubble velocity and size. The averaged gas fraction was 5.2% for the bubble column (with a superficial liquid velocity of zero) and 5.5% for the bubbly pipe flow at a superficial liquid velocity of 0.175 m s−1. From a hydrodynamical point of view, the two modes of operation are very similar. It is found that in many respects the bubbly pipe flow is the superposition of the flow in the bubble column mode and single-phase flow at the same superficial liquid velocity.

The radial gas fraction profiles are the same and the velocity profiles differ only by a constant offset: the superficial liquid velocity. This means that the well-known large-scale liquid circulation (in a time-averaged sense) of the bubble column is also present in the bubbly pipe flow. For the turbulence intensities it is found that the bubbly pipe flow is like the superposition of the bubble column and the single-phase flow at the superficial liquid velocity of the pipe flow, the former being at least an order of magnitude higher than the latter. The large vortical structures that have been found in the bubble columns are also present in the bubbly pipe flow case, partly explaining the much higher ‘turbulence’ levels observed.

To describe the acoustic instabilities in the combustion chambers of laterally burning solid propellant rockets the interaction of the mean flow with the acoustic waves is analysed, using multiple scale techniques, for realistic cases in which the combustion chamber is slender and the nozzle area is small compared with the cross-sectional area of the chamber. Associated with the longitudinal acoustic oscillations we find vorticity and entropy waves, with a wavelength typically small compared with the radius of the chamber, penetrating deeply into the chamber. We obtain a set of differential equations to calculate the radial and axial dependence of the amplitude of these waves. The boundary conditions are provided by the acoustic admittance of the propellant surface, given by an existing analysis of the thin gas-phase reaction layer adjacent to the solid–gas interface, and of the nozzle, accounting here for the possible effect of the vorticity and entropy waves. The equations are integrated in closed form and the results provide the growth rate of the disturbances, which we use to determine the conditions for instability of the longitudinal oscillations.

The complex flow and wave pattern following an initially planar shock wave transmitted through a double-bend duct is studied experimentally and theoretically/numerically. Several different double-bend duct geometries are investigated in order to assess their effects on the accompanying flow and shock wave attenuation while passing through these ducts. The effect of the duct wall roughness on the shock wave attenuation is also studied. The main flow diagnostic used in the experimental part is either an interferometric study or alternating shadow–schlieren diagnostics. The photos obtained provide a detailed description of the flow evolution inside the ducts investigated. Pressure measurements were also taken in some of the experiments. In the theoretical/numerical part the conservation equations for an inviscid, perfect gas were solved numerically. It is shown that the proposed physical model (Euler equations), which is solved by using the second-order-accurate, high-resolution GRP (generalized Riemann problem) scheme, can simulate such a complex, time-dependent process very accurately. Specifically, all wave patterns are numerically simulated throughout the entire interaction process. Excellent agreement is found between the numerical simulation and the experimental results. The efficiency of a double-bend duct in providing a shock wave attenuation is clearly demonstrated.

A geostrophic circulation and a pair of oblique oscillating shear layers arise in a spherical uid cavity contained in a slowly precessing rigid body. Both are caused by the breakdown of the Ekman boundary layer at two critical circles. We rely on numerical modelling to characterize these motions for very small Ekman numbers. Both the O(E1/5) amplitude of the velocity in the oscillating shear layer and the width (also O(E1/5)) of these oblique layers are the result of in ux into the interior from the regions where the Ekman layer breaks down. The oscillating motions are confined to narrow shear layers and their amplitude decays exponentially away from the characteristic surfaces. Nonlinear interactions inside the boundary layer drive the geostrophic shear layer attached to the critical circles. This steady layer, again of O(E1/5) thickness, contains O(E−3/10) velocities. Our results are in good agreement with the experimental measurement by Malkus of the geostrophic velocity arising in a slowly precessing spheroid.

Laboratory and numerical experiments are used to study flow of a uniform-density fluid on the β-plane around a thin zonally elongated island (or ridge segment in the abyss). This orientation is chosen specifically to highlight the roles of the zonal boundary layer dynamics in controlling the circulation around the island. There are examples of deep ocean topography that fall into this category which make the work directly applicable to oceanic flows. Linear theory for the transport around the island and the flow structure is based on a modification of the Island Rule (Pedlosky et al. 1997; Pratt & Pedlosky 1999). The linear solution gives a north–south symmetric flow around the island with novel features, including stagnation points which divide the zonal boundary layers into eastward and westward flowing zones, and a western boundary layer of vanishing length, and zonal jets. Laboratory experiments agree with the linear theory for small degrees of nonlinearity, as measured by the ratio of the inertial to Munk boundary layer scales. With increasing nonlinearity the north–south symmetry is broken. The southern stagnation point (for anticyclonic forcing) moves to the eastern tip of the island. The flow rounding the eastern tip from the northern side of the island now separates from the island. Time-dependence emerges and recirculation cells develop on the northern side of the island. Mean transport around the island is relatively unaffected by nonlinearity and given to within 20% by the modified Island Rule. Numerical solutions of the shallow water equations are in close agreement with the laboratory results. The transition from zonal to meridional island orientation occurs for island inclinations from zonal greater than about 20°.

In a two-fluid system where the upper surface of the upper fluid is free, there are two independent modes of oscillation about the state of equilibrium, an ‘internal’ mode and an ‘external’ mode, which are described by two distinct dispersion curves. An efficient numerical scheme based on Fourier series expansions is used to calculate periodic waves of permanent form and of finite amplitude. Three kinds of waves are calculated: combination waves resulting from the interaction between an ‘internal’ mode and an ‘external’ mode with the same phase speed but wavelengths in a ratio of 2 (1:2 resonance), combination waves resulting from the interaction between a long ‘internal’ mode and a short ‘external’ mode with the same phase speed, and pure ‘external’ waves. It is shown that the 1:2 resonance, which is well-known for capillary – gravity surface waves and can profoundly affect wave field evolution, can affect pure gravity waves in a two-fluid system, but not in oceanic conditions. On the other hand, it is shown that the long/short wave resonance can occur in ocean-type conditions. Finally it is confirmed that pure external waves of finite amplitude behave like surface waves.

This study concentrates on a relatively simple model of a mushy layer originally proposed by Amberg & Homsy (1993) and later studied in further detail by Anderson & Worster (1995). We extend this model to the case in which the system is in a state of uniform rotation about the vertical. Of particular interest is to determine how the rotation of the system controls the bifurcating convection with both the oblique-roll planform and the planform of hexagonal symmetry. We find that two-dimensional oblique rolls can be either subcritically or supercritically bifurcating, depending on a pair of parameters (K1/CS, [Tscr ]), where K1 measures how the permeability linearly varies with the local solid fraction, CS relates the compositional difference between the liquid and solid phases to the variation of composition throughout the mushy layer, and the Taylor number [Tscr ] gives a measure of the local Coriolis acceleration relative to the viscous dissipation in a porous medium. The three-dimensional convection with hexagonal symmetry is found to be transcritical. Furthermore, distorted hexagons with upflow at the centres can be either subcritical or supercritical, depending on the value of the Taylor number [Tscr ].

An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite-element solution solving the same potential flow equations. The test geometry taken is representative of a high-bypass turbofan aircraft engine, with typical Mach numbers of 0.5–0.7, circumferential mode numbers m of 10–40, dimensionless wavenumbers of 10–50, and both hard and acoustically treated inlet walls of impedance Z = 2 − i. Of special interest is the presence of the spinner, which incorporates a geometrical complexity which could previously only be handled by fully numerical solutions. The results for predicted power attenuation loss show in general a very good agreement. The results for iso-pressure contour plots compare quite well in the cases where scattering into many higher radial modes can occur easily (high frequency, low angular mode), and again a very good agreement in the other cases.

The motion of a triple junction is investigated. We consider only the two-dimensional case and assume that initially the fluid is in the form of three inviscid wedges. A similarity solution is determined which accounts for a balance of force at the triple junction. This similarity solution is computed numerically using boundary integral methods. Results are presented for different initial wedge angles and surface tension ratios. In particular the location of the triple junction and the resulting capillary waves along the interfaces are discussed.

The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turn-over time, where P is a Péclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.