The Lighthill formalism for jet noise prediction is extended to accommodate wave transport by the mean jet flow. The extended theory combines the simplicity of the Lighthill approach with the generality of the more complex Lilley approach. There is full allowance for ‘flow-acoustic’ effects: shielding, as well as the refractive ‘cone of (relative) silence’. A source term expansion yielda a convected wave equation that retains the basic Lighthill source term. This leads to a general formula for power spectral density emitted from unit volume as the Lighthill-based value multiplied by a squared ‘normalized’ Green's function. The Green's function, referred to a stationary point source, delineates the refraction dominated ‘cone of silence’. The convective motion of the sources, with its powerful amplifying effect, also directional, is accounted for in the Lighthill factor. Source convection and wave convection are thereby decoupled, in contrast with the Lilley approach: this makes the physics more transparent. Moreover, the normalized Green's function appears to be near unity outside the ‘cone of silence’. This greatly reduces the labour of calculation: the relatively simple Lighthill-based prediction may be used beyond the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected ‘point’ source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are coaxial or shrouding jets: in that case the difference from unity will quantify the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g. hot jets).

Numerical investigation of laminar, transitional and chaotic flows in converging–diverging channels are performed by direct numerical simulations in the Reynolds number range 10 < Re < 850. The temporal flow evolution and the onset of turbulence are investigated by combining classical fluid dynamics representations with dynamical system flow characterizations. Modern dynamical system techniques such as timedelay reconstructions of pseudophase spaces, autocorrelation functions, fractal dimensions and Eulerian Lyapunov exponents are used for the dynamical flow characterization of laminar, transitional and chaotic flow regimes. As a consequence of these flow characterizations, it is verified that the transitional flow evolves through intermediate states of periodicity, two-frequency quasi-periodicity, frequency-locking periodicity, and multiple-frequency quasi-periodicity before reaching a non-periodic unpredictable behaviour corresponding to low-dimensional deterministic chaos.

Qualitative and quantitative differences in Eulerian dynamical flow parameters are identified to determine the predictability of transitional flows and to characterize chaotic, weak turbulent flows in converging–diverging channels. Autocorrelation functions, pseudophase space representations and Poincaré maps are used for the qualitative identification of chaotic flows, assertion of their unpredictable nature, and recognition of the topological structure of the attractors for different flow regimes. The predictability of transitional flows is determined by analysing the autocorrelation functions and by representing their attractors in the reconstructed pseudophase spaces. The transitional flow behaviour is examined by the geometric visualization of the evolution of the attractors and Poincaré maps until the appearance of a strange attractor at the onset of chaos. Eulerian Lyapunov exponents and fractal dimensions are quantitative parameters to establish the onset of chaos, the persistence of chaotic flow behaviour, and the long-term persistent unpredictability of chaotic Eulerian flow regimes. Lastly, three-dimensional simulations for converging–diverging channel flow are performed to determine the effect of the spanwise direction on the route of transition to chaos.

An experimental study is presented that examines the interaction of a vortex ring with a free surface. The main objective of this study is to identify the physical mechanisms that are responsible for the self-disconnection of vortex filaments in the near-surface region and the subsequent connection of disconnected vortex elements to the free surface. The understanding of those mechanisms is essential for the identification and estimation of the appropriate spatial and temporal scales of the disconnection and connection process. In this regard, the velocity and vorticity fields of an obliquely approaching laminar vortex ring with a Reynolds number of 1150 were mapped by using Digital Particle Image Velocimetry (DPIV). The evolution of the near-surface vorticity field indicates that the connection process starts in the side regions of the approaching vortex ring where surface-normal vorticity already exists in the bulk. A local strain rate analysis was conducted to support this conclusion. Disconnection in the near-surface tip region of the vortex ring occurs because of the removal of surfaceparallel vorticity by the viscous flux of vorticity through the surface. Temporal and spatial mapping of the vorticity field at the surface and in the perpendicular plane of symmetry shows that the viscous flux is balanced by a local deceleration of the flow at the surface. It is found that the observed timescales of the disconnection and connection process scale with the near-surface vorticity gradient rather than with the core diameter of the vortex ring.

A Hamiltonian formulation is used to investigate irrotational capillary wave dynamics. Dissipation is accounted for by putting the wave system in contact with a ‘heat bath’. The generation of short waves by longer waves is studied. It is found that millimetre-wavelength waves tend to be created on the forward face of a steep longer wave, while centimetre waves tend to form near the crest. Generation of capillary waves by wind waves is investigated. The results are compared with predictions of the Hasselmann transport equation. It is found that off-resonance interactions lead to significant corrections to the transport theory. The relative importance of three-wave and four-wave interactions is studied, as well as the role of triad resonances. For the capillary phenomena studied here, the four-wave terms in most cases lead to quantitative, but not qualitative, corrections to the three-wave only calculations. However, restricting interactions to the neighbourhood of triad resonances can give quite erroneous results. Use of a canonical transformation to pseudo-wave variables can greatly reduce numerical computation times.

A theoretical study of the character and stability of thermomagnetic flow in a microgravity environment is performed. Convection is driven owing to imposed radial magnetic and temperature gradients in a cylindrical shell containing a ferrofluid. Linear, nonlinear, and computational methods are employed. It is shown that convection sets in as a stable supercritical bifurcation. Results obtained for a specific shell configuration are in good agreement with experiments.

A mathematical model is proposed to describe atmospheric solitary waves at the interface between a ‘shallow’ layer of fluid near the ground and a stationary upper layer of compressible air. The lower layer is in motion relative to the ground, perhaps as a result of a distant thunderstorm or a sea breeze, and possesses constant vorticity. The upper fluid is compressible and isothermal, so that its density and pressure both decrease exponentially with height. The profile and speed of the solitary wave are determined, for a wave of given amplitude, using a boundary-integral method. Results are discussed in relation to the ‘morning glory’, which is a remarkable meteorological phenomenon evident in the far north of Australia.

A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds number Re = 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up to Re = 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 [les ] Re [les ] 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.

The effect of wall cooling on hypersonic boundary-layer separation near a compression ramp is considered. Two cases are identified corresponding to the value of the average Mach number $\overline{M}$ across the upstream boundary layer approaching the compression ramp. The flow is referred to as supercritical for $\overline > 1$ and subcritical for $\overline{M} < 1$. The interaction is described by triple-deck theory, and numerical results are given for both cases for various ramp angles and levels of wall cooling. The effect of wall cooling on the absolute instability described recently by Cassel, Ruban & Walker (1995) for an uncooled wall is of particular interest; a stabilizing effect is observed for supercritical boundary layers, but a strong destabilizing influence occurs in the subcritical case. Wall cooling also influences the location and size of the separated region. For supercritical flow, progressive wall cooling reduces the size of the recirculating-flow region, the separation point moves downstream, and upstream influence is diminished. In contrast for the subcritical case downstream influence is reduced with increased cooling. In either situation, a sufficient level of wall cooling eliminates separation altogether for the ramp angles considered. The present numerical results closely confirm the strong wall cooling theory of Kerimbekov, Ruban & Walker (1994).

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients.

Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.

We consider a long-wave evolution equation that governs a draining film on a heated plate and hence is capable of describing both surface-wave and thermocapillary instabilities. When the flow and heat transfer rates are moderate, we show, via weakly nonlinear analysis of a truncated system and numerical simulation of the full nonlinear evolution equation, that coupled temporal instabilities can create surface deformations that lead to an array of rivulets aligned with the flow. This work thus demonstrates a mechanism of rivulet formation based solely on instability phenomena.

Turbulent convection into stratified two-layer fluid systems in the presence of rotation has been investigated in a cylindrical laboratory tank. For a wide range of conditions the vertical stability of the flow depends only on the Richardson number Ri = g′h0/(B0R)2/3 (here, g′ = gδ ρi/ρ0 is the jump in the reduced gravity across the density interface, δ ρi is the jump in density itself, h0 is the depth of the top layer, B0 is the surface buoyancy flux and R is the radius of the source). We have found that for values of Ri greater than a critical value of Ric ≈ 11, the convective flow did not penetrate through the density interface, regardless of the values of the convective Rossby number Ro* = (B0/f3h02)1/2 of the flow (here f is the Coriolis parameter). In this case after the convective layer interacted with the density interface the mixed fluid, of intermediate density, propagated radially along the interface in the form of an intrusion. Later, if Ro* was less than approximately 5, mesoscale vortices with mean diameter D ≈ 8(RoR)2/3 and maximum swirl velocity v ≈ (B0R)1/3 were generated at the edge of this propagating front (here RoR = (B0/f3R2)1/2 is the Rossby number based on R). When Ri was less than 11, the convective flow eventually penetrated through the density interface and into the bottom layer. This occurred through the formation of discrete ‘convective holes’ beneath the source. At large values of Ro*, and at early times, one turbulent plume penetrated into the bottom layer from each hole. Later the initial holes coalesced to create one large lesion beneath the source.

In a series of laboratory experiments the growth of double-diffusive salt fingers from an initial configuration of two homogeneous reservoirs with salt in the lower and sugar in the upper layer was investigated. For most of the experiments the stability ratio was between 2.5 and 3, where the latter value is at the upper limit (the ratio of salt to sugar diffusivities) for which fingers can exist. In these experiments long slender fingers are generated at the interface. Essentially all theories or physical bases for models of salt fingers presuppose such a configuration of long fingers. Our measurements show that the length of fingers at high stability ratio increases with time like t1/2, with a coefficient that is consistent with the diffusive spread of the faster diffusing component (salt). When the initial stability ratio is closer to unity, fingers penetrate into the reservoirs very rapidly carrying with them large anomalies of salt and sugar which give rise to convective overturning of the reservoirs. The convection sweeps away the ends of the fingers, and when it is intense enough (as it is when the sugar anomaly is large) it can reduce the finger height to a value less than the width. After this initial phase the finger length grows linearly with time as has been found in previous studies. These results show that salt fingers can evolve in quite different ways depending on the initial stability ratio and must cast doubt on the use of simple similarity arguments to parameterize the heat and salt fluxes produced by fingers.

Rigorous upper bounds on the viscous dissipation rate are identified for two commonly studied precessing fluid-filled configurations: an oblate spheroid and a long cylinder. The latter represents an interesting new application of the upper-bounding techniques developed by Howard and Busse. A novel ‘background’ method recently introduced by Doering & Constantin is also used to deduce in both instances an upper bound which is independent of the fluid's viscosity and the forcing precession rate. Experimental data provide some evidence that the observed viscous dissipation rate mirrors this behaviour at sufficiently high precessional forcing. Implications are then discussed for the Earth's precessional response.

In this paper, we discuss experimental evidence for radial particle segregation in a parallel-plate geometry. The motion of coloured tracer particles of a size different from the bulk suspension is followed as a function of time. The tracer particles are seen to experience a constant drift velocity independent of their radial position. This is in addition to the random-walk motion arising from their interactions with other particles in the suspension. These observations are found to be consistent with the shear-induced migration model of Leighton & Acrivos (1987 a,b) as well as the tracer diffusivity measurements of Phan & Leighton (1996). In the experiments of Abbott et al. (1991), it was observed that larger particles migrated radially outward to regions of lower shear stress in a wide-gap Couette device. In our experiments large tracers were also observed to migrate radially outward. In this case, however, the radial migration resulted in migration to regions of higher shear stress, contrary to expectations. This apparent discrepancy is explained in terms of a model that incorporates both the stress-induced migration of earlier studies and a curvature-induced migration flux (which in turn is shear-induced) as an opposing effect.

A three-dimensional computer simulation of a concentrated emulsion in shear flow has been developed for low-Reynolds-number finite-capillary-number conditions. Numerical results have been obtained using an efficient boundary integral formulation with periodic boundary conditions and up to twelve drops in each periodically replicated unit cell. Calculations have been performed over a range of capillary numbers where drop deformation is significant up to the value where drop breakup is imminent. Results have been obtained for dispersed-phase volume fractions up to 30% and dispersed- to continuous-phase viscosity ratios in the range of 0 to 5. The results reveal a complex rheology with pronounced shear thinning and large normal stresses that is associated with an anisotropic microstructure that results from the alignment of deformed drops in the flow direction. The viscosity of an emulsion is only a moderately increasing function of the dispersed-phase volume fraction, in contrast to suspensions of rigid particles or undeformed drops. Unlike rigid particles, deformable drops do not form large clusters.

A number of new experiments have been performed on the rise of air bubbles in clean mixtures of distilled water and pure, reagent grade, glycerine covering a range of the relevant parameter, the Morton number, Mo = gv4ρ3/σ3, of 1013. Here g is the acceleration due to gravity, v the kinematic viscosity, ρ the density and σ the surface tension of the mixture. In these careful measurements several scaling regimes have been found that have not been discussed before in the extensive literature on the subject. The transitions between these regimes have been delineated and attempts made to discuss the dynamical processes that might be important in each of them.