We depict and analyse the successive steps of atomization of a liquid jet when a fast gas stream blows parallel to its surface. Experiments performed with various liquids in a fast air flow show that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid. The transient acceleration experienced by the liquid suggests that a Rayleigh–Taylor type of instability is triggered at the wave crests, producing liquid ligaments which further stretch in the air stream and break into droplets. The primary wavelength $\lambda\,{\sim}\,\delta (\rho_{1}/\rho_{2})^{1/2}$ is set by the vorticity thickness $\delta$, in the fast air stream and the liquid/gas density ratio $\rho_{1}/\rho_{2}$. The transverse corrugations of the crests have a size $\lperp\,{\sim}\,\delta {\We_{\delta}}^{-1/3} (\rho_{1}/\rho_{2})^{1/3}$, where $\We_{\delta}\,{=}\,\rho_{2}u_{2}^{2}\delta/\sigma$ is the Weber number constructed on the gas velocity $u_{2}$ and liquid surface tension $\sigma$. The ligament dynamics gives rise, after break-up, to a well-defined droplet size distribution whose mean is given by $\lperp$. This distribution bears an exponential tail characteristic of the broad size statistics in airblast sprays.

In turbulent flow past rigid boundaries, there can be distinguished regions close to the wall in which the local rates of energy production and dissipation are so large that aspects of the turbulent motion concerned with these processes are determined almost solely by the distribution of shear stress within the region and are independent of conditions outside it. These regions are here called equilibrium layers because of the equilibrium existing between local rates of energy production and dissipation. Three kinds of equilibrium layer have been studied experimentally, the constant-stress layer, the transpiration layer and the zero-stress layer, but there are other possible forms. One that is of importance in the theory of self-preserving flow in boundary layers and in diffusers is the ‘linear-stress’ layer in which the stress increases linearly with distance from the wall. The properties of these various equilibrium layers are considered and the distributions of mean velocity are derived from the equation for the turbulent kinetic energy and certain assumptions of flow similarity.

The theory of self-preserving wall flow, usually expressed as a combination of the law of the wall and the defect law, assumes compatibility between the outer flow and the equilibrium layer, and the course of development depends on the kind of equilibrium layer. Earlier work by the author, which assumed the defect law, is only valid if the whole of the equilibrium layer is a constant-stress layer and this is not true in strong adverse pressure gradients. A consistent theory is developed for these flows by assuming a ‘linear-stress’ layer, and the solutions show the relation between flows of finite stress and of zero stress and provide a plausible explanation of the phenomenon of downstream instability observed by Clauser. Self-preserving flow in wedges is treated on similar lines.

A turbulent round jet of air discharging into quiescent air was studied experimentally. Some × -wire hot-wire probes mounted on a moving shuttle were used to eliminate rectification errors due to flow reversals in the intermittent region of the jet. Moments of velocity fluctuations up to fourth order were measured to characterize turbulent transport in the jet and to evaluate current models for triple moments that occur in the Reynolds stress equations. Fourth moments were very well described in terms of second moments by the quasi-Gaussian approximation across the entire jet including the intermittent region. Profiles of third moments were found to be significantly different from earlier measurements: 〈uv2〉, 〈uw2〉 and 〈u2v〉 are found to be negative near the axis of the jet. The Basic triple moment model that included turbulent production and models for the dissipation and the return-to-isotropy part of the pressure correlations was found to be unsatisfactory. When mean-strain production and a model for rapid pressure correlations were also included, predictions were satisfactory in the fully turbulent region. The consistency of the measurements with the equations of motion was assessed: momentum flux across the jet was found to be within ±5% of the nozzle input and the integral of radial diffusive flux of turbulent kinetic energy across the jet calculated from the measured third moments was found to be close to zero.

We consider the deformation and burst of small fluid droplets in steady linear, two-dimensional motions of a second immiscible fluid. Experiments using a computer-controlled, four-roll mill to investigate the effect of flow type are described, and the results compared with predictions of several available asymptotic deformation and burst theories, as well as numerical calculations. The comparison clarifies the range of validity of the theories, and demonstrates that they provide quite adequate predictions over a wide range of viscosity ratio, capillary number, and flow type.

The position of the region of transition to turbulence and the manner in which turbulence develops are investigated using a hot-wire anemometer to study the character of the flow in the wake of a circular cylinder. In the range of Reynolds numbers greater than 200 in which turbulent motion is developed, the region of transition to turbulence moves towards the cylinder with increasing Reynolds number. The manner of transition to turbulence appears to undergo a basic change as the region of transition moves from the periodic wake into the region of flow immediately behind the cylinder where the separated layers have not rolled into vortices, that is, as the Reynolds number increases from Roshko's transition range to his irregular range. When transition occurs in the periodic wake it is a result of distortion due to large-scale three-dimensional effects. Turbulence, when it develops in the separated layers, is preceded by two-dimensional Tollmien-Schlichting waves which eventually degenerate to turbulence by the action of small-scale three-dimensionalities.

The wall structure of the turbulent boundary layer was examined using hot-wire rakes and conditional sampling techniques. Instantaneous velocity measurements indicate a high degree of coherence over a considerable area in the direction normal to the wall. At y+ = 15, there is some evidence of large-scale correlation in the spanwise direction, but almost no indication of the streamwise streaks that exist in the lower regions of the boundary layer. Conditional sampling showed that the normal velocity is directed outwards in regions of strong stream-wise-momentum deficit, and inwards when the streamwise velocity exceeds its mean value. The conditionally averaged Reynolds shear stress was approximately an order of magnitude greater than its conventionally averaged value and decayed slowly downstream.

The dynamics of laser-produced cavitation bubbles near a solid boundary and its dependence on the distance between bubble and wall are investigated experimentally. It is shown by means of high-speed photography with up to 1 million frames/s that jet and counterjet formation and the development of a ring vortex resulting from the jet flow are general features of the bubble dynamics near solid boundaries. The fluid velocity field in the vicinity of the cavitation bubble is determined with time-resolved particle image velocimetry. A comparison of path lines deduced from successive measurements shows good agreement with the results of numerical calculations by Kucera & Blake (1988). The pressure amplitude, the profile and the energy of the acoustic transients emitted during spherical bubble collapse and the collapse near a rigid boundary are measured with a hydrophone and an optical detection technique. Sound emission is the main damping mechanism in spherical bubble collapse, whereas it plays a minor part in the damping of aspherical collapse. The duration of the acoustic transients is 20-30 ns. The highest pressure amplitudes at the solid boundary have been found for bubbles attached to the boundary. The pressure inside the bubble and at the boundary reaches about 2.5 kbar when the maximum bubble radius is 3.5 mm. The results are discussed with respect to the mechanism of cavitation erosion.

This paper describes the use of a hot film flowmeter in the sea and presents experimental measurements of the ‘downstream’ component of turbulent velocity in a tidal channel. The Reynolds number of the flow is about 108 and the scale of the turbulence is so large that a ship is carried about to a considerable extent by the energy-containing eddies. Under these conditions, a velocity measuring probe attached to a ship cannot be used for reliable measurements in the energy-containing range of the spectrum. It is possible, however, to observe the intertial and dissipation ranges. Records have been made at various stages of the tide. The one-dimensional spectra are found to be proportional to $k|^{-{\frac {5}{3}}}$ for several decades in k as predicted by Kolmogoroff, and a value is given for Kolmogoroff's constant. In the dissipation range there is close agreement with both Kovasznay's theory and Heisenberg's theory. These two theories are not very different in the low wave-number end of the range and the observations do not extend to high enough wave-numbers to distinguish between them.

A model for the movement of a small viscous droplet on a surface is constructed that is based on the lubrication equations and uses the dynamic contact angle to describe the forces acting on the fluid at the contact line. The problems analysed are: the spreading or retraction of a circular droplet; the advance of a thin two-dimensional layer; the creeping of a droplet or cell on a coated surface to a region of greater adhesion; the distortion of droplet shape owing to surface contamination. Relevant biological problems concerning cell movement and adhesion are described.

The radial dynamics of a spherical bubble in a compressible liquid is studied by means of a simplified singular-perturbation method to first order in the bubble-wall Mach number. It is shown that, at this order, a one-parameter family of approximate equations for the bubble radius exists, which includes those previously derived by Herring and Keller as special cases. The relative merits of these and other equations of the family are judged by comparison with numerical results obtained from the complete partial-differential-equation formulation by the method of characteristics. It is concluded that an equation close to the Keller form, but written in terms of the enthalpy of the liquid at the bubble wall, rather than the pressure, is most accurate, at least for the cases considered of collapse in a constant-pressure field and collapse driven by a Gaussian pressure pulse. A physical discussion of the magnitude and nature of compressibility effects is also given.

The mechanisms of sound generation in a Mach 0.9, Reynolds number 3600 turbulent jet are investigated by direct numerical simulation. Details of the numerical method are briefly outlined and results are validated against an experiment at the same flow conditions (Stromberg, McLaughlin & Troutt 1980). Lighthill's theory is used to define a nominal acoustic source in the jet, and a numerical solution of Lighthill's equation is compared to the simulation to verify the computational procedures. The acoustic source is Fourier transformed in the axial coordinate and time and then filtered in order to identify and separate components capable of radiating to the far field. This procedure indicates that the peak radiating component of the source is coincident with neither the peak of the full unfiltered source nor that of the turbulent kinetic energy. The phase velocities of significant components range from approximately 5% to 50% of the ambient sound speed which calls into question the commonly made assumption that the noise sources convect at a single velocity. Space–time correlations demonstrate that the sources are not acoustically compact in the streamwise direction and that the portion of the source that radiates at angles greater than 45° is stationary. Filtering non-radiating wavenumber components of the source at single frequencies reveals that a simple modulated wave forms for the source, as might be predicted by linear stability analysis. At small angles from the jet axis the noise from these modes is highly directional, better described by an exponential than a standard Doppler factor.

It is now well-known that the wake transition regime for a circular cylinder involves two modes of small-scale three-dimensional instability (modes A and B), depending on the regime of Reynolds number (Re), although almost no understanding of the physical origins of these instabilities, or indeed their effects on near-wake formation, have hitherto been made clear. We address these questions in this paper. In particular, it is found that the two different modes A and B scale on different physical features of the flow. Mode A has a larger spanwise wavelength of around 3–4 diameters, and scales on the larger physical structure in the flow, namely the primary vortex core. The wavelength for mode A is shown to be the result of an ‘elliptic instability’ in the nearwake vortex cores. The subsequent nonlinear growth of vortex loops is due to a feedback from one vortex to the next, involving spanwise-periodic deformation of core vorticity, which is then subject to streamwise stretching in the braid regios. This mode gives an out-of-phase streamwise vortex pattern.

In contrast, mode-B instability has a distinctly smaller wavelength (1 diameter) which scales on the smaller physical structure in the flow, the braid shear layer. It is a manifestation of an instability in a region of hyperbolic flow. It is quite distinct from other shear flows, in that it depends on the reverse flow of the bluff-body wake; the presence of a fully formed streamwise vortex system, brought upstream from a previous half-cycle, in proximity to the newly evolving braid shear layer, leads to an in-phase stream-wise vortex array, in strong analogy with the ‘Mode 1’ of Meiburg & Lasheras (1988) for a forced unseparated wake. In mode B, we also observe amalgamation of streamwise vortices from a previous braid with like-sign vortices in the subsequent braid.

It is deduced that the large scatter in previous measurements concerning mode A is due to the presence of vortex dislocations. Dislocations are triggered at the sites of some vortex loops of mode A, and represent a natural breakdown of the periodicity of mode A instability. By minimizing or avoiding the dislocations which occur from end contamination or which occur during wake transition, we find an excellent agreement of both critical Re and spanwise wavelength of mode A with the recent secondary stability analysis of Barkley & Henderson (1996).

Wake transition is further characterized by velocity and pressure measurements. It is consistent that, when mode-A instability and large-scale dislocations appear, one finds a reduction of base suction, a reduction of (two-dimensional) Reynolds stress level, a growth in size of the formation region, and a corresponding drop in Strouhal frequency. Finally, the present work leads us to a new clarification of the possible flow states through transition. Right through this regime of Re, there exist two distinct and continuous Strouhal frequency curves: the upper one corresponds with purley small- scale instabilities (e.g. denoted as mode A), while the lower curve corresponds with a combination of small-scale plus dislocation structures (e.g. mode A*). However, some of the flow states are transient or ‘unstable’, and the natural transitioning wake appears to follow the scenario: (2D→A*→B).

The onset of steady, cellular convection driven by surface tension gradients on a thin layer of liquid is examined in an extension of Pearson's (1958) stability analysis. By accounting for the possibility of shape deformations of the free surface it is found that there is no critical Marangoni number for the onset of stationary instability and that the limiting case of ‘zero wave-number’ is always unstable. Surface viscosity of a Newtonian interface is found to inhibit stationary instability. A simple criterion is found for distinguishing visually the dominant force, buoyancy or surface tension, in cellular convection in liquid pools.

An experimental study of the response of a thin uniformly heated rotating layer of fluid is presented. It is shown that the stability of the fluid depends strongly upon the three parameters that described its state, namely the Rayleigh number, the Taylor number and the Prandtl number. For the two Prandtl numbers considered, 6·8 and 0·025 corresponding to water and mercury, linear theory is insufficient to fully describe their stability properties. For water, subcritical instability will occur for all Taylor numbers greater than 5 × 104, whereas mercury exhibits a subcritical instability only for finite Taylor numbers less than 105. At all other Taylor numbers there is good agreement between linear theory and experiment.

The heat flux in these two fluids has been measured over a wide range of Rayleigh and Taylor numbers. Generally, much higher Nusselt numbers are found with water than with mercury. In water, at any Rayleigh number greater than 104, it is found that the Nusselt number will increase by about 10% as the Taylor number is increased from zero to a certain value, which depends on the Rayleigh number. It is suggested that this increase in the heat flux results from a perturbation of the velocity boundary layer with an ‘Ekman-layer-like’ profile in such a way that the scale of boundary layer is reduced. In mercury, on the other hand, the heat flux decreases monotonically with increasing Taylor number. Over a range of Rayleigh numbers (at large Taylor numbers) oscillatory convection is preferred although it is inefficient at transporting heat. Above a certain Rayleigh number, less than the critical value for steady convection according to linear theory, the heat flux increases more rapidly and the convection becomes increasingly irregular as is shown by the temperature fluctuations at a point in the fluid.

Photographs of the convective flow in a silicone oil (Prandtl number = 100) at various rotation rates are shown. From these a rough estimate is obtained of the dominant horizontal convective scale as a function of the Rayleigh and Taylor numbers.

A detailed experimental study has been made to clarify the mechanism of impulsive pressure generation from a single bubble collapsing in a static fluid – this is the most essential and important research task concerned with cavitation damage. First, the general feature of impulsive pressure generation is discussed, and then the impulsive pressure directly contributing to damage is investigated by various means. As a result, it is found that the impulsive pressure causing plastic deformation of material is closely related, directly or indirectly, to the behaviour of a liquid jet. Further more, it is demonstrated that the interaction of a tiny bubble with a shock wave or a pressure wave must be an important effect in producing a local high pressure which causes damage to material. The damage pit caused by the bubble-shock-wave interaction essentially results from the impact pressure from a liquid microjet.

Modelling of the complete second-order structure of homogeneous, neutrally stratified atmospheric boundary-layer turbulence, including spectra of all velocity components and cross-spectra of any combination of velocity components at two arbitrarily chosen points, is attempted. Two models based on Rapid Distortion Theory (RDT) are investigated. Both models assume the velocity profile in the height interval of interest to be approximately linear. The linearized Navier–Stokes equation together with considerations of ‘eddy’ lifetimes are then used to modify the spatial second-order structure of the turbulence. The second model differs from the first by modelling the blocking by the surface in addition to the shear. The resulting models of the spectral velocity tensor contain only three adjustable parameters: a lengthscale describing the size of the largest energy-containing eddies, a non-dimensional number used in the parametrization of ‘eddy’ lifetime, and the third parameter is a measure of the energy dissipation.

Two atmospheric experiments, both designed to investigate the spatial structure of turbulence and both running for approximately one year, are used to test and calibrate the models. Even though the approximations leading to the models are very crude they are capable of predicting well the two-point second-order statistics such as cross-spectra, coherences and phases, on the basis of measurements carried out at one point. The two models give very similar predictions, the largest difference being in the coherences involving vertical velocity fluctuations, where the blocking by the surface seems to have a significant effect.

Measurements of heat transfer from circular wires placed normal to a horizontal airstream have been made in the Reynolds number range 0·01 to 140. The Nusselt number can be related to the Reynolds number and temperature loading by an expression of the form $N \left(\frac {T_m}{T_\infty} \right)^{-0\cdot 17} = A + BR^n,$

where the values of n, A and B (see table 3) depend on whether the Reynolds number is above or below the value for which a vortex street exists in the wake of the wire. This value of the Reynolds number (R [eDot ] 44) is independent of the intensity and scale of the stream turbulence. The theoretical heat transfer relation based on the Oseen approximation is approached asymptotically as R → 0, provided free convection is negligible.

Free convection effects diminish rapidly with increasing Reynolds number so that the orientation of the wire with respect to the vertical has a negligible influence on heat transfer except at very low velocities. For horizontal wires at very low Reynolds numbers, free convection is significant, when, roughly speaking, the Reynolds number is less than the cube root of the Grashof number.

We develop a robust numerical method for modelling nonlinear gravity waves which is based on the Zakharov equation/mode-coupling idea but is generalized to include interactions up to an arbitrary order M in wave steepness. A large number (N = O(1000)) of free wave modes are typically used whose amplitude evolutions are determined through a pseudospectral treatment of the nonlinear free-surface conditions. The computational effort is directly proportional to N and M, and the convergence with N and M is exponentially fast for waves up to approximately 80% of Stokes limiting steepness (ka ∼ 0.35). The efficiency and accuracy of the method is demonstrated by comparisons to fully nonlinear semi-Lagrangian computations (Vinje & Brevig 1981); calculations of long-time evolution of wavetrains using the modified (fourth-order) Zakharov equations (Stiassnie & Shemer 1987); and experimental measurements of a travelling wave packet (Su 1982). As a final example of the usefulness of the method, we consider the nonlinear interactions between two colliding wave envelopes of different carrier frequencies.

An efficient and robust computational method, based on the lattice-Boltzmann method, is presented for analysis of impermeable solid particle(s) suspended in fluid with inertia. In contrast to previous lattice-Boltzmann approaches, the present method can be used for any solid-to-fluid density ratio. The details of the numerical technique and implementation of the boundary conditions are presented. The accuracy and robustness of the method is demonstrated by simulating the flow over a circular cylinder in a two-dimensional channel, a circular cylinder in simple shear flow, sedimentation of a circular cylinder in a two-dimensional channel, and sedimentation of a sphere in a three-dimensional channel. With a solid-to-fluid density ratio close to one, new results from two-dimensional and three-dimensional computational analysis of dynamics of an ellipse and an ellipsoid in a simple shear flow, as well as two-dimensional and three-dimensional results for sedimenting ellipses and prolate spheroids, are presented.

If granular materials comprising particles of identical material but different sizes are sheared in the presence of a gravitational field, the particles are segregated according to size. The small particles fall to the bottom and the larger ones drift to the top of the sheared layer. In an attempt to isolate and study some of the essential segregation mechanisms, the paper considers a simplified problem involving the steady two-dimensional flow of a binary mixture of small and large spherical particles flowing down a roughened inclined chute. The flow is assumed to take place in layers that are in motion relative to one another as a result of the mean shear. For relatively slow flows, it is proposed that there are two main mechanisms responsible for the transfer of particles between layers. The first mechanism, termed the ‘random fluctuating sieve’, is a gravity-induced, size-dependent, void-filling mechanism. The probability of capture of a particle in one layer by a randomly generated void space in the underlying layer is calculated as a function of the relative motion of the two layers. The second, termed the ‘squeeze expulsion’ mechanism, is due to imbalances in contact forces on an individual particle which squeeze it out of its own layer into an adjacent one. It is assumed that this mechanism is not size preferential and that there is no inherent preferential direction for the layer transfer. This second physical mechanism in particular was proposed on the basis of observations of video recordings that were played back at slow speed. Since the magnitude of its contribution is determined by the satisfaction of overall mass conservation, the exact physical nature of the mechanism is of less importance. By combining these two proposed mechanisms the net percolation velocity of each species is obtained. The mass conservation equation for fines is solved by the method of characteristics to obtain the development of concentration profiles with downstream distance. Although the theory involves a number of empirical constants, their magnitude can be estimated with a fair degree of accuracy. A solution for the limiting case of dilute concentration of fine particles and a more general solution for arbitrary concentrations are presented. The analyses are compared with experiments which measured the development of concentration profiles during the flow of a binary mixture of coarse and fine particles down a roughened inclined chute. Reasonable agreement is found between the measured and predicted concentration profiles and the distance required for the complete separation of fine from coarse particles.