Inkjet technology is a commendable tool in many applications including graphics printing, bioengineering and micro-electromechanical systems (MEMS). Droplet stability is a key factor influencing inkjet performance. The stability can be analysed using dimensionless numbers that usually combine thermophysical properties and system dimensions. In this paper, a drop-on-demand (DOD) inkjet experimental system is established. A numerical model is developed to investigate the influence of the operating conditions on droplet stability, including nozzle dimensions, driving parameters (the pulse amplitude and width used to drive droplet formation) and fluid properties. The results indicate that the stability can be improved by decreasing the pulse amplitude and width, decreasing the fluid density and viscosity or increasing the nozzle diameter and fluid surface tension. Based on case analysis and modelling, a dimensionless number ($Z$), the reciprocal of the Ohnesorge number, is numerically determined for a stable droplet to lie in a range between 4 and 8. To explicitly combine the driving parameters, a new stability criterion, $Pj$, is further proposed. A general rule taking into account both $Pj$ and $Z$ is proposed for choosing appropriate driving parameters to eject stable droplets for a known nozzle and fluid, which is further validated by experiments.

A reduced model is developed for low-Rossby-number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominantly aligned with the axis of rotation, Ekman boundary layers immediately adjacent to the bounding plates, and thermal wind layers driven by Ekman pumping in between. The reduced model uses a classical Ekman pumping parameterization to alleviate the need to resolve the Ekman boundary layers. Results are presented for both linear stability theory and a special class of nonlinear solutions described by a single horizontal spatial wavenumber. It is shown that Ekman pumping (which correlates positively with interior convection) allows for significant enhancement in the heat transport relative to that observed in simulations with stress-free boundaries. Without the intermediate thermal wind layer, the nonlinear feedback from Ekman pumping would be able to generate heat transport that diverges to infinity at finite Rayleigh number. This layer arrests this blowup, resulting in finite heat transport at a significantly enhanced value. With increasing buoyancy forcing, the heat transport transitions to a more efficient regime, a transition that is always achieved within the regime of asymptotic validity of the theory, suggesting that this behaviour may be prevalent in geophysical and astrophysical settings. As the rotation rate increases, the slope of the heat transport curve below this transition steepens, a result that is in agreement with observations from laboratory experiments and direct numerical simulations.

Active control of flow over a sphere at $\hbox{\it Re}\,{=}\,10^5$, based on the free-stream velocity $U_{\infty}$ and sphere diameter $d$, is carried out for drag reduction using a time-periodic blowing and suction from a slit on the sphere surface. The forcing frequency range considered is one to thirty times the natural vortex-shedding frequency. With the forcing, the drag on the sphere significantly decreases by nearly 50% for the forcing frequencies larger than a critical frequency (about $2.85 U_\infty$/{\it d}$). For the forcing frequencies smaller than this critical frequency, the drag is either nearly the same as, or slightly smaller than, that without forcing. The critical forcing frequency is found to be closely associated with the onset of the boundary-layer instability. It is shown from the surface-pressure measurement, surface oil-flow visualization and near-wall streamwise velocity measurement that the disturbances from the high-frequency forcing grow inside the boundary layer and delay the first separation while maintaining laminar separation, and they grow further along the separated shear layer and high momentum in the free stream is entrained toward the sphere surface, resulting in the reattachment of the flow (thus forming a separation bubble above the sphere surface) and the delay of the main separation. The reverse flow region in the wake is significantly reduced and the motion in that region also becomes weak owing to the forcing. Finally, the variation of drag by the present forcing with respect to the Reynolds number is very similar to that by dimples on the surface, but is different from that by surface roughness.

This paper describes the behaviour of a turbulent boundary layer on a smooth, axisymmetric body exposed to an adverse pressure gradient of sufficient strength to cause a short region of mean reverse flow ('separation’). The pressure distribution is tailored such that the boundary layer reattaches and then develops in a nominally zero pressure gradient. Hot-wire and pulsed-wire measurements are presented over the separated region and downstream of reattachment. The response of the turbulence quantities to separation and to reattachment is discussed, with emphasis on the relaxation behaviour after reattachment. Over the separation bubble, the response is characteristic of that seen by other workers: the Reynolds stresses in the inner region are reduced and stress peaks develop away from the wall. At reattachment, the skewness of the fluctuating wall shear stress vanishes, as it is known to do at separation. After reattachment, the outer-layer stresses decay towards levels typical of unperturbed boundary layers. But the inner-layer relaxation is unusual. As the viscous wall stress increases downstream of reattachment, the recovery does not start at the wall and travel outward via the formation of an ‘internal’ layer, the process observed in many other relaxing flows. In fact, the inner layer responds markedly more slowly than the outer layer, even though response times are shortest near the wall. It is concluded that the large-scale, outer structures in the turbulent boundary layer survive the separation process and interfere with the regeneration of Reynolds stresses in the inner region after reattachment. This behaviour continues for at least six bubble lengths (20 boundary-layer thicknesses) after reattachment and is believed to have profound implications for our understanding of the interaction between inner and outer layers in turbulent boundary layers.

We study the effect of interactions between objects floating at fluid interfaces, for the case in which the objects are primarily supported by surface tension. We give conditions on the density and size of these objects for equilibrium to be possible and show that two objects that float when well-separated may sink as the separation between them is decreased. Finally, we examine the equilbrium of a raft of strips floating at an interface, and find that rafts of sufficiently low density may have infinite spatial extent, but that above a critical raft density, all rafts sink if they are sufficiently large. We compare our numerical and asymptotic results with some simple table-top experiments, and find good quantitative agreement.

In this paper we used simulation tools to study turbulent boundary-layer structures in the roughness sublayer. Of particular interest is the case of a neutrally-stratified atmospheric boundary layer in which the lower boundary is covered by a homogeneous plant canopy. The goal of this study was to formulate a consistent conceptual model for the creation and evolution of the dominant coherent structures associated with canopy roughness and how they link with features observed in the overlying inertial sublayer. First, coherent structures were examined using temporally developing flow where the full range of turbulent scales had not yet developed, which allowed for instantaneous visualizations. These visualizations were used to formulate a conceptual model, which was then further tested using composite-averaged structure realizations from fully-developed flow with a very large Reynolds number. This study concluded that quasi two-dimensional mixing-layer-like roller structures exist in the developed flow and give the largest contributions to mean Reynolds stresses near the canopy. This work fully acknowledges the presence of highly three-dimensional and localized vortex pairing processes. The primary argument is that, as in a mixing layer, the smaller three-dimensional vortex interactions do not destroy the larger two-dimensional structure. Because the flow has a very large Reynolds number, the roller-like structures are not well-defined vortices but rather are a conglomerate of a large range of smaller-scale vortex structures that create irregularities. Because of this, the larger-scale structure is more difficult to detect in correlation or conditional sampling analyses. The frequently reported ‘scalar microfronts’ and associated spikes in pressure occur in the slip-like region between adjacent rollers. As smaller vortices within roller structures stretch, they evolve to form arch- and hairpin-shaped structures. Blocking by the low-flux canopy creates vertical asymmetry, and tends to impede the vertical progression of head-down structures. Head-up hairpins are allowed to continually stretch upward into the overlying inertial sublayer, where they evolve into the hairpin structures commonly reported to populate wall-bounded flows. This process is thought to be modulated by boundary-layer-scale secondary instability, which enhances head-up hairpin formation along quasi-streamwise transects.

We present numerical solutions for two-dimensional laminar symmetric vortex systems descending in a stably stratified fluid, within the Boussinesq approximation. Three types of flows are considered: (I) tight vortices; (II) those deriving from an elliptical wing lift distribution; and (III) those deriving from a ‘high-lift’ distribution, with a part-span flap on the wing. The non-dimensional stratification ranges from zero to moderate, as it does for airliners. For Types I and II, with high Reynolds numbers and weak stratification, the solutions confirm the theory of Scorer & Davenport (1970) (their article lacks a crucial link which we provide, equivalent to one of Crow (1974)). Contrary to common conceptions and observations in small-scale experiments, the descent velocity increases exponentially with time, as the distance between vortices decreases and the circulation of the vortices proper is conserved. With moderate stratification, wakes with sufficient energy also attain the accelerating régime, until the vortex cores make contact. However, they first experience a rebound, which is both of practical importance and out of reach of simple formulas. Type III wakes produce two durable vortex pairs which tumble, and mitigate the buoyancy effect by exchanging fluid with the surroundings. These phenomena are obscured by low wing aspect ratios, Reynolds numbers below about 105, or appreciable surrounding turbulence; this may explain why neither a clear rebound nor an acceleration can be reconciled with experiments to date. We argue that airliner wakes have very little inherent diffusion, and that a rapid end to the wake's descent must reveal effects other than simple buoyancy. In particular, stratification promotes the Crow instability.

Theoretical and experimental studies have been performed on fully developed twodimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u* for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. A Coriolis region where the Coriolis force effect predominates is shown to exist in addition to conventional regions such as viscous and buffer regions. A flow regime diagram that indicates ranges of these regions as a function of Re* and |Ω|v/u2* is given from which the overall flow structure in a rotating channel can be obtained.

Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u2* ≤ 0.0030 (these values correspond to Re = 2UmD/v from 1700 to 10000 and rotation number R0 = 2|Ω|D/Um up to 0.055; Um is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.

Finite-difference calculations with random and single-mode perturbations are used to study the three-dimensional instability of vortex rings. The basis of current understanding of the subject consists of a heuristic inviscid model (Widnall, Bliss & Tsai 1974) and a rigorous theory which predicts growth rates for thin-core uniform vorticity rings (Widnall & Tsai 1977). At sufficiently high Reynolds numbers the results correspond qualitatively to those predicted by the heuristic model: multiple bands of wavenumbers are amplified, each band having a distinct radial structure. However, a viscous correction factor to the peak inviscid growth rate is found. It is well described by the first term, 1 – α1(β)/Res, for a large range of Res. Here Res is the Reynolds number defined by Saffman (1978), which involves the curvature-induced strain rate. It is found to be the appropriate choice since then α1(β) varies weakly with core thickness β. The three most nonlinearly amplified modes are a mean azimuthal velocity in the form of opposing streams, an n = 1 mode (n is the azimuthal wavenumber) which arises from the interaction of two second-mode bending waves and the harmonic of the primary second mode. When a single wave is excited, higher harmonics begin to grow successively later with nonlinear growth rates proportional to n. The modified mean flow has a doubly peaked azimuthal vorticity. Since the curvature-induced strain is not exactly stagnation-point flow there is a preference for elongation towards the rear of the ring: the outer structure of the instability wave forms a long wake consisting of n hairpin vortices whose waviness is phase shifted π/n relative to the waviness in the core. Whereas the most amplified linear mode has three radial layers of structure, higher radial modes having more layers of radial structure (hairpins piled upon hairpins) are excited when the initial perturbation is large, reminiscent of visualization experiments on the formation of a turbulent ring at the generator.

The purpose of this analytical work is twofold: first, to clarify the physical mechanisms triggering the one-dimensional instabilities of plane detonations in gases; secondly to provide a nonlinear description of the longitudinal dynamics valid even far from the bifurcation. The fluctuations of the rate of heat release result from the temperature fluctuations of the shocked gas with a time delay introduced by the propagation of entropy waves. The motion of the shock is governed by a mass conservation resulting from the gas expansion across the reaction zone whose position fluctuates relative to the inert shock. The effects of longitudinal acoustic waves are quite negligible in pistonsupported detonations at high overdrives with a small difference of specific heats. This limit leads to a useful quasi-isobaric approximation for enlightening the basic mechanism of galloping detonations. Strong nonlinear effects, free from the spurious singularities of the square-wave model, are picked up by considering two different temperature sensitivities of the overall reaction rate: one governing the induction length, another one the thickness of the exothermic zone. A nonlinear integral equation for the longitudinal dynamics of overdriven detonations is obtained as an asymptotic solution of the reactive Euler equations. The analysis uses a distinguished limit based on an infinitely large temperature sensitivity of the induction kinetics and a small difference of specific heats. Comparisons with numerical calculations show a satisfactory agreement even outside the limits of validity of the asymptotic solution.

The statistics of unsteady turbulence with uniform stratification $N$ (Brunt–Väisälä frequency) and shear $\alpha ({=}\,{\rm d}U_{1}/{\rm d}x_{3})$ are analysed over the entire time range ($0 \,{<}\, \alpha t \,{<}\, \infty$) using rapid distortion theory (RDT) over a wide range of Richardson number ${\hbox{\it Ri}} ({=}\,N^{2}/\alpha^{2})$, and initial conditions. The solutions are found to be described by the Legendre functions of complex degree with pure-imaginary argument and are compared with previously published results of both direct numerical simulations (DNS) and experiments. In the initial stage of development many of the characteristics are similar to those in stratified flow with no shear, since the turbulence is determined by $\hbox{\it Nt}$ at the leading order, and the effects of vertical shear $\alpha$ generally appear at higher order. It is shown how in developing turbulence for ${\hbox{\it Ri}} \,{>}\, 0$ and ${\hbox{\it Ri}} \,{>}\, 0.25$ respectively, oscillatory momentum and positive and negative density fluxes develop. Above a critical value of ${\hbox{\it Ri}}_{\hbox{\scriptsize\it crit}} ({\sim}\,0.3)$, their average values are persistently countergradient. This structural change in the turbulence is the primary mechanism whereby stable stratification reduces the fluxes and the production of variances. It is quite universal and differs from the energy and stability mechanisms of Richardson (1926) and Taylor (1931). The long-time asymptotics of the energy ratio ER$({=}\,\hbox{\it PE/VKE}$) of the potential energy to the vertical kinetic energy generally decreases with ${\hbox{\it Ri}}({\geq}\,0.25)$, reaching the smallest value of $3/2$ when there is no shear (${\hbox{\it Ri}} \,{\rightarrow}\, \infty$). For strong mean shear (${\hbox{\it Ri}}\,{<}\,0.25$), RDT significantly overestimates ER since (as in unstratified shear flow) it underestimates the vertical kinetic energy VKE. The RDT results show that the asymptotic values of the energy ratio ER and the normalized vertical density flux are independent of the initial value of ER, in agreement with DNS. This independence of the initial condition occurs because the ratios of the contributions from the initial values $P\!E_{0}$ and $K\!E_{0}$ are the same for PE and VKE and can be explained by the linear processes. Stable stratification generates buoyancy oscillations in the direction of the energy propagation of the internal gravity wave and suppresses the generation of turbulence by mean shear. Because the shear distorts the wavenumber fluctuations, the low-wavenumber spectrum of the vertical kinetic energy has the general form $E_{33}(k)\,{\propto}\, (\alpha tk)^{-1}$, where $(L_{X} \alpha t)^{-1} \,{\ll}\,k \,{\ll}\,L_{X}^{-1}$ ($L_{X}$: integral scale). The viscous decay is controlled by the shear, so that the components of larger streamwise wavenumber $k_{1}$ decay faster. Then, combined with the spectrum distortion by the shear, the energy and the flux are increasingly dominated by the small-$k_{1}$ components as time elapses. They oscillate at the buoyancy period $\pi/N$ because even in a shear flow the components as $k_{1} \,{\rightarrow}\, 0$ are weakly affected by the shear. The effects of stratification $N$ and shear $\alpha$ at small scales are to reduce both VKE and PE. Even for the same ${\hbox{\it Ri}}$, larger $N$ and $\alpha$ reduce the high-wavenumber components of VKE and PE. This supports the applicability of the linear assumption for large $N$ and $\alpha$. At large scales, the stratification and shear effects oppose each other, i.e. both VKE and PE decrease due to the stratification but they increase due to the shear. We conclude that certain of these unsteady results can be applied directly to estimate the properties of sheared turbulence in a statistically steady state, but others can only be applied qualitatively.

A hot-film anemometer has been used to investigate the mean velocity and turbulence intensity distributions in turbulent radial jets. A geometric parameter termed the constraint ratio, defined as the ratio of nozzle diameter to separation distance, is shown to characterize radial-jet behaviour. Large values of the constraint ratio typify ‘constrained’ radial jets, for which the nozzle walls constrain the flow leaving the orifice to be parallel; a small constraint ratio is representative of two opposing free axisymmetric jets, the collision of which produces an ‘impinged’ radial jet. It is found that the well-behaved constrained radial jet spreads at the same rate as does the familiar plane jet, whereas the impinged radial jet spreads at a rate more than three times as fast. Neither type of radial jet is amenable to a self-similar analytic solution; however, while the impinged jet is shown to require numerical solution techniques, an empirical solution for the constrained jet is demonstrated.

Particle-size segregation commonly occurs in both wet and dry granular free-surface flows through the combined processes of kinetic sieving and squeeze expulsion. As the granular material is sheared downslope, the particle matrix dilates slightly and small grains tend to percolate down through the gaps, because they are more likely than the large grains to fit into the available space. Larger particles are then levered upwards in order to maintain an almost uniform solids volume fraction through the depth. Recent experimental observations suggest that a single small particle can percolate downwards through a matrix of large particles faster than a large particle can be levered upwards through a matrix of fines. In this paper, this effect is modelled by using a flux function that is asymmetric about its maximum point, differing from the symmetric quadratic form used in recent models of particle-size segregation. For illustration, a cubic flux function is examined in this paper, which can be either a convex or a non-convex function of the small-particle concentration. The method of characteristics is used to derive exact steady-state solutions for non-diffuse segregation in two dimensions, with an inflow concentration that is (i) homogeneous and (ii) normally graded, with small particles above the large. As well as generating shocks and expansion fans, the new asymmetric flux function generates semi-shocks, which have characteristics intersecting with the shock just from one side. In the absence of diffusive remixing, these can significantly enhance the distance over which complete segregation occurs.

A general theory which can be used to derive bounds on solutions to the Navier-Stokes equations is presented. The behaviour of the resolvent of the linear operator in the unstable half-plane is used to bound the energy growth of the full nonlinear problem. Plane Couette flow is used as an example. The norm of the resolvent in plane Couette flow in the unstable half-plane is proportional to the square of the Reynolds number (R). This is now used to predict the asymptotic behaviour of the threshold amplitude below which all disturbances eventually decay. A lower bound is found to be R−21/4. Examples, obained through direct numerical simulation, give an upper bound on the threshold curve, and predict a threshold of R−1. The discrepancy is discussed in the light of a model problem.

In high Reynolds-number turbulence, local scalar turbulence structure parameters,$( C_{\theta }^{2}) _{r}$, local scalar variance dissipation rates, $\chi _{r}$, and local energy dissipation rates, $\varepsilon _{r}$, vary randomly in time and space. This variability, commonly referred to as intermittency, is known to increase with decreasing $r$, where $r$ is the linear dimension of the local averaging volume. Statistical relationships between $\chi _{r}$, $\varepsilon _{r}$, and $( C_{\theta }^{2}) _{r}$ are of practical interest, for example, in optical and radar remote sensing. Some of these relationships are studied here, both theoretically and on the basis of recent observations. Two models for the conditionally averaged local temperature structure parameter, $\langle( C_{\theta }^{2}) _{r}| \varepsilon _{r}\rangle $, are derived. The first model assumes that the joint probability density function (j.p.d.f.) of $\chi _{r}$ and $\varepsilon _{r}$ is bivariate lognormal and that the Obukhov–Corrsin relationship, $( C_{\theta }^{2}) _{r}=\gamma\varepsilon _{r}^{-1/3}\chi _{r}$, where $\gamma\,{=}\,1.6$, is locally valid. In the second model, small-scale intermittency is ignored and $C_{\theta }^{2}$ and $\varepsilon $ are treated traditionally, that is, as averages over many outer scale lengths, such that $C_{\theta }^{2}$ and $\varepsilon $ change only as a result of large-scale intermittency. Both models lead to power-law relationships of the form $\langle( C_{\theta }^{2}) _{r}| \varepsilon _{r}\rangle \,{=}\,c\hspace{0.03in}\varepsilon _{r}^{\delta}$, where $c$ is a constant. Both models make predictions for the value of the power-law exponent $\delta$. The first model leads to $\delta\,{=}\,\rho _{xy}\sigma _{y}/\sigma _{x}-1/3$, where $\sigma _{x}$ and $\sigma _{y}$ are the standard deviations of the {logarithms} of $\varepsilon _{r}$ and $\chi _{r}$, respectively, and $\rho _{xy}$ is the correlation coefficient of the logarithms of $\chi _{r}$ and $\varepsilon _{r}$. This model leads to $\delta\,{=}\,1/3$ if $\rho _{xy}\,{=}\,2/3$ and if $\sigma _{x}\,{=}\,\sigma _{y}$. The second model predicts $\delta\,{=}\,2/3$, regardless of whether (i) static stability and shear are statistically independent, or (ii) they are connected through a Richardson-number criterion. These theoretical predictions are compared to fine-wire measurements that were taken during the night of 20/21 October 1999, at altitudes of up to 500 m in the nocturnal boundary layer and the overlying residual layer above Kansas. The fine-wire sensors were moved up and down with the University of Colorado's Tethered Lifting System (TLS). The data were obtained during the Cooperative Atmosphere-Surface Exchange Study 1999 (CASES-99). An interesting side result is that the observed frequency spectra of the logarithms of $\varepsilon _{r}$ and $\chi _{r}$ are described well by an $f^{-1}$ law. A simple theoretical explanation is offered.

Results from the numerical simulation of the two-dimensional incompressible unsteady Navier–Stokes equations for streaming flow past a rotating circular cylinder are presented in this study. The numerical solution of the equations of motion is conducted with a commercial computational fluid dynamics package which discretizes the equations applying the control volume method. The numerical set-up is validated by comparing results for a Reynolds number based on the free stream of $\hbox{\it Re}$ = 200 and dimensionless peripheral speed of $\tilde{q}$ = 3, 4 and 5 with results from the literature. After the validation stage, various pairs of $\hbox{\it Re}$ and $\tilde{q}$ are specified in order to carry out the numerical experiments. These values are $\hbox{\it Re}$ = 200 with $\tilde{q}$ = 4 and 5; $\hbox{\it Re}$ = 400 with $\tilde{q}$ = 4, 5 and 6, and $\hbox{\it Re}$ = 1000 with $\tilde{q}$ = 3. In all these cases, gentle convergence to fully developed steady state is reached. From the numerical vorticity distribution, the position of the outer edge of the vortical region is determined as a function of the angular coordinate. This position is found by means of a reasonable criterion set to define the outmost curve around the cylinder where the vorticity magnitude reaches a certain cut-off value. By considering the average value of this profile, a uniform vortical region thickness is specified for every pair of $\hbox{\it Re}$ and $\tilde{q}$.

Next, the theoretical approach of Wang & Joseph (2006a; see the companion paper) and the numerical results are used to determine two different values of the effective vortical region thickness for every pair of $\hbox{\it Re}$ and $\tilde{q}$. One effective thickness $\delta_D/a$ is obtained from the match between the additional drag on the outer edge of the vortical region according to the viscous correction of viscous potential flow (VCVPF) and the corresponding numerical profile while the other thickness $\delta_L/a$ is determined from the match between the pressure lift on the cylinder obtained from Wang & Joseph (2006a)'s simple modification of the boundary-layer analysis due to Glauert (Proc. R. Soc. Lond. A, vol. 242, 1957, p. 108) and the numerical value of the pressure lift coefficient. The values of $\delta_D/a$ and $\delta_L/a$ are used in the computation of various parameters associated with the flow, namely, the torque on the rotating cylinder, the circulatory velocity at the edge of the vortical region, which links the cylinder's angular velocity with the circulation of the irrotational flow of the viscous fluid outside this region, and the viscous dissipation. Predictions from the approaches of Glauert (1957) and Wang & Joseph (2006a) are also included for comparison. The values of both effective thicknesses, $\delta_D/a$ and $\delta_L/a$, are found to have the same order of magnitude. Then, we show that choosing $\delta_D/a$ as a unique effective thickness, the modification of Glauert's boundary-layer analysis and the VCVPF approach as proposed by Wang & Joseph (2006a) produce results which are in better general agreement with the values from numerical simulation than those from Glauert's solution.

The use of steady, normal and oblique shock configurations is explored in calculating the pressure and deformation produced by the impact of a liquid mass on a plane solid surface. Since pressures generated are very large, the change in bulk modulus of the liquid (water) is accounted for by using an equation of state following Field, Lesser & Davies (1979). The impact of a plane-ended liquid mass is analysed using a normal shock for the cases of a rigid surface and a perfectly plastic surface. For the former, it is found that pressures somewhat in excess of the ‘water-hammer’ pressure of linear acoustic theory are predicted, and for the latter there is a critical impact velocity below which no deformation occurs. Above this velocity the surface deforms at a constant rate, producing a pit with maximum depth at the centre.

If the liquid mass is wedge-shaped then an oblique shock is formed, which is attached to the contact point provided that the impact Mach number is large enough, as originally shown by Heymann (1969). Pressure and deformation velocity can again be calculated for the cases of rigid and perfectly plastic surfaces respectively. For a rigid surface it is confirmed that pressures considerably in excess of the plane-ended case are produced at shock detachment. For the plastic surface, it is found that there is no critical impact velocity and deformation can occur at any velocity as shock detachment is approached. For a cylindrical liquid mass with a conical tip, the pit produced again has maximum depth at the centre, but with a considerably increased value. The possible use of these models for pitting caused by microjets associated with cavitation bubbles and by impact of liquid drops is discussed.

The transport properties of a diffusive interface with diffusivity ratio $\kappa_S/\kappa_T = {\textstyle\frac{1}{3}}$ have been measured, using salt and sugar as the diffusing components. The flux ratio is constant and equal to (κS/κT)½. The normalized salt flux is related to the density anomaly ratio Rρ = βΔS/αΔT by the power law F*T = 2·59Rρ−12.6 over four decades. Optical measurements show that the vertical gradients of concentration of salt and sugar within the interface are those required if molecular diffusion is to account for the whole flux of each component.

The two-dimensional stationary flow past a rotating cylinder is investigated for both two- and three-dimensional perturbations. The instability mechanisms are analysed using linear stability analysis and the complete neutral curve is presented. It is shown that the first bifurcation in the case of the rotating cylinder occurs for stationary three-dimensional perturbations, confirming recent experiments. Interestingly, the critical Reynolds number at high rotation rates is lower than that for the stationary circular cylinder. The spatial characteristics of the disturbance and a qualitative comparison with the results obtained for linear flows suggest that the stationary unstable three-dimensional mode could be of hyperbolic nature.