Many experimenters have used oscillating grids to produce turbulence for various laboratory purposes, especially in studies of mixing, but there have been few direct measurements of the properties of the turbulence itself. In the present paper we report experiments which attempt to relate the turbulent velocity and length scales to the external parameters, the frequency and amplitude, for three forms of grid oscillated in a tank of water. Turbulent velocities have been measured in the absence of a mean flow by using a hot film moved through the fluid to provide its own mean velocity. The output is stored and analysed in a small computer, which rapidly evaluates velocity and length scale statistics from an ensemble of records. The spatial variation of these quantities with distance from the stirrer is of special interest. It agrees with results suggested by an inertial-decay theory, and with previous measurements made by Bouvard & Dumas (1967) using a different form of stirrer. A particular purpose of the work has been to ‘calibrate’ the entrainment experiments of Turner (1968), by providing absolute scales of velocity and length in the fluid near a mixing interface, for the same grid as was used in the earlier experiments. Evidence is presented which suggests that other forms of grid may not be calibrated simply by extrapolating these results.

Experimental measurements of the advancing head of a gravity current are described. The head, of depth d in mean cross-section and advancing at mean speed U, has an elevated nose whose mean height h satisfies h/d = 0·61 Re-0·23±0·01 through the range 300 < Re < 10000 (Re = Ud/ν). A shifting pattern of lobes and clefts ranges across the head, in which the mean lobe width $\overline{b}$ is found experimentally to satisfy $\overline{b}/d = 7.4\,Re^{-0.39\pm 0.02}$. By moving the floor in the direction of the current, or by introducing a thin dense layer beneath it, the lobes and clefts can be suppressed and a purely two-dimensional flow obtained. It is concluded that the lower boundary plays an essential role in determining the substructure of the head and that this originates in convective instability as the head rides over less dense fluid.

The shape evolution of small droplets attached to a conducting surface and subjected to relatively strong electric fields is studied both experimentally and numerically. The problem is motivated by the phenomena characteristic of the electrospinning of nanofibres. Three different scenarios of droplet shape evolution are distinguished, based on numerical solution of the Stokes equations for perfectly conducting droplets. (i) In sufficiently weak (subcritical) electric fields the droplets are stretched by the electric Maxwell stresses and acquire steady-state shapes where equilibrium is achieved by means of the surface tension. (ii) In stronger (supercritical) electric fields the Maxwell stresses overcome the surface tension, and jetting is initiated from the droplet tip if the static (initial) contact angle of the droplet with the conducting electrode is $\alpha_{s}\,{<}\,0.8\pi $; in this case the jet base acquires a quasi-steady, nearly conical shape with vertical semi-angle $\beta \,{\leq}\, 30^{\circ}$, which is significantly smaller than that of the Taylor cone ($\beta_{T}\,{=}\,49.3^{\circ}$). (iii) In supercritical electric fields acting on droplets with contact angle in the range $0.8\pi \,{<}\,\alpha_{s}\,{<}\,\pi $ there is no jetting and almost the whole droplet jumps off, similar to the gravity or drop-on-demand dripping. The droplet–jet transitional region and the jet region proper are studied in detail for the second case, using the quasi-one-dimensional equations with inertial effects and such additional features as the dielectric properties of the liquid (leaky dielectrics) taken into account. The flow in the transitional and jet region is matched to that in the droplet. By this means, the current–voltage characteristic $I\,{=}\,I(U)$ and the volumetric flow rate $Q$ in electrospun viscous jets are predicted, given the potential difference applied. The predicted dependence $I\,{=}\,I(U)$ is nonlinear due to the convective mechanism of charge redistribution superimposed on the conductive (ohmic) one. For $U\,{=}\,O(10kV)$ and fluid conductivity $\sigma \,{=}\,10^{-4}$ S m$^{-1}$, realistic current values $I\,{=}\,O(10^{2}nA)$ were predicted.

The laminar separation bubble on an SD7003 aerofoil at a Reynolds number Re = 66000 was investigated to determine the dominant frequencies of the transition process and the flapping of the bubble. The measurements were performed with a high-resolution time-resolved particle image velocimetry (TR-PIV) system. Contrary to typical measurements performed through conventional PIV, the different modes can be identified by applying TR-PIV. The interaction between the shed vortices is analysed, and their significance for the production of turbulence is presented. In the shear layer above the bubble the generation and amplification of vortices due to Kelvin–Helmholtz instabilities is observed. It is found that these instabilities have a weak coherence in the spanwise direction. In a later stage of transition these vortices lead to a three-dimensional breakdown to turbulence.

An experiment on the Saffman-Taylor instability with wetting fluids is presented that explores a greater range of capillary numbers than did the original experiment of Saffman and Taylor. It turns out that no clear one-half plateau for the finger size is observed, and that the ensemble of experiments cannot be analysed in terms of a single control parameter. The effect of the film of oil left behind the finger is important, and we measure its thickness. A qualitative discussion of the instabilities of the fingers for large capillary numbers is presented, the first instability leading to asymmetrical fingers. Tip splitting appears for larger values of 1/B. The 1/B value for the onset of instabilities is shown to be noise dependent.

We present an experimental investigation of flexible panels actuated with heave oscillations at their leading edge. Results are presented from kinematic video analysis, particle image velocimetry, and direct force measurements. Both the trailing edge amplitude and the mode shapes of the panel are found to scale with dimensionless parameters originating from the Euler–Bernoulli beam equation. The time-averaged net thrust increases with heaving frequency, but experiences localized boosts near resonant frequencies where the trailing edge amplitude is maximized. These boosts correspond to local maxima in the propulsive efficiency. For a constant heave amplitude, the time-averaged net thrust coefficient is shown to be a function of Strouhal number over a wide range of conditions. It appears, therefore, that self-propelled swimming (zero net thrust) only occurs over a small range of Strouhal numbers. Under these near-constant Strouhal number conditions, the propulsive economy increases with higher flexibilities and slower swimming speeds.

We study the initial-value problem posed by the small-amplitude (linearized) free oscillations of free drops, gas bubbles, and drops in a host liquid when viscous effects cannot be neglected. It is found that the motion consists of modulated damped oscillations, with the damping parameter and frequency approaching only asymptotically the results of the normal-mode analysis. The connexion with the normal-mode method is demonstrated explicitly and the experimental relevance of our results is discussed.

Perturbations of channel geometry (like variations of channel curvature or channel width) in meandering rivers give rise to morphodynamic effects which display themselves through the development of large-scale perturbations of bottom topography in the form of stationary bars developing in the longitudinal direction. The latter may then drive the lateral migration of the channel by enhancing bank erosion at bar pools: through this mechanism local perturbations of channel geometry may affect the planimetric development of meandering rivers on large timescales. The problem tackled herein is whether such morphodynamic influence is invariably felt downstream as the commonly employed model of river meandering would suggest.

In order to solve this problem, we derive the exact solution of the linearized form of the mathematical problem of river morphodynamics. Linear analysis had pointed out the existence of a resonance phenomenon: in a linear (hence ideal) context, resonance occurs when the meander wavenumber and the width ratio of the channel take values (λR and βR, respectively) such as to force free spatial modes of the system consisting of free bars which neither grow nor decay either in time or in space. Channels characterized by values of the width ratio β larger (smaller) than βR are called super- (sub-)resonant. The present solution, which applies to channels with constant width and arbitrary curvature distribution, shows that two distinct scenarios may occur: downstream influence is associated with sub-resonant channels and vice versa dominant upstream influence occurs in super-resonant channels. Small-amplitude waves of bottom topography are shown to migrate downstream in the former case and may migrate upstream in the latter, as resonance also defines the threshold conditions below (above) which small-amplitude alternate bar perturbations (may) migrate downstream (upstream).

These results have several implications. In the present paper we examine the overdeepening phenomenon whereby abrupt variations of channel curvature, as in sequences of straight and constant curvature reaches, lead to sequences of stationary alternate bars with amplitude decaying in the longitudinal direction. We show that, along with downstream overdeepening, an upstream overdeepening scenario is predicted in the super-resonant regime.

Implications of the upstream influence on planimetric development of meandering rivers are investigated in Part 2.

A model problem is analysed to study the microscopic flow near the surface of two-dimensional porous media. In the idealized problem we consider axial flow through infinite and semi-infinite lattices of cylindrical inclusions. The effect of lattice geometry and inclusion shape on the permeability and surface flow are examined. Calculations show that the definition of a slip coefficient for a porous medium is meaningful only for extremely dilute systems. Brinkman's equation gives reasonable predictions for the rate of decay of the mean velocity for certain simple geometries, but fails for to predict the correct behaviour for media anisotropic in the plane normal to the flow direction.

Simultaneous planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) yield measurements of two-dimensional jet fluid concentration and velocity fields in turbulent crossflowing jets. The jet-to-crossflow velocity ratio is $r = 5.7$ and the jet exit Reynolds number is approximately 5000. The measurements are focused on the developing region of the flow. Two flow configurations are studied, one in which the jet nozzle is flush with the tunnel wall and the other where the nozzle protrudes into the uniform region of the tunnel flow. The jet nozzle in both cases is a simple pipe. The averaged scalar and velocity fields show a strong similarity in growth rates and centreline decay rates between the two nozzle configurations when using the centreline downstream coordinate $s$. This suggests that the flow geometry is less important than, for example, jet exit conditions in determining the initial flow development. The velocity fields show indications of jet-like scaling in the near field, and a possible approach to wake-like scaling in the far field. These canonical scalings are less evident in the scalar fields. Results are presented for the averaged scalar variance, $\langle C^{'2}\rangle$, the scalar flux components, $\langle u_{i}'C'\rangle$, the turbulent normal stresses, $\langle u^{\prime 2}\rangle$ and $\langle v^{\prime 2}\rangle$, and the turbulent shear stress, $\langle u'v'\rangle$. We also discuss the resolution issues bearing on the determination of small-scale fluctuations.

A new continuum model is formulated for dilute suspensions of swimming microorganisms with asymmetric mass distributions. Account is taken of randomness in a cell's swimming direction, p, by postulating that the probability density function for p satisfies a Fokker–Planck equation analogous to that obtained for colloid suspensions in the presence of rotational Brownian motion. The deterministic torques on a cell, viscous and gravitational, are balanced by diffusion, represented by an isotropic rotary diffusivity Dr, which is unknown a priori, but presumably reflects stochastic influences on the cell's internal workings. When the Fokker-Planck equation is solved, macroscopic quantities such as the average cell velocity Vc, the particle diffusivity tensor D and the effective stress tensor Σ can be computed; Vc and D are required in the cell conservation equation, and Σ in the momentum equation. The Fokker-Planck equation contains two dimensionless parameters, λ and ε; λ is the ratio of the rotary diffusion time D-1r to the torque relaxation time B (balancing gravitational and viscous torques), while ε is a scale for the local vorticity or strain rate made dimensionless with B. In this paper we solve the Fokker–Planck equation exactly for ε = 0 (λ arbitrary) and also obtain the first-order solution for small ε. Using experimental data on Vc and D obtained with the swimming alga, Chamydomonas nivalis, in the absence of bulk flow, the ε = 0 results can be used to estimate the value of λ for that species (λ ≈ 2.2; Dr ≈ 0.13 s−1). The continuum model for small ε is then used to reanalyse the instability of a uniform suspension, previously investigated by Pedley, Hill & Kessler (1988). The only qualitatively different result is that there no longer seem to be circumstances in which disturbances with a non-zero vertical wavenumber are more unstable than purely horizontal disturbances. On the way, it is demonstrated that the only significant contribution to Σ, other than the basic Newtonian stress, is that derived from the stresslets associated with the cells’ intrinsic swimming motions.

When two liquid drops come into contact, they coalesce rapidly, owing to the large curvature and unbalanced surface-tension forces in the neck region. We use an ultra-high-speed video camera to study the coalescence of a pendent and a sessile drop, over a range of drop sizes and liquid viscosities. For low viscosity, the outward motion of the liquid contact region is successfully described by a dynamic capillary-inertial model based on the local vertical spacing between the two drop surfaces. This model applies even when the drops are of different sizes. Increasing viscosity slows down the coalescence when the Reynolds number $\hbox{\it Re}_v \,{=}\,\rho R_{\hbox{\scriptsize\it ave}}\sigma/\mu^2\,{<}\,5000$, where $R_{\hbox{\scriptsize\it ave}}$ is the average of the tip radii of the two similar size drops, $\rho$ is the liquid density, $\sigma$ is the surface tension and $\mu$ the dynamic viscosity. At $\hbox{\it Re}_v\,{\simeq}\,50$, the growth-rate of the neck radius has reduced by a half, which for water corresponds to a drop diameter of only 2\,$\umu$m. For the largest viscosities, the neck region initially grows in size at a constant velocity. The neck curvature also becomes progressively sharper with increasing viscosity. The results are compared to previously predicted power laws, finding slight, but significant deviations from the predicted exponents. These deviations are most probably caused by the finite initial contact radius.

The present study is to investigate the structure of space-time correlations of bursting motions, such as ejections and sweeps in an open-channel flow, by a new conditional sampling analysis of the instantaneous velocity and Reynolds-stress signals measured simultaneously by two dual-sensor hot-film probes. One probe was fixed near the edge of the buffer layer, while the other probe was moved in the streamwise, vertical and spanwise directions. The sorted instantaneous Reynolds-stress signals obtained from the fixed probe were used as a detecting information of the occurrences of ejection or sweep events. The streamwise and vertical spatial characteristics of the ejection-sweep motions, and their convection process are investigated in detail. Also, the spanwise spatial properties of the high- and low-speed streaks in the bursting motions are examined experimentally by the present conditional sampling method.

Next, a qualitative model is proposed which attempts to explain the space-time structures of the bursting phenomenon, on the basis of the above anemometry information and other visual observations.

The work presented here focuses on the analysis of a turbulent boundary layer saturated with saltating particles. Experiments were carried out in a wind tunnel 15m long and 0.6m wide at the University of Aarhus in Denmark with sand grains 242 μm in size for wind speeds ranging from the threshold speed to twice its value. The saltating particles were analysed using particle image velocimetry (PIV) and particle-tracking velocimetry (PTV), and vertical profiles of particle concentration and velocity were extracted. The particle concentration was found to decrease exponentially with the height above the bed, and the characteristic decay height was independent of the wind speed. In contrast with the logarithmic profile of the wind speed, the grain velocity was found to vary linearly with the height. In addition, the measurements indicated that the grain velocity profile depended only slightly on the wind speed. These results are shown to be closely related to the features of the splash function that characterizes the impact of the saltating particles on a sandbed. A numerical simulation is developed that explicitly incorporates low-velocity moments of the splash function in a calculation of the boundary conditions that apply at the bed. The overall features of the experimental measurements are reproduced by simulation.

The average thickness of the wetting film left behind during the slow passage of an air bubble in a water-filled capillary tube of circular cross-section has been determined experimentally as a function of bubble speed and bubble length. For bubbles of length many times the tube radius, the ratio of film thickness to tube radius is found to be a function of the capillary number only, in agreement with previous experimental studies. As has been found previously, the asymptotic result of Bretherton (1961) significantly underpredicts the film thickness, the discrepancy being greatest at the lowest speeds. For bubbles of length less than about 20 tube radii, on the other hand, good agreement with the Bretherton theory is obtained over two orders of magnitude in bubble speed. The theoretical profile of long bubbles is shown to be unstable; however the explanation of the observed behaviour is, as yet, incomplete.

The spatial distribution of the mean velocity in a two-dimensional turbulent wall jet was measured for a variety of nozzle Reynolds numbers. It was determined that the bulk of the flow is self-similar and it depends on the momentum flux at the nozzle and on the viscosity and density of the fluid. The width of the nozzle which was commonly used to reduce these data has no part in the similarity considerations as has already been suggested by Narasimha et al. (1973). This type of self-similarity can be easily applied to determine the skin friction, which can otherwise only be determined with considerable difficulty. It was also shown that the ‘law of the wall’ applies only to the viscous sublayer. The Reynolds stress in the inviscid, inner portion of the flow is not constant thus the assumption of a ‘constant stress layer’ is not applicable. The applicability and universality of the ‘outer scaling law’ (i.e. Coles’ law of the wake) has been verified throughout the inviscid inner portion of the wall jet. The logarithmic velocity distribution cannot be derived by making the usual assumptions based on the constancy of the Reynolds stresses or on the thinness of the logarithmic region relative to the thickness of the inner layer.

Particle dispersion in an axisymmetric jet is analysed numerically by following particle trajectories in a jet flow simulated by discrete vortex rings. Important global and local flow quantities reported in experimental measurements are successfully simulated by this method.

The particle dispersion results demonstrate that the extent of particle dispersion depends strongly on γτ, the ratio of particle aerodynamic response time to the characteristic time of the jet flow. Particles with relatively small γτ values are dispersed at approximately the fluid dispersion rate. Particles with large γτ values are dispersed less than the fluid. Particles at intermediate values of γτ may be dispersed faster than the fluid and actually be flung outside the fluid mixing region of the jet. This result is in agreement with some previous experimental observations. As a consequence of this analysis, it is suggested that there exists a specific range of intermediate γτ at which optimal dispersion of particles in the turbulent mixing layer of a free jet may be achieved.

We address the sequence of events accompanying the transition from an initially compact volume of liquid – a drop – into dispersed fragments when it impacts a solid surface. We describe the change of topology of the drop to a radially expanding sheet and discuss the reasons of its rim destabilization, responsible for the emergence of radial ligaments which ultimately fragment into smaller drops. The dynamics ruling the radius of the sheet, its stability and the resulting fragment drop size distribution are documented experimentally. The radius dynamics results from a simple balance between inertia of the initial drop and capillary restoring forces at the rim, with damping due to the continuous transfer of momentum from the sheet to the rim. The ligaments expelled from the rim originate from a Rayleigh–Taylor mechanism localized at the rim. The final drop size distribution in the spray is shown to be a linear superposition of gamma distributions characteristic of ligament breakup, leading generically to Bessel functions.

Based on a hydrodynamic length, which is typically larger than the nominal flame thickness, a premixed flame can be viewed as a surface of density discontinuity, advected and distorted by the flow. The velocities and the pressure suffer abrupt changes across the flame front that consist of Rankine–Hugoniot jump conditions, to leading order, with corrections of the order of the flame thickness that account for transverse fluxes and accumulation. To complete the formulation, expressions for the flame temperature and propagation speed, which vary along the flame as a result of local non-uniformities in the flow field and of flame front curvature, are derived. Unlike previous studies that assumed a mixture consisting of a single deficient reactant, the present study uses a two-reactant scheme and thus considers mixtures whose compositions vary from lean to rich conditions. Furthermore, non-unity and general reaction orders are considered in an attempt to mimic a wider range of reaction mechanisms and, to better represent actual experimental conditions, all transport coefficients are allowed to depend arbitrarily on temperature. The present model, expressed in a coordinate-free form, is valid for flames of arbitrary shape propagating in general fluid flows, either laminar or turbulent.

Recently a new system of field equations for the accurate description of flows in rarefied gases, called regularized 13-moment equations, was obtained by means of a hybrid gas kinetic approach. The first part of this paper discusses the relationship of the new system to classical high-order theories like the Burnett and super-Burnett equations as well as to modified models like the augmented and regularized Burnett equations. In the second part, shock structure calculations with the new theory are presented and compared to direct-simulation Monte Carlo (DSMC) solutions and to solutions of the Burnett models. Owing to additional higher-order dissipation in the system, the profiles are smooth for any Mach number, in contrast to the results of Grad's 13-moment case. The results show reliable quantitative agreement with DSMC simulations for Mach numbers up to $M_{0}\approx 3.0$. The agreement is better for Maxwell molecules than for hard spheres. The results of the augmented Burnett equations are comparable, but these equations are shown to be spatially unstable. Additionally, a validiation procedure for the new equations is presented by investigating the positivity of Grad's distribution function.