Results from a wind tunnel study of aerodynamically rough turbulent boundary-layer flow over a sinusoidal surface are presented. The waves had a maximum slope (ak) of 0.5 and two surface roughnesses were used. For the relatively rough surface the flow separated in the wave troughs while for the relatively smooth surface it generally remained attached. Over the relatively smooth-surfaced waves an organized secondary flow developed, consisting of vortex pairs of a scale comparable to the boundary-layer depth and aligned with the mean flow. Large-eddy simulation studies model the flows well and provide supporting evidence for the existence of this secondary flow.

Laboratory experiments are used to study the initial response of a stratified fluid to the action of a wind stress. The experiments are described in the context of a parameterization scheme that quantifies the strength of the applied stress relative to the bulk stability of the fluid and also the duration of the wind stress relative to the periods of the waves generated by the stress. This study concentrates on the first fundamental internal wave period in experiments where the fluid is considered to have upwelled, i.e. the stratified region of the fluid reaches the surface at the upwind endwall. The majority of the experiments use three-layer initial density profiles as an approximation to a continuously stratified water column.

A linear model using normal modes proved successful prior to the commencement of upwelling and this enabled an estimate to be made of the time at which upwelling occurred. At this point the wave development ceased and the flows developed via entrainment mechanisms. Consideration of the energy budget showed that little of the input energy was stored in the system. The initial mixing efficiency, defined as the ratio of the mean potential energy gained to the energy imparted by the belt, never exceeded 30%. Peak efficiency occurred when the surface stress was just sufficient to bring the interfacial region to the surface.

Experiments have been performed on the tip vortex trailing from a rectangular NACA 0012 half-wing. Preliminary studies showed the vortex to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful velocity measurements could therefore be made using hot-wire probes.

Detailed analysis of the effects of wandering was performed to properly reveal the flow structure in the core region and to give confidence in measurements made outside the core. A theory has been developed to correct mean-velocity profiles for the effects of wandering and to provide complete quantitative estimates of its amplitude and contributions to Reynolds stress fields. Spectral decomposition was found to be the most effective method of separating these contributions from velocity fluctuations due to turbulence.

Outside the core the flow structure is dominated by the remainder of the wing wake which winds into an ever-increasing spiral. There is no large region of axisymmetric turbulence surrounding the core and little sign of turbulence generated by the rotational motion of the vortex. Turbulence stress levels vary along the wake spiral in response to the varying rates of strain imposed by the vortex. Despite this complexity, the shape of the wake spiral and its turbulent structure reach an approximately self-similar form.

On moving from the spiral wake to the core the overall level of velocity fluctuations greatly increases, but none of this increase is directly produced by turbulence. Velocity spectra measured at the vortex centre scale in a manner that implies that the core is laminar and that velocity fluctuations here are a consequence of inactive motion produced as the core is buffeted by turbulence in the surrounding spiral wake. Mean-velocity profiles through the core show evidence of a two-layered structure that dies away with distance downstream.

We describe a mechanistic picture of the essential dynamical processes in the growing Tollmien-Schlichting wave in a Blasius boundary layer and similar flows. This picture depends on the interaction between two component parts of a disturbance (denoted ‘partial modes’), each of which is a complete linear solution in some idealization of the system. The first component is an inviscid mode propagating on the vorticity gradient of the velocity profile with the free-slip boundary condition, and the second, damped free viscous modes in infinite uniform shear with the no-slip condition. There are two families of these viscous modes, delineated by whether the phase lines of the vorticity at the wall are oriented with or against the shear, and they are manifested as resonances in a forced system. The interaction occurs because an initial ‘inviscid’ disturbance forces a viscous response via the no-slip condition at the wall. This viscous response is large near the resonance associated with the most weakly damped viscous mode, and in the unstable parameter range it has suitable phase at the outer part of the boundary layer to increase the amplitude of the inviscid partial mode by advection.

New instabilities affecting the meniscus of a viscous fluid are presented. They occur in an experimental set-up introduced previously by Rabaud et al. (1990) in which a small quantity of a viscous fluid is placed in the narrow gap between two rotating cylinders. In this geometry the downstream meniscus located in the region where the two solid surfaces move away from each other is known to be unstable and to exhibit directional viscous fingering. In the present article it is shown that the upstream meniscus can also be unstable. Two types of instabilities are observed. In the first supercritical transition the front becomes time-dependent with either standing or propagating waves. In a second transition, which is subcritical, parallel fingers of finite amplitude are formed. The various types of spatio-temporal dynamical behaviour are discussed.

In this paper the phenomenon of chemical reactivity in hypersonic rarefied flows is examined. A new model is developed to describe the reactions and post-collision energy exchange processes that take place under conditions of molecular non-equilibrium. The new scheme, which is applied within the framework of the direct simulation Monte Carlo (DSMC) method, draws its inspiration from the principles of maximum entropy which were developed by Levine & Bernstein. Sample hypersonic flow fields, typical of spacecraft re-entry conditions in which reactions play an important role, are presented and compared with results from experiments and other DSMC calculations. The latter use traditional methods for the modelling of chemical reactions and energy exchange. The differences are discussed and evaluated.

To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. Only one mode of instability, the interfacial mode, is obtained in the long-wave asymptotic limit. The generalized eigenvalue problem, formed by spectral decomposition and solution of the general two-layer Orr-Sommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. Results from the stability analysis of the flow near the contact line where air entrainment occurs are consistent with previous experimental observations.

The three-dimensionality of the velocity field in the wake of a circular cylinder has excited considerable interest and debate over the past decade. Presented here are experimental results that characterize the underlying vorticity field of such wakes. Using particle image velocimetry (PIV), instantaneous velocity fields were measured and from these the vorticity of the longitudinal vortices lying in the region between Kármán vortices was found. Near the saddle point, induced by the stretching of the Kármán vortices, the vorticity of the longitudinal vortices was found to be greater than the Kármán vortices themselves. Their circulation was of the order of 10% of the Kármán vortices. The high levels of vorticity result from the stretching of the longitudinal vortices, as evident in the topology of the vortices. It is shown that the longitudinal vortices are locked in phase to the KármánK vortices, effectively riding on their backs in the braid region. While only one mode of longitudinal vortex formation was observed, evidence was found of a step change in the vorticity levels at a Reynolds number of approximately 200. This is consistent with the transition point between the two modes of vortex shedding shown to exist by Williamson (1988). It had previously been proposed that the observed vortex patterns were consistent with the evolution of the longitudinal vortices from perturbations of vortex lines in the separating shear layer which experience self-induction and stretching from the Kármán vortices. Evidence is presented that supports this model.

Self-diffusion in a suspension of spherical particles in steady linear shear flow is investigated by following the time evolution of the correlation of number density fluctuations. Expressions are presented for the evaluation of the self-diffusivity in a suspension which is either raacroscopically quiescent or in linear flow at arbitrary Peclet number $Pe = \dot{\gamma}a^2/2D$, where $\dot{\gamma}$ is the shear rate, a is the particle radius, and D = kBT/6πa is the diffusion coefficient of an isolated particle. Here, kB is Boltzmann's constant, T is the absolute temperature, and η is the viscosity of the suspending fluid. The short-time self-diffusion tensor is given by kBT times the microstructural average of the hydrodynamic mobility of a particle, and depends on the volume fraction $\phi = \frac{4}{3}\pi a^3n$ and Pe only when hydrodynamic interactions are considered. As a tagged particle moves through the suspension, it perturbs the average microstructure, and the long-time self-diffusion tensor, D∞s, is given by the sum of D0s and the correlation of the flux of a tagged particle with this perturbation. In a flowing suspension both D0s and D∞ are anisotropic, in general, with the anisotropy of D0s due solely to that of the steady microstructure. The influence of flow upon D∞s is more involved, having three parts: the first is due to the non-equilibrium microstructure, the second is due to the perturbation to the microstructure caused by the motion of a tagged particle, and the third is by providing a mechanism for diffusion that is absent in a quiescent suspension through correlation of hydrodynamic velocity fluctuations.

The self-diffusivity in a simply sheared suspension of identical hard spheres is determined to O(øPe3/2) for Pe ≤ 1 and ø ≤ 1, both with and without hydro-dynamic interactions between the particles. The leading dependence upon flow of D0s is 0.22DøPeÊ, where Ê is the rate-of-strain tensor made dimensionless with $\dot{\gamma}$. Regardless of whether or not the particles interact hydrodynamically, flow influences D∞s at O(øPe) and O(øPe3/2). In the absence of hydrodynamics, the leading correction is proportional to øPeDÊ. The correction of O(øPe3/2), which results from a singular advection-diffusion problem, is proportional, in the absence of hydrodynamic interactions, to øPe3/2DI; when hydrodynamics are included, the correction is given by two terms, one proportional to Ê, and the second a non-isotropic tensor.

At high ø a scaling theory based on the approach of Brady (1994) is used to approximate D∞s. For weak flows the long-time self-diffusivity factors into the product of the long-time self-diffusivity in the absence of flow and a non-dimensional function of $\bar{P}e = \dot{\gamma}a^2/2D^s_0(\phi)$. At small $\bar{P}e$ the dependence on $\bar{P}e$ is the same as at low ø.

Bedload sheets are coherent migrating patterns of bed material recently observed both in flume studies and in field streams with beds of coarse sand and fine gravel. This newly recognized feature is inherently associated with the heterogeneous character of the sediment and consists of sorting waves with distinct coarse fronts only one or two coarse grains high.

The question of the formation of bedload sheets poses an interesting and peculiar stability problem for the grain size distribution. Sorting waves are essentially two-dimensional migrating perturbations associated with variations of this distribution. We show that their growth is strictly associated with grain sorting. In fact the latter gives rise to perturbations of bedload transport which drive small perturbations of bottom elevation the amplitude of which scales with grain size. The sorting wave also induces spatial variations of bottom roughness, and consequently alters the fluid motion, which conversely exerts a spatially varying stress on the bed. The feature of bedload sheets which allows them to be distinguished from dunes over beds with coarse sand or fine gravel is then the fact that sorting is the dominant effect controlling their growth, rather than being a relatively small perturbation of the mechanism which gives rise to dunes in the case of uniform sediment.

The requirement that perturbations should not alter the sediment budget leads to an integral condition which gives rise to an integro-differential mathematical problem. With the help of recently developed bedload relationships suitable for mixtures, as well as appropriate modelling of turbulent channel flow over a bed with spatially periodic perturbations of bottom elevation and roughness we are able to derive a general dispersion relation which can be readily solved in terms of undisturbed size densities in the form of sums of Dirac distributions.

Perturbations are found to be unstable within a range of wavenumbers depending on the relative roughness and Froude number. We show that when the effects of perturbations of bottom elevation are neglected the unstable region corresponds to the range of conditions where the bottom stress leads bottom roughness, a range distinct from that which characterizes the formation of dunes. This result is given a physical explanation which depends crucially on the deviation from equal mobility of different grain sizes in the surface layer. The effect of perturbations of bottom elevation is however not negligible when the bottom roughness is fairly large compared to depth. In the latter case perturbations of bottom elevation and of bottom roughness are equally important, and gravel sheets are not easily distinguished from small-amplitude dunes.

Comparison with the field observations of Whiting et al. (1985, 1988) is satisfactory insofar as the bedload sheet mode is unstable under the conditions of the experiments, and the predicted wavelengths fall within the experimental range. The laboratory observations of Kuhnle & Southard (1988), on the other hand, appear to fall within a range of bottom roughness where the observed bedforms do not exhibit features unambiguously distinct from those of small-amplitude dunes.

A rotational shear flow is examined in the parallel plate geometry for the Oldroyd-B fluid. The Stokes solution is found to have eigenfunctions in an unbounded radial domain while it is unique for general boundary conditions in a finite radial domain. Critical conditions for the onset of an axisymmetric secondary flow are determined for the viscoelastic fluid, and we show that there is an almost linear relationship between the aspect ratio of the plates and the critical Deborah number for this model, especially at small values of the aspect ratio. The form of the initial secondary flow is also in agreement with experimental results obtained for a Boger fluid.

When a body interacts with small-amplitude surface waves in an ideal fluid, the resulting velocity potential may be split into a part due to the scattering of waves by the fixed body and a part due to the radiation of waves by the moving body into otherwise calm water. A formula is derived which expresses the two-dimensional scattering potential in terms of the heave and sway radiation potentials at all points in the fluid. This result generalizes known reciprocity relations which express quantities such as the exciting forces in terms of the amplitudes of the radiated waves. To illustrate the use of this formula beyond the reciprocity relations, equations are derived which relate higher-order scattering and radiation forces. In addition, an expression for the scattering potential due to a wave incident from one infinity in terms of the scattering potential due to a wave from the other infinity is obtained.

When a pendant drop of weakly conducting fluid is raised to a high electric potential, it frequently adopts the shape of a Taylor cone from whose apex a thin, charged jet is emitted. Such a jet can display surprising longevity, but eventually breaks up into fine droplets, a fact utilized in electro-spraying devices. This paper examines the linear stability of an incompressible cylindrical jet carrying surface charge q in a tangential electric field E, for various values of the permittivity ratio λ and the finite rate of charge relaxation, τ. The viscosity is assumed to be large. It is shown that all axisymmetric temporal modes can be stabilized for suitable values of (q, E), but sinuous modes with logarithmically large wavelengths are unstable. If these very long waves are excluded, the jet can sometimes be completely stabilized. It is also shown that an uncharged jet with low permittivity is unstable to sinuous waves for large E, contrary to previous belief.

We examine the dynamics of a rotating viscous fluid following an abrupt change in the angular velocity of the solid bounding surface. We include the effects of a density stratification and compressibility which are important in astrophysical objects such as neutron stars. We confirm and extend the conclusions of previous studies that stratification restricts the Ekman pumping process to a relatively thin layer near the boundary, leaving much of the interior fluid unaffected. We find that finite compressibility further inhibits Ekman pumping by decreasing the extent of the pumped layer and by increasing the time for spin-up. The results of this paper are important for interpreting the spin period discontinuities (‘glitches’) observed in rotating neutron stars.

The phenomenon of Tollmien-Schlichting wave generation in a boundary layer by free-stream turbulence is analysed theoretically by means of asymptotic solution of the Navier-Stokes equations at large Reynolds numbers (Re → ∞). For simplicity the basic flow is taken to be the Blasius boundary layer over a flat plate. Free-stream turbulence is taken to be uniform and thus may be represented by a superposition of vorticity waves. Interaction of these waves with the flat plate is investigated first. It is shown that apart from the conventional viscous boundary layer of thickness O(Re−1/2), a ‘vorticity deformation layer’ of thickness O(Re−1/4) forms along the flat-plate surface. Equations to describe the vorticity deformation process are derived, based on multiscale asymptotic techniques, and solved numerically. As a result it is shown that a strong singularity (in the form of a shock-like distribution in the wall vorticity) forms in the flow at some distance downstream of the leading edge, on the surface of the flat plate. This is likely to provoke abrupt transition in the boundary layer. With decreasing amplitude of free-stream turbulence perturbations, the singular point moves far away from the leading edge of the flat plate, and any roughness on the surface may cause Tollmien-Schlichting wave generation in the boundary layer. The theory describing the generation process is constructed on the basis of the ‘triple-deck’ concept of the boundary-layer interaction with the external inviscid flow. As a result, an explicit formula for the amplitude of Tollmien-Schlichting waves is obtained.

Experimental results for a reactive non-buoyant plume of nitric oxide (NO) in a turbulent grid flow doped with ozone (O3) are presented. The Damköhler number (ND) for the experiment is of order unity indicating the turbulence and chemistry have similar timescales and both affect the chemical reaction rate. Continuous measurements of two components of velocity using hot-wire anemometry and the two reactants using chemiluminescent analysers have been made. A spatial resolution for the reactants of four Kolmogorov scales has been possible because of the novel design of the experiment. Measurements at this resolution for a reactive plume are not found in the literature. The experiment has been conducted relatively close to the grid in the region where self-similarity of the plume has not yet developed. Statistics of a conserved scalar, deduced from both reactive and non-reactive scalars by conserved scalar theory, are used to establish the mixing field of the plume, which is found to be consistent with theoretical considerations and with those found by other investigators in non-reactive flows. Where appropriate the reactive species means and higher moments, probability density functions, joint statistics and spectra are compared with their respective frozen, equilibrium and reaction-dominated limits deduced from conserved scalar theory. The theoretical limits bracket reactive scalar statistics where this should be so according to conserved scalar theory. Both reactants approach their equilibrium limits with greater distance downstream. In the region of measurement, the plume reactant behaves as the reactant not in excess and the ambient reactant behaves as the reactant in excess. The reactant covariance lies outside its frozen and equilibrium limits for this value of ND. The reaction rate closure of Toor (1969) is compared with the measured reaction rate. The gradient model is used to obtain turbulent diffusivities from turbulent fluxes. Diffusivity of a non-reactive scalar is found to be close to that measured in non-reactive flows by others.