Structural features resulting from the interaction of a turbulent jet issuing transversely into a uniform stream are described with the help of flow visualization and hot-wire anemometry. Jet-to-crossflow velocity ratios from 2 to 10 were investigated at crossflow Reynolds numbers from 3800 to 11400. In particular, the origin and formation of the vortices in the wake are described and shown to be fundamentally different from the well-known phenomenon of vortex shedding from solid bluff bodies. The flow around a transverse jet does not separate from the jet and does not shed vorticity into the wake. Instead, the wake vortices have their origins in the laminar boundary layer of the wall from which the jet issues. It is argued that the closed flow around the jet imposes an adverse pressure gradient on the wall, on the downstream lateral sides of the jet, provoking 'separation events’ in the wall boundary layer on each side. These result in eruptions of boundary-layer fluid and formation of wake vortices that are convected downstream. The measured wake Strouhal frequencies, which depend on the jet-crossflow velocity ratio, match the measured frequencies of the separation events. The wake structure is most orderly and the corresponding wake Strouhal number (0.13) is most sharply defined for velocity ratios near the value 4. Measured wake profiles show deficits of both momentum and total pressure.

The flat interface between two fluids in a vertically vibrating vessel may be parametrically excited, leading to the generation of standing waves. The equations constituting the stability problem for the interface of two viscous fluids subjected to sinusoidal forcing are derived and a Floquet analysis is presented. The hydrodynamic system in the presence of viscosity cannot be reduced to a system of Mathieu equations with linear damping. For a given driving frequency, the instability occurs only for certain combinations of the wavelength and driving amplitude, leading to tongue-like stability zones. The viscosity has a qualitative effect on the wavelength at onset: at small viscosities, the wavelength decreases with increasing viscosity, while it increases for higher viscosities. The stability threshold is in good agreement with experimental results. Based on the analysis, a method for the measurement of the interfacial tension, and the sum of densities and dynamic viscosities of two phases of a fluid near the liquid-vapour critical point is proposed.

A family of Lagrangian stochastic models for the joint motion of particle pairs in isotropic homogeneous stationary turbulence is considered. The Markov assumption and well-mixed criterion of Thomson (1990) are used, and the models have quadratic-form functions of velocity for the particle accelerations. Two constraints are derived which formally require that the correct one-particle statistics are obtained by the models. These constraints involve the Eulerian expectation of the ‘acceleration’ of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particle's position. The Navier-Stokes equations, with Gaussian Eulerian probability distributions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calculations show that the constraints do not always guarantee good one-particle statistics, but it is possible to select a constrained model that does. Thomson's model has good one-particle statistics, but is shown to have unphysical conditional accelerations. Comparisons of relative dispersion for the models are made.

This paper describes laboratory experiments on dipolar vortex structures in a linearly stratified fluid. The dipoles are generated by a pulsed horizontal injection of a small volume of fluid, by which a localized three-dimensionally turbulent flow region is created. After the subsequent gravitational collapse the flow becomes approximately two-dimensional, and eventually a single vortex dipole emerges, as the result of the self-organizing properties of such flows. The flow evolution has been visualized both by dye and tracer particles, through which qualitative as well as quantitative information was obtained. By application of digital image analysis, the spatial distribution of the velocity ν, vorticity ω and stream function ψ were determined. It was found that dipoles in the turbulent-injection experiments are characterized by a nonlinear sinh-like relationship between ω and ψ, whereas in the case of laminar injection the (ω, ψ)-scatter plots of the dipoles reveal a linear relationship. Notwithstanding these differences, both types of dipoles show a dynamical structure that agrees very well with the Lamb–Chaplygin dipole, as was found by comparing the size, position of maximum vorticity, cross-sectional distributions of ν and ω, characteristics of the (ω, ψ)-relationship, and the translation speed of the experimental and the model dipole.

A model for the low-Reynolds-number flow of a capsule through a constriction is developed for either constant-flow-rate or constant-pressure-drop conditions. Such a model is necessary to infer quantitative information on the intrinsic properties of capsules from filtration experiments conducted on a dilute suspension of such particles. A spherical capsule, surrounded by an infinitely thin Mooney-Rivlin membrane, is suspended on the axis of a hyperbolic constriction. This configuration is fully axisymmetric and allows the entry and exit phenomena through the pore to be modelled. An integral formulation of the Stokes equations describing the flow in the internal and external domains is developed. It provides a representation of the velocity at any location in the flow as a function of the unknown forces exerted by the boundaries on the fluids. The problem is solved by a collocation technique in the case where the internal and external viscosities are equal. Microscopic quantities (instantaneous geometry, centre of mass velocity, elastic tensions in the membrane) as well as macroscopic quantities (entry time, additional pressure drop or flow rate reduction) are predicted as a function of the capsule intrinsic properties and flow characteristics. The results obtained for a capsule whose initial diameter is larger than that of the constriction throat show that the maximum energy expenditure occurs when the particle centre of mass is still upstream of the throat (typically 1 diameter away), and is thus due to the entry process. For large enough or rigid enough capsules, the model predicts entrance or exit plugging, in agreement with experimental observations. It is then possible to correlate the variation of the pore hydraulic resistance to the flow capillary number (ratio of viscous to elastic forces) and to the size ratio between the pore and the capsule.

This paper is concerned with the linear inviscid stability of parallel flow over a compliant or flexible wall. A Fjørtoft-type criterion providing a necessary condition for instability in terms of the basic velocity field and its second-order derivative is established. This criterion assumes a simple form for basic flows with zero velocity at the wall. For the latter flows, another necessary condition for stability is given. The results are helpful in the search for unstable modes in flow over a compliant wall.

The structure of diffusing planar and axisymmetric vortices of the hyperviscous Navier-Stokes equations is studied for different orders of the dissipative operator. It is found that, except for the classical Newtonian case, the vorticity decays at large distances by means of oscillatory tails, containing circulation of alternating signs. This oscillation becomes stronger for large hyperviscosity orders, and the limit of infinite order is studied. It is argued that these solutions would become unstable for large enough Reynolds numbers, and may contribute non-trivial spurious dynamics to flow simulations using hyperviscosity.

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

The hydrodynamic theory of slender bodies is used to model electrophoretic motion of a slender particle having a charge (zeta potential) that varies with position along its length. The theory is limited to systems where the Debye screening length of the solution is much less than the typical cross-sectional dimension of the particle. A stokeslet representation of the hydrodynamic force is combined with the Lorentz reciprocal theorem for Stokes flow to develop a set of linear equations which must be solved for the components of the translational and angular velocities of the particle. Sample calculations are presented for the electrophoretic motion of straight spheroids and cylinders and a torus in a uniform electric field. The theory is also applied to a straight uniformly charged particle in a spatially varying electric field. The uniformly charged particle rotates into alignment with the principal axes of ∇E∞; we suggest that such alignment can lead to electrophoretic transport of particles through a small aperture in an otherwise impermeable wall. The theory developed here is more general than just for electrophoresis, since the final result is expressed in terms of a general 'slip velocity’ at the surface of the particle. Thus, the results are applicable to diffusiophoresis of slender particles if the proper slip-velocity coefficient is used.

The importance of vorticity production in combustion systems has been highlighted previously by several authors (Markstein 1964; Picone et al. 1984). The consequent distortion and enlargement of flame surfaces can lead to substantial enhancement of the burning rate which may be beneficial or disastrous depending on the physical context. We describe the results of numerical simulations of an experimental configuration similar to that described by Scarinci & Thomas (1992), who examined the effect of initially planar pressure signals on two-dimensional flame balls. The flame ball is here set-up from ignition using a code, based on the second-order Godunov scheme described by Falle (1991). A simple Arrhenius reaction scheme is adopted in modelling a unimolecular decomposition. As in previous papers (Batley et al. 1993 a, b) the thermal conductivity is assumed to vary linearly with temperature, and the Lewis and Prandtl numbers are taken as unity. A short time after ignition, when the flame ball has reached a radius of approximately 2 cm, a very short-lengthscale pressure step disturbance is introduced, propagating towards the combustion region. As the signal crosses the flame, the interaction of the sharp, misaligned pressure and density gradients, creates a strong vorticity field. The resulting roll-up of the flame eventually divides it into two smaller rotating reacting regions. In order to gauge the effect of the chemical reaction and in particular the viscous diffusion on the evolution of the vorticity field, the results are compared with analogous solutions of the Euler equations.

This paper is devoted to the analysis of the turbulent mass flux and, more generally, of the density fluctuation correlation (d.f.c.) effects in variable-density fluid motion. The situation is restricted to the free turbulent binary mixing of an inhomogeneous round jet discharging into a quiescent atmosphere. Based on conventional (Reynolds) averaging, a ternary regrouping of the correlations occurring in the statistical averaging of the open equations is first introduced. Then an exact algebraic relationship between the d.f.c. terms and the second-order moments is demonstrated. Some consequences of this result on the global behaviour of variable-density jets are analytically discussed. The effects of the d.f.c. terms are shown to give a qualitative explanation of the influence of the ratio of the densities of the inlet jet and ambient fluid on the centerline decay rates of mean velocity and mass fraction, the entrainment rate and the restructuring of the jet. Finally, the sensitivity of second-order modelling to the d.f.c. terms is illustrated and it is suggested that such terms should be considered as independent variables in the closing procedure.

Water with constant initial salt stratification was mixed with a horizontally moving vertical rod. The initially linear density profile turned into a series of steps when mixing was weak, in agreement with instability theory by Phillips (1972) and Posmentier (1977). For stronger mixing no steps formed. However, in all cases mixed layers formed next to the top and bottom boundaries and expanded into the interior due to the no-flux condition at the horizontal boundaries. The critical Richardson number Rie, dividing experiments with steps and ones without, increases with Reynolds number Re as Rie ≈ exp(Re/900). Steps evolved over time, with small ones forming first and larger ones appearing later. The interior seemed to reach an equilibrium state with a collection of stationary steps. The boundary mixed layers continued to penetrate into the interior. They finally formed two mixed layers separated by a step, and ultimately acquired the same densities so the fluid became homogeneous. The length scale of the equilibrium steps, ls, is a linear function of U/Ni, where U is the speed of the stirring rod and Ni is the buoyancy frequency of the initial stratification. The mixing efficiency Rf also evolved in relation to the evolution of the density structure. During the initiation of the steps, Rf showed two completely different modes of evolution depending on the overall Richardson number of the initial state, Rio. For Rio [Gt ] Rie, Rf increased initially. However for Rio near Rie, Rf decreased. Then the steps reached an equilibrium state where Rf was constant at a value that depended on the initial stratification. The density flux was measured to be uniform in the layered interior irrespective of the interior density gradient during the equilibrium state. Thus, the density (salt) was transported from the bottom boundary mixed layer through the layered interior to the top boundary mixed layer without changing the interior density structure. The relationship between Ril and Rf was found for Ril > 1, where Ril is the Richardson number based on the thickness of the interface between the mixed layers. Rf decreases as Ril increases, consistent with the most crucial assumption of the instability theory of Phillips/Posmentier.

The virtually instantaneous three-dimensional concentration fields in the self-similar region of natural or unexcited, circularly excited and weakly buoyant round jets of Reynolds number based on nozzle diameter of 1000 to 4000 are measured experimentally at a spatial resolution of the order of the Kolmogorov length scale. Isoconcentration surfaces are extracted from the concentration field. These surfaces along with their geometrical parameters are used to deduce the structure and modal composition of the jet. The concentration gradient field is calculated, and its local topology is classified using critical-point concepts.

Large-scale structure is evident in the form of ‘clumps’ of higher-concentration jet fluid. The structure, which has a downstream extent of about the local jet diameter, is roughly axisymmetric with a conical downstream end. This structure appears to be present only in fully turbulent jets. The antisymmetric two-dimensional images previously thought to be axial slices of an expanding spiral turn out in our data to instead be slices of a simple sinusoid in three dimensions. This result suggests that the helical mode, when present, is in the form of a pair of counter-rotating spirals, or that the +1 and −1 modes are simultaneously present in the flow, with their relative phase set by initial conditions.

In terms of local structure, regions with a large magnitude in concentration gradient are shown to have a local topology which is roughly axisymmetric and compressed along the axis of symmetry. Such regions, which would be locally planar and sheet-like, may correspond to the superposition of several of the layer-like structures which are the basic structure of the fine-scale passive scalar field (Buch & Dahm 1991; Ruetsch & Maxey 1991).

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.

We examine the free surface flow over a fixed bed covered by rigid sinusoidal dunes. The mean current velocity is near the critical value at which the linearized theory predicts unbounded response. By allowing transients we examine the instability of the steady and nonlinear solution of Mei (1969) and the possibility of chaos when the current has a small oscillatory component.