An experimental and analytical study into the vortex dynamics of a stratified shear layer subjected to a spatial acceleration is presented. The outer flow is dictated by a hydraulically controlled wedge flow which provides a spatially accelerating shear layer and baroclinic generation of vorticity along the inclined interface. A new, finite-amplitude mechanism is observed in which the core of the growing vortex is separated from the vorticity source at the interface. A secondary core develops and an altered vortex pairing interaction is observed. A spatial linear stability analysis reveals that one of two modified Kelvin–Helmholtz modes is dominant, resulting in the centre of the instability being offset from the density interface into the slower moving stream. Digital particle imaging velocimetry (DPIV) measurements are presented along with flow visualization which indicate that the mechanism is a result of the offset in the vortex core from the source of vorticity at the interface combined with the effects of spatial acceleration and buoyancy. The mixing induced by the interfacial instabilities is such that a sharp density interface remains near the high-momentum stream, with a low-gradient region extending into the low-momentum stream.

The role of interfacial shear in the onset of instability of a cylindrical viscous liquid jet in a viscous gas surrounded by a coaxial circular pipe is elucidated by use of an energy budget associated with the disturbance. It is shown that the shear force at the liquid–gas interface retards the Rayleigh-mode instability which leads to the breakup of the liquid jet into drops of diameter comparable to the jet diameter, due to capillary force. On the other hand the interfacial shear and pressure work in concert to cause the Taylor-mode instability which leads the jet to break up into droplets of diameter much smaller than the jet diameter. While the interfacial pressure plays a slightly more important role than the interfacial shear in amplifying the longer-wave spectrum in the Taylor mode, the shear stress plays the main role of generating the disturbances of shorter wavelength.

The reflection of a straight-crested gravity wave by a non-secular perturbation h1(x) in depth relative to an otherwise flat bottom of depth h0 is calculated through an expansion in ε∝h1/h0. Explicit results are developed up to second order for the sinusoidal patch h1=−bsin(mπx/l), 0<x<l, and reduced for Bragg resonance. Trapped modes are absent at first order but appear at second order and contribute O(ε2)/O(ε3) to the maximum (Bragg-resonant) reflection coefficient for odd/even m. A third-order approximation that includes the dominant contributions of the third-order components of the resonant peak of the reflection coefficient for large m, but neglects the trapped modes, predicts resonant peaks that agree with the values measured by Davies & Heathershaw (1984).

The flow near the cavity detachment region of stable attached cavitation was examined using qualitative and quantitative flow visualization. The non-cavitating and cavitating flows around a hydrophilic brass and hydrophobic Teflon sphere and cylinder were examined. The location of non-cavitating boundary layer separation and cavity detachment was related to the free-stream Reynolds and cavitation numbers. The shape of the cavity near the detachment was greatly affected by the material of the cavitating object. The cavity interface on the hydrophilic test objects curved downstream to form a forward facing step. A region of recirculating fluid existed upstream of the cavity interface. The cavity detachment on the hydrophobic test objects was much closer to the location of boundary layer separation. The forward facing step and the recirculating region were nearly absent.

The measured flow field near the surface of the brass sphere, cylinder, and hydrofoils under cavitating and non-cavitating conditions was used to calculate the position of two-dimensional laminar boundary layer separation. Thwaites' and Stratford's methods were used to predict the location of boundary layer separation upstream of the cavity detachment. The predictions compared well with the observed position of separation.

Local and global three-dimensionality of cavity interfaces near detachment was examined. Cavities forming on hydrophilic test objects at higher Reynolds numbers (Re>105) exhibited a local flow structure in the cavity interface called ‘divots’. Divots resulted from a local breakdown of the two-dimensional laminar boundary separation. Divots did not form on hydrophobic test objects. Instead, at higher Reynolds numbers (Re>105), the cavity at detachment was composed of a series of wedge shaped structures. Flows with strong adverse pressure gradients upstream of cavity detachment exhibited only local three-dimensionality near one cavity detachment. Flows with weak adverse pressure gradients upstream of cavity detachment were more susceptible to breakdown into global three-dimensionality. This was the case for cavitation on the hydrofoils. Holographic particle imaging velocimetry (HPIV) was used to examine the spanwise and streamwise variation of the flow upstream of the cavity detachment. Three-dimensionality of the cavity detachment was associated with strong variations of the flow upstream of the cavity in the direction perpendicular to the mean flow direction.

We report on the results from a set of incompressible, shear-layer flow experiments, at high Reynolds number (Reδ≡ρΔUδT(x)/ μ≃2×105), in which the inflow conditions of shear-layer formation were varied (δT is the temperature-rise thickness for chemically-reacting shear layers). Both inert and chemically-reacting flows were investigated, the latter employing the (H2+NO)/F2 chemical system in the kinetically-fast regime to measure molecular mixing. Inflow conditions were varied by perturbing each, or both, boundary layers on the splitter plate separating the two freestream flows, upstream of shear-layer formation. The results of the chemically-reacting ‘flip experiments’ reveal that seemingly small changes in inflow conditions can have a significant influence not only on the large-scale structure and shear-layer growth rate, as had been documented previously, but also on molecular mixing and chemical-product formation, far downstream of the inflow region.

It is noted that the central limit theorem does not constrain the probability distribution of the components of the turbulent velocity fluctuations to be Gaussian, if their spectral slope is steeper than k−1. It is shown that, in a model of homogeneous turbulence in which each wavenumber of the energy spectrum predominantly receives contributions from eddies with roughly homogeneous amplitudes and coherence lengths, the p.d.f. would be slightly sub-Gaussian. This agrees with the available experimental evidence.

The sedimentation of fibre suspensions at low Reynolds number is studied using two different, but complementary, numerical simulation methods: (1) Monte Carlo simulations, which consider interparticle hydrodynamic interactions at all orders within the slender-body theory approximation (Mackaplow & Shaqfeh 1996), and (ii) dynamic simulations, which consider point–particle interactions and are accurate for suspension concentrations of nl3=1, where n and l are the number density and characteristic half-length of the fibres, respectively. For homogeneous, isotropic suspensions, the Monte Carlo simulations show that the hindrance of the mean sedimentation speed is linear in particle concentration up to at least nl3=7. The speed is well predicted by a new dilute theory that includes the effect of two-body interactions. Our dynamic simulations of dilute suspensions, however, show that interfibre hydrodynamic interactions cause the spatial and orientational distributions to become inhomogeneous and anisotropic. Most of the fibres migrate into narrow streamers aligned in the direction of gravity. This drives a downward convective flow within the streamers which serves to increase the mean fibre sedimentation speed. A steady-state orientation distribution develops which strongly favours fibre alignment with gravity. Although the distribution reaches a steady state, individual fibres continue to rotate in a manner that can be qualitatively described as a flipping between the two orientations aligned with gravity. The simulation results are in good agreement with published experimental data.

The goal of this study is to characterize the various breakdown states taking place in a swirling water jet as the swirl ratio S and Reynolds number Re are varied. A pressure-driven water jet discharges into a large tank, swirl being imparted by means of a motor which sets into rotation a honeycomb within a settling chamber. The experiments are conducted for two distinct jet diameters by varying the swirl ratio S while maintaining the Reynolds number Re fixed in the range 300<Re<1200. Breakdown is observed to occur when S reaches a well defined threshold Sc≈1.3–1.4 which is independent of Re and nozzle diameter used. This critical value is found to be in good agreement with a simple criterion derived in the same spirit as the first stage of Escudier & Keller's (1983) theory. Four distinct forms of vortex breakdown are identified: the well documented bubble state, a new cone configuration in which the vortex takes the form of an open conical sheet, and two associated asymmetric bubble and asymmetric cone states, which are only observed at large Reynolds numbers. The two latter configurations differ from the former by the precession of the stagnation point around the jet axis in a co-rotating direction with respect to the upstream vortex flow. The two flow configurations, bubble or cone, are observed to coexist above the threshold Sc at the same values of the Reynolds number Re and swirl parameter S. The selection of breakdown state is extremely sensitive to small temperature inhomogeneities present in the apparatus. When S reaches Sc, breakdown gradually sets in, a stagnation point appearing in the downstream turbulent region of the flow and slowly moving upstream until it reaches an equilibrium location. In an intermediate range of Reynolds numbers, the breakdown threshold displays hysteresis lying in the ability of the breakdown state to remain stable for S<Sc once it has taken place. Below the onset of breakdown, i.e. when 0<S<Sc, the swirling jet is highly asymmetric and takes the shape of a steady helix. By contrast above breakdown onset, cross-section visualizations indicate that the cone and the bubble are axisymmetric. The cone is observed to undergo slow oscillations induced by secondary recirculating motions that are independent of confinement effects.

Turbulence and secondary flow measurements were undertaken using a two-component laser-Doppler anemometer in meander channels with straight flood plain banks. The most interesting feature of the compound meandering channel flow was found to be the behaviour of the secondary flow. The difference in direction of rotation of the flow before and after inundation at a bend section was confirmed by the detailed velocity measurements. In addition, by performing the measurement over a half wavelength of meander, the originating and developing processes of the secondary flow were also clarified. In contrast to the centrifugal force for inbank flow, the interaction between the main channel flow and the flood plain flow in the cross-over region was found to play an important role in developing a shear produced secondary flow in the overbank cases. New experimental evidence concerning the spatial distribution of Reynolds stress −ρuw, −ρuv and −ρvw are presented for sinuous compound meander channels. In such channels, large interfacial shear stresses were induced at around the bankfull level, especially in the cross-over region, and were found to be larger than the bed shear stress in magnitude. Particular importance is placed on −ρvw, which is usually small compared with other stress components, as the cause of the secondary flow in the lower layer. The influence of secondary flow on eddy viscosity was found also to be significant. These turbulence data are particularly useful in understanding the flow mechanisms that occur in meandering channels and in developing proper turbulence models for such flows.

Bounds on convective heat transport in a porous layer heated from below are derived using the background field variational method (Constantin & Doering 1995a, b, 1996; Doering & Constantin 1992, 1994, 1996; Nicodemus, Holthaus & Grossmann 1997a) based on the technique introduced by Hopf (1941). We consider the infinite Prandtl–Darcy number model in three spatial dimensions, and additionally the finite Prandtl–Darcy number equations in two spatial dimensions, relevant for the related Hele-Shaw problem. The background field method is interpreted as a rigorous implementation of heuristic marginal stability concepts producing rigorous limits on the time-averaged convective heat transport, i.e. the Nusselt number Nu, as a function of the Rayleigh number Ra. The best upper bound derived here, although not uniformly optimal, matches the exact value of Nu up to and immediately above the onset of convection with asymptotic behaviour, Nu[les ]9/256Ra as Ra→∞, exhibiting the Howard–Malkus–Kolmogorov–Spiegel scaling anticipated by classical scaling and marginally stable boundary layer arguments. The relationship between these results and previous works of the same title (Busse & Joseph 1972; Gupta & Joseph 1973) is discussed.

The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the ‘formation number’, are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depend on the velocity profile. Non-impulsive velocity programmes slightly increase the formation number, while non-uniform velocity profiles may decrease it significantly. In the case of a parabolic velocity profile of the discharged flow, for example, the formation number decreases by a factor as large as four. These findings indicate that a major source of the experimentally found small variations in the formation number is the different evolution of the velocity profile of the discharged flow.

In contrast to the Miles–Howard theorem for inviscid steady shear flow in stably stratified fluids, explicit elementary time-periodic solutions of the Boussinesq equations are developed here which are unstable for arbitrarily large Richardson numbers. These elementary flows are parameterized through solutions of a nonlinear pendulum equation and involve spatially constant but temporally varying vorticity and density gradients which interact through advection and baroclinic vorticity production. Exact nonlinear solutions for arbitrary wave-like disturbances for these flows are developed here and Floquet theory combined with elementary numerical calculations is utilized to demonstrate instability at all large Richardson numbers. The dominant inviscid instability for these non-parallel flows is a purely two-dimensional parametric instability with twice the period of the elementary flow and persists for all Reynolds numbers and the wide range of Prandtl numbers, 1[les ]Pr[les ]200, investigated here. Similar elementary time-periodic solutions of the Boussinesq equations in a constant external strain field are developed here which reduce to uniform shear flows in one extreme limit and the time-periodic vortical flows in the other extreme limit. These flows are stable in a strict sense for large Richardson numbers; however there is transient large-amplitude non-normal behaviour which yields effective instability for a wide range of Richardson numbers. For example, suitable initial perturbations can amplify by at least a factor of fifty with exponential growth for short times for [Rscr ]i=1, [mid ]σ[mid ][les ]0.5 and [Rscr ]i=5, [mid ]σ[mid ][les ]0.1, with σ the amplitude of the external strain.

Linear stability and weak nonlinear theories are used to investigate analytically the Coriolis effect on three-dimensional gravity-driven convection in a rotating porous layer heated from below. Major differences as well as similarities with the corresponding problem in pure fluids (non-porous domains) are particularly highlighted. As such, it is found that, in contrast to the problem in pure fluids, overstable convection in porous media is not limited to a particular domain of Prandtl number values (in pure fluids the necessary condition is Pr<1). Moreover, it is also established that in the porous-media problem the critical wavenumber in the plane containing the streamlines for stationary convection is not identical to the critical wavenumber associated with convection without rotation, and is therefore not independent of rotation, a result which is quite distinct from the corresponding pure-fluids problem. Nevertheless it is evident that in porous media, just as in the case of pure fluids subject to rotation and heated from below, the viscosity at high rotation rates has a destabilizing effect on the onset of stationary convection, i.e. the higher the viscosity the less stable the fluid. Finite-amplitude results obtained by using a weak nonlinear analysis provide differential equations for the amplitude, corresponding to both stationary and overstable convection. These amplitude equations permit one to identify from the post-transient conditions that the fluid is subject to a pitchfork bifurcation in the stationary convection case and to a Hopf bifurcation associated with the overstable convection. Heat transfer results were evaluated from the amplitude solution and are presented in terms of Nusselt number for both stationary and overstable convection. They show that rotation has in general a retarding effect on convective heat transfer, except for a narrow region of small values of the parameter containing the Prandtl number where rotation enhances the heat transfer associated with overstable convection.