A formula is derived for the longitudinal shear dispersion coefficient of a solute in a laminar flow along and around a rotating cylindrical axle in an off-centre closely fitting shaft. The rotation drives a circulation which augments diffusive mixing around the axle and reduces the eventual rate of longitudinal spreading. A simple approximation is shown to give accurate results for the important special case of a cylindrical shaft.

A study is made of some two-dimensional flows of an inviscid, uniformly conducting fluid in the presence of applied magnetic fields, for the case in which the magnetic Reynolds number (the ratio of induced fields to applied fields) is small but the magnetic force coefficient (the ratio of electromagnetio forces to inertia forces) is of order unity.

Perturbations of uniform incompressible and compressible flows through aligned and crossed fields are considered. All these perturbations are strongly dependent upon the magnitude of the magnetic force coefficient. An experimental analogy of the flow through an aligned field is described.

Numerical simulations of benthic gravity-driven currents along continental shelves suggest they exhibit considerable time and spatial variability and tend to organize themselves into large-scale bottom-intensified cold domes or eddies. Attempts to derive simple relations governing the evolution of the spatial moments of the mass equation for baroclinic eddies have failed because it is not clear how to express the form or wave drag stresses associated with the excited (topographic) Rossby wave field in the surrounding fluid in terms of the eddy moments. We develop a simple model for the leading-order time evolution of a cold dome configuration which initially nearly satisfies the Mory–Stern isolation constraint. As the topographic Rossby wave field in the surrounding fluid interacts with the cold dome, higher azimuthal modes are excited within the cold dome which develop into spiral-like filamentary structures on the eddy boundary. The trajectory followed by the position of the maximum height of the cold dome corresponds to sub-inertial along- and cross-slope oscillations superimposed on a mean along-slope drift (well described by the Nof velocity). Nevertheless, the theory suggests that there are no oscillations (at least to second order) in the horizontal spatial moments of the eddy height, that is, the centre of mass of the eddy moves steadily in the along- and down-slope directions (i.e. ‘southwestward’ relative to the topographic β-plane). The theoretical analysis is in good agreement with a nonlinear numerical simulation which we present.

In order better to understand the processes that lead to the generation of magnetic fields of finite amplitude, we study dynamo action driven by turbulent Boussinesq convection in a rapidly rotating system. In the limit of infinite Prandtl number (the ratio of viscous to thermal diffusion) the inertia term drops out of the momentum equation, which becomes linear in the velocity. This simplification allows a decomposition of the velocity into a thermal part driven by buoyancy, and a magnetic part driven by the Lorentz force. While the former velocity defines the kinematic dynamo problem responsible for the exponential growth of the magnetic field, the latter encodes the magnetic back reaction that leads to the eventual nonlinear saturation of the dynamo. We argue that two different types of solution should exist: weak solutions in which the saturated velocity remains close to the kinematic one, and strong solutions in which magnetic forces drive the system into a new strongly magnetised state that is radically different from the kinematic one. Indeed, we find both types of solutions numerically. Interestingly, we also find that, in our inertialess system, both types of solutions exist on the same subcritical branch of solutions bifurcating from the non-magnetic convective state, in contrast with the more traditional situation for systems with finite inertia in which weak and strong solutions are thought to exist on different branches. We find that for weak solutions, the force balance is the same as in the non-magnetic case, with the horizontal size of the convection varying as the one-third power of the Ekman number (the ratio of viscous to Coriolis forces), which gives rise to very small cells at small Ekman numbers (i.e. high rotation rates). In the strong solutions, magnetic forces become important and the convection develops on much larger horizontal scales. However, we note that even in the strong cases the solutions never properly satisfy Taylor’s constraint, and that viscous stresses continue to play a role. Finally, we discuss the relevance of our findings to the study of planetary dynamos in rapidly rotating systems such as the Earth.

Results are presented from laboratory experiments on lateral intrusive flows driven by horizontal gradients of properties in double-diffusive systems. These are variations on the classical experiments in which salt stratified fluid was separated from a sugar stratified fluid by a removable barrier. With the removal of this barrier, lateral intrusions of sugar solution into the salt solution alternated in the vertical with salt intrusions into the sugar solution. In our present study, the fluid has continuous horizontal gradients of sugar, density-compensated by opposing horizontal gradients of salt, rather than the discontinuity of properties in the classical experiments.

Observations of these new experiments include: shadowgraphs, PTV (particle tracking velocimetry) showing the structure of the flow, and PIV (particle-image velocimetry) from which velocity vector fields on a vertical plane were obtained; from these, mean flows, Reynolds stresses, and associated momentum fluxes were computed.

These experiments have been conducted for three regimes of vertical stratification: (i) Salt-finger favourable (‘hot and salty’ above); (ii) Diffusive convection favourable (‘hot and salty’ below); (iii) Doubly stable (‘cold and salty’ below).

One of our main conclusions concerns the driving mechanism for the horizontal intrusive flow. Away from the front or ‘nose’ of the intrusions, the lateral flows are no longer tilted but are horizontal. Here, finger layers alternate in the vertical with convecting layers. In these convecting layers, vertical transport of horizontal momentum by the Reynolds stress plays a major role in maintaining the lateral motion against viscous dissipation.

We study experimentally the effects of spanwise confinement on turbulent miscible fountains issuing from a round source of radius $r_{0}$. A dense saline solution is ejected vertically upwards into a fresh-water environment between two parallel plates, separated by a gap of width $W$, which provide restraint in the spanwise direction. The resulting fountain, if sufficiently forced, rapidly attaches to the side plates as it rises and is therefore ‘confined’. We report on experiments for five confinement ratios $W/r_{0}$, spanning from strongly confined ($W/r_{0}\rightarrow 2$) to weakly confined ($W/r_{0}\approx 24$), and for source Froude numbers $Fr_{0}$ ranging between $0.5\leqslant Fr_{0}\leqslant 96$. Four distinct flow regimes are observed across which the relative importance of confinement, as manifested by the formation and growth of quasi-two-dimensional structures, varies. The onset of each regime is established as a function of both $W/r_{0}$ and $Fr_{0}$. From our analysis of the time-averaged rise heights, we introduce a ‘confined’ Froude number $Fr_{c}\equiv Fr_{0}(W/r_{0})^{-5/4}$, which encompasses the effects of confinement and acts as the governing parameter for confined fountains. First-order statistics extracted from the flow visualisation, such as the time-averaged rise height and lateral excursions, lend further insight into the flow and support the proposed classification into regimes. For highly confined fountains, the flow becomes quasi-two-dimensional and, akin to quasi-two-dimensional jets and plumes, flaps (or meanders). The characteristic frequency of this flapping motion, identified through an ‘eddy counting’ approach, is non-dimensionalised to a Strouhal number of $St=0.12{-}0.16$, consistent with frequencies found in quasi-two-dimensional jets and plumes.

The problem considered is that of the steady motion of a series of neutrally buoyant, flat-faced, rigid, cylindrical capsules along the axis of a pipeline under the influence of a hydraulic pressure gradient. The Navier-Stokes equations are non-dimensionalized and expressed in central-difference form. Numerical solutions are found by the method of relaxation for Reynolds numbers up to 20 000 and a close agreement is obtained with readings from a laboratory apparatus for Reynolds numbers up to 2200.

The flow is examined in detail and the existence of toroidal vortices between successive capsules is demonstrated. Their shape is shown to be increasingly influenced by inertial forces as the Reynolds number increases, but the overall pressure gradient is not greatly dependent on the Reynolds number.

The classical Kelvin-Helmholtz problem of the instability of the vortex sheet between two uniform streams is extended to allow for non-uniformity in the streams. A small-wavelength approximation shows that the most unstable disturbances have a growth rate proportional to the greatest discontinuity of velocity at the vortex sheet. The solution for all wavelengths is found for two cases when the variation in the stream velocity is small compared with the stream velocity itself. One of these cases indicates that a transverse variation in the stream velocity can increase the instability for long wavelengths, but only to a small extent.

A thin, flexible hydrofoil has been used as a model to simulate the swimming of a two-dimensional fish in an ideal, incompressible fluid, as treated in recent theoretical papers. The apparatus is described in some detail and typical data are compared with the predictions of theory. An error analysis is given, showing that, within the expected errors and limits of validity of theory, experimental verification of theory is very good.

Instabilities of nanoparticle-laden non-isothermal flows in homogeneous porous media are investigated. The study is conducted for two representative systems; a hot fluid displacing a cold one (HDC) and a cold fluid displacing a hot one (CDH). The effects of Brownian diffusion and of thermophoresis, representing the average motion of the nanoparticles as a result of temperature gradients, are analysed. In the HDC case, the synergetic Brownian and thermophoretic effects induce a migration of nanoparticles towards the cold fluid and tend systematically to enhance the instability. In particular, because of these combined effects, an initially stable displacement can actually be destabilized. In the CDH case however, Brownian diffusion still acts towards the transport of nanoparticles downstream into the hot fluid while thermophoresis tends to resist such migration. These counteracting effects lead to the generation of local accumulations of nanoparticles at the front and engender the development of local stable regions in the flow. These stable regions hinder the growth of the instabilities, especially those of backward-developing fingers. It is concluded that, in this case, thermophoresis acts against Brownian diffusion and results in less unstable displacements compared to flows where thermophoresis is absent. This effect, exclusively associated with thermophoresis, will not be observed in nanoparticle-free non-isothermal displacements. Finally, it is found that the main effects of Brownian diffusion and thermophoresis arise mainly from their contributions to nanoparticle transport while their effects on the energy balance are negligible and can be disregarded.

In this paper we discuss the initial evolution of wind-generated, gravity-capillary waves by means of a dynamical model that includes the effects of wind input, viscous dissipation and three-wave interactions. In particular, we study the generation of the initial wavelets by wind and the subsequent migration of the peak of the spectrum to lower wavenumbers. Under certain conditions a sudden migration of the peak wavenumber is found. It is argued that this sudden migration is related to the phenomenon of second-harmonic resonance. We also observe that during the generation of the initial wavelets by wind, nonlinear three-wave interactions may be important. Therefore, the experimental determination of the growth rate of the waves by wind by just analysing the time series of the surface elevation (as is done by e.g. Kawai 1979 and Plant & Wright 1977) might be in error.

This study is motivated by controlling transient growth and subsequent bypass transition of the laminar boundary layer to turbulence. In experiments employing a model problem, an active roughness element is used to introduce steady/unsteady streak disturbances in a Blasius boundary layer. This tractable arrangement enables a systematic investigation of the evolution of the disturbances and of potential methods to control them in real time. The control strategy utilizes wall-shear-stress sensors, upstream and downstream of a plasma actuator, as inputs to a model-based controller. The controller is designed using empirical input/output data to determine the parameters of simple models, approximating the boundary layer dynamics. The models are used to tune feedforward and feedback controllers. The control effect is examined over a range of roughness-element heights, free stream velocities, feedback sensor positions, unsteady disturbance frequencies and control strategies; and is found to nearly completely cancel the steady-state disturbance at the downstream sensor location. The control of unsteady disturbances exhibits a limited bandwidth of less than 1.3 Hz. However, concurrent modelling demonstrates that substantially higher bandwidth is achievable by improving the feedforward controller and/or optimizing the feedback sensor location. Moreover, the model analysis shows that the difference in the convective time delay of the roughness- and actuator-induced disturbances over the control domain must be known with high accuracy for effective feedforward control. This poses a limitation for control effectiveness in a stochastic environment, such as in bypass transition beneath a turbulent free stream; nonetheless, feedback can remedy some of this limitation.

Three velocity components of water particles in a plunging breaker over a horizontal step on the bed of a two-dimensional laboratory wave tank have been determined simultaneously by means of an elaborate flowmeter that measures the flow drag on three ‘tension threads’, with each recording a separate flow component.

It is found that all three of the r.m.s. values in the plunging breaker become maximum at x/L ≈ 0·7, where x is the distance from the breaking point to the shore and L is the wavelength. It is found that both the velocity and r.m.s. values of the transverse flow component generated by the shoaling and wave breaking become comparable to those of the other two flow components.

On the basis of spectral analyses it is found that major wave frequencies in both the longitudinal and vertical flow components of the original two-dimensional wave survive even after experiencing relatively strong shoaling and wave breaking, and part of the original wave energy is transferred to the transverse flow component and is located at these major frequencies. It is found that the majority of the higher-harmonic-frequency components (or turbulent fluctuations) are generated in the shoaling process and that the wave breaking provides a relatively minor contribution to the generation. Finally, it is found that, through the shoaling and wave breaking, the original wave energy is transported to a frequency range lower than the primary wave frequency (negative cascade), as well as to the higher frequency range (positive cascade) in each flow component.