Free-stream turbulence (FST) is perhaps the most important source inducing by-pass transition in boundary layer flows. The present study describes the initial energy growth of streamwise-oriented disturbances in the boundary layer originating from the presence of FST with intensities between 1.4% and 6.7%, but the study is mainly focused on the modelling of the transition zone. For this study three passive and one active turbulence-generating grids were used. The active grid was used in order to vary the turbulence intensity ($Tu$) without changing the setup in the test section. It is shown that the initial disturbance energy in the boundary layer is proportional to $Tu^2$. The experiments also show that the energy grows in linear proportion to the Reynolds number based on the downstream distance. Furthermore the transitional Reynolds number is shown to be inversely proportional to $Tu^2$ for the whole range of $Tu$ studied. The intermittency in the transitional zone was determined and it was shown that the intermittency function has a universal shape if the downstream distance is scaled with the length of the transition zone. The Reynolds number based on this transition zone length was found to increase linearly with the transition Reynolds number; however it was also noted that this non-dimensional length has a minimum value. With these results we were able to formulate an expression for the spot production rate which has a better physical base than previous models.

The effect of an opposing wind on the stratification and flow produced by a buoyant plume rising from a heat source on the floor of a ventilated enclosure is investigated. Ventilation openings located at high level on the windward side of the enclosure and at low level on the leeward side allow a wind-driven flow from high to low level, opposite to the buoyancy-driven flow. One of two stable steady flow regimes is established depending on a dimensionless parameter $F$ that characterizes the relative magnitudes of the wind-driven and buoyancy-driven velocities within the enclosure, and on the time history of the flow. A third, unstable steady flow solution is identified. For small opposing winds (small $F$) a steady, two-layer stratification and displacement ventilation is established. Exterior fluid enters through the lower leeward openings and buoyant interior fluid leaves through the upper windward openings. As the wind speed increases, the opposing wind may cause a reversal in the flow direction. In this case, cool exterior fluid enters through the high windward openings and mixes the interior fluid, which exits through the leeward openings. There are now two possibilities. If the rate of heat input by the source exceeds the rate of heat loss through the leeward openings, the temperature of the interior increases and this flow reversal is only maintained temporarily. The buoyancy force increases with time, the flow reverts to its original direction, and steady two-layer displacement ventilation is re-established and maintained. In this regime, the increase in wind speed increases the depth and temperature of the warm upper layer, and reduces the ventilation flow rate. If, on the other hand, the heat loss exceeds the heat input, the interior cools and the buoyancy-driven flow decreases. The reversed flow is maintained, the stratification is destroyed and mixing ventilation occurs. Further increases in wind speed increase the ventilation rate and decrease the interior temperature.

The transitions between the two ventilation flow patterns exhibit hysteresis. The change from displacement ventilation to mixing ventilation occurs at a higher $F$ than the transition from mixing to displacement. Further, we find that the transition from mixing to displacement ventilation occurs at a fixed value of $F$, whereas the transition from displacement to mixing flow is dependent on the details of the time history of the flow and the geometry of the openings, and is not determined solely by the value of $F$.

Theoretical models that predict the steady stratification profiles and flow rates for the displacement and mixing ventilation, and the transitions between them, are presented and compared with measurements from laboratory experiments. The transition between these ventilation patterns completely changes the internal environment, and we discuss some of the implications for the natural ventilation of buildings.

The effect of a temperature-dependent solute diffusion coefficient on a model of unidirectional solidification of a binary melt with a quasi-equilibrium mushy (two-phase) zone is studied. The Soret effect (thermodiffusion) is also included in the analysis. The concentration field in the liquid, solid and mushy phases, as well as the rate of solidification and mushy zone thickness, are found analytically as functions of all thermophysical parameters. The role of the nonlinear solute transport is detailed in the analysis. On the basis of analytical solutions, the regime of solidification with a quasi-equilibrium mushy zone is replaced by an equivalent discontinuity surface (frontal) regime with new boundary conditions.

We formulate a simple model which describes the interplay between electromagnetic forces, inertia, and gravity in liquid-metal current-limiting devices utilizing the electromagnetic pinch effect. The dynamics of this system, called an H-trough, is completely described by a nonlinear ordinary differential equation for the fluid's cross-section as a function of time. A bifurcation analysis of stationary states is performed. For a wide range of geometry parameters the cross-section of the fluid is found to be a discontinuous function of the electrical current. The jump in cross-section above some critical current is accompanied by a strong increase of the total electric resistance of the system and results in the current-limiting action of the device by the pinch effect. An experimental study of the system confirms the predicted switching behaviour. For low electric current the experiment is in excellent quantitative agreement with the theory, while for high electric current three-dimensional instabilities and end effects render the agreement with the one-dimensional model less satisfactory. Our model enables us to isolate the pertinent non-dimensional parameters for liquid-metal current limiters and to derive the scaling law of the critical electric current as a function of the geometry and material properties of the system.

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 transport and dynamics of an isolated liquid oxygen (LOX) droplet in a supercritical hydrogen stream has been numerically studied based on the complete conservation equations in axisymmetric coordinates. The approach employs a unified treatment of general fluid thermodynamics and transport, and accommodates rapid variations of fluid properties in the transcritical regime. Surface tension of the droplet is ignored in consistency with the supercritical thermodynamic condition. The analysis allows for a systematic investigation into droplet behaviour over broad ranges of fluid thermodynamic states and ambient flow conditions. Detailed flow structures and transport phenomena are examined to reveal various key mechanisms underlying droplet vaporization in a supercritical forced convective environment. In addition, correlations of droplet lifetime and drag coefficient are established in terms of fluid properties, pressure, and free-stream Reynolds number.

Diffusion of neutrally buoyant spherical particles in concentrated monodisperse suspensions under simple shear flow is investigated. We consider the case of non-Brownian particles in Stokes flow, which corresponds to the limits of infinite Péclet number and zero Reynolds number. Using an approach based upon ideas of dynamic light scattering we compute self- and gradient diffusion coefficients in the principal directions normal to the flow numerically from Accelerated Stokesian Dynamics simulations for large systems (up to 2000 particles). For the self-diffusivity, the present approach produces results identical to those reported earlier, obtained by probing the particles' mean-square displacements (Sierou & Brady, J. Fluid Mech. vol. 506, 2004 p. 285). For the gradient diffusivity, the computed coefficients are in good agreement with the available experimental results. The similarity between diffusion mechanisms in equilibrium suspensions of Brownian particles and in non-equilibrium non-colloidal sheared suspensions suggests an approximate model for the gradient diffusivity: ${\textsfbi D}^\triangledown\,{\approx}\,{\textsfbi D}^s/S^{eq}(0)$, where ${\textsfbi D}^s$ is the shear-induced self-diffusivity and $S^{eq}(0)$ is the static structure factor corresponding to the hard-sphere suspension at thermodynamic equilibrium.

Turbulent swirling flows injected into a coaxial dump chamber at different swirl numbers were studied using large-eddy simulations. The Favre-filtered conservation equations of mass, momentum, and energy in three dimensions were solved numerically by means of a finite-volume approach. Results have been validated against experimental data in terms of mean flow velocity and turbulence properties. The work provides insight into several salient features of swirling flows, including vortex breakdown, shear-layer instability, and vortico-acoustic interactions. The dominant acoustic mode in the chamber was found to be sensitive to unsteady vorticity evolution, which in turn strongly depends on the swirl number. Low-frequency acoustic oscillations may arise from large-scale coherent motions in the central toroidal recirculation zone at high swirl numbers. In contrast, the shear-layer instability downstream of the backward-facing step results in high-frequency acoustic waves at low swirl numbers.

We present an experimental study of a new surfactant-driven fingering phenomenon in a Hele-Shaw cell. First, the threshold of instability is examined and compared with the linear theory. Second, the nonlinear evolution of fingering is quantified, and steady and unsteady patterns are distinguished. A wide range of dynamical behaviour is observed from drifting and merging fingers to cusp formation between fingers and subsequent ejection of air bubbles. All experiments are performed with a pure surfactant – sodium dodecyl sulphate – thus allowing us to obtain a well-defined bifurcation map for the specific kinetic and material properties of this surface-active substance. The measurements are conducted in a Hele-Shaw cell with smooth and roughened walls. A basic physical model is proposed to obtain further insight into the influence of the surfactant properties on the dip-coating process and, as a result, on the critical phenomena. The study allows us to resolve the discrepancies between previous experimental results and linear theory.

In very gradually shoaling coastal water the energy of incident waves appears to be absorbed not by breaking at the upper surface, but predominantly by turbulent dissipation near the rippled sea bed. The question has been asked whether there can be then any wave set-up, that is any increase in the mean water level, at, or close to, the shoreline.

To answer this question the equations of wave energy and momentum in water of slowly varying depth are generalized so as to include the presence of a dissipative boundary layer at the bottom. It is then shown that the resulting equation for the mean surface slope can be integrated exactly, to give the mean surface depression (the ‘set-down’) in terms of the local wave amplitude and water depth, outside the surf zone. In the special case of a uniform beach slope $s$, a closed expression is obtained for the wave amplitude in terms of the local depth, under two different sets of conditions: (i) when the thickness of the boundary layer at the bottom is assumed to be constant, and (ii) for waves over a rippled bed, when the boundary-layer thickness corresponds to the measured dissipation of energy in oscillatory waves over steep sand ripples. In both cases it is found that there exists a maximum bottom slope $s$ below which the wave amplitude must diminish monotonically towards the shoreline. This maximum value of $s$ is of order $10^{-3}$. The waves can indeed penetrate close to the shoreline without breaking, and the corresponding wave set-up is negligible. An example of where suitable conditions exist is on the continental shelf off North Carolina.

The evolution of a localized flow in a half-plane bounded by a rigid wall is analysed when the total mass is not conserved within the equivalent-barotropic quasi-geostrophic (QG) approximation. A simple formula expressing the total geostrophic mass in terms of the QG potential vorticity is derived and used to estimate the range of the geostrophic mass variability. The behaviour of the total mass is analysed for a system of two point vortices interacting with a wall. Distributed localized perturbations are examined by means of numerical experiments using the QG model. Two types of time variability of the total geostrophic mass are revealed: oscillating (the mass oscillates near some mean value) and limiting (the mass tends to some constant value with increasing time).

In the framework of a rotating shallow-water model, the QG model is known to describe the slow evolution of the geostrophic vorticity, assuming the Rossby number to be small. Consideration of the next-order dynamics shows that conservation of the total mass and circulation is provided by a compensating jet taking away the surplus or shortage of mass from the localized geostrophic disturbance. The along-wall jet expands with the fast speed of Kelvin waves to the right of the initial perturbation. The slow time-dependent amplitude determines the jet sign and intensity at each instant. The dynamics of the compensating jet are discussed for both oscillating and limiting regimes revealed by the QG analysis.

The role of Kelvin waves in establishing the usual Phillips condition for conservation of circulation of the along-wall QG velocity is discussed. In the case of periodic motion or motion in a finite domain, the approximation of an infinitely long boundary can be used if (i) the typical basin scale greatly exceeds the typical size of the localized perturbation and the Rossby scale; and (ii) the time does not exceed the typical time required for the Kelvin wave to travel the typical basin scale. Both these conditions are typical of synoptic variability in the ocean.

In the present work the effect of spanwise oscillations on the most unstable Görtler vortex is studied. The wavenumber of the most unstable disturbance is very large, so that the parabolic character of the problem is eliminated. After the disturbances are expanded in a Fourier series in time, the eigenvalue problem is solved for various amplitudes and frequencies of the oscillation. Due to numerical difficulties the treatment of very high amplitudes and/or very low frequencies becomes prohibitively expensive. Therefore an approximate formulation was developed for high magnitudes of the spanwise speed of the oscillation $E$. The results, which were obtained in all cases, indicate that the disturbances move away from the wall in a logarithmic way, reducing the effects of the oscillation. Consequently, it is impossible to stabilize the flow completely. However, it is shown that a large reduction of the growth rate can be achieved even for moderate values of $E$.

New types of electromagnetic parametric instability have been observed at the periphery of the free surface of a liquid metal pool in the presence of a low-frequency magnetic field. An experimental set-up is used to observe the motion of a mercury layer on a substrate located in a solenoidal coil supplied with low-frequency alternating electric currents. The Lorentz body forces produced are mainly oscillatory and generate motion in the liquid. Various regular and irregular free-surface patterns are observed. Two-dimensional stability analysis shows that axisymmetric waves are directly forced by the electromagnetic forces while azimuthal waves are the result of instability. The experimental stability diagram exhibits ‘tongues’ as already observed for parametric resonance instability. For high magnetic field strengths, the free-surface patterns become highly unstructured. High-amplitude ‘fingers’ as well as solitary waves are observed. Measurements of the deformation observed on photographs are compared with rough theoretical estimates.

The Benney equation including thermocapillary effects is considered to study a liquid film flowing down a homogeneously heated inclined wall. The link between the finite-time blow-up of the Benney equation and the absence of the one-hump travelling-wave solution of the associated dynamical system is accurately demonstrated in the whole range of linearly unstable wavenumbers. Then the blow-up boundary is tracked in the whole space of parameters accounting for flow rate, surface tension, inclination and thermocapillarity. In particular, the latter two effects can strongly reduce the validity range of the Benney equation. It is also shown that the subcritical bifurcation found for falling films with the Benney equation is related to the blow-up of solutions and is unphysical in all cases, even with the thermocapillary effect though in contrast to horizontally heated films. The accuracy of bounded solutions of the Benney equation is determined by comparison with a reference weighted integral boundary layer model. A distinction is made between closed and open flow conditions, when calculating travelling-wave solutions; the former corresponds to the conservation of mass and the latter to the conservation of flow rate. The open flow condition matches experimental conditions more closely and is explored for the first time through the associated dynamical system. It yields bounded solutions for larger Reynolds numbers than the closed flow condition. Finally, solutions that are conditionally bounded are found to be unstable to disturbances of larger periodicity. In this case, coalescence is the pathway yielding finite-time blow-up.

The dynamics of small perturbations on a buoyant coastal current is investigated. The system is described using a one and a half-layer model where the active upper layer vanishes at a certain distance from the coast, forming a front. Perturbations are imposed on a steady basic state with no along-coast variation. Analytical solutions are discussed for two special configurations of the basic state: (i) constant along-shore velocity, i.e. a coastal current with triangular cross-section, and (ii) a constant potential vorticity current. Two wave modes are found in both cases: a slowly moving frontally trapped wave, and a coastally trapped wave that moves with approximately the internal Kelvin wave speed plus the speed of the current at the coast. However, these two wave modes are not sufficient to construct a generally shaped initial perturbation. The part of the initial perturbation not covered by the two wave modes will in case (i) split into an infinite number of higher wave modes all travelling faster than the frontal wave and in case (ii) be advected and slowly smeared out by the current. Under the assumption that the current is unidirectional we find that the perturbations always move in the direction of a Kelvin wave, i.e. in the same direction as the coastal current, for all physically relevant cases.

The stability of fluid flow through a narrow conduit with elastic walls is explored, treating the fluid as incompressible and viscous, and the walls as semi-infinite linear Hookean solids. Instabilities analogous to roll waves occur in this system; we map out the physical regime in which they are excited. For elastic wave speeds much higher than the fluid speed, a critical Reynolds number is required for instability. However, that critical value depends linearly on wavenumber, and so can be made arbitrarily small for long waves. For smaller elastic wave speeds, the critical Reynolds number is reduced still further, and Rayleigh waves can be destabilized by the fluid even at zero Reynolds number. A brief discussion is given of the nonlinear dynamics of the instabilities for large elastic wave speed, and the significance of the results to the phenomenon of volcanic tremor is presented. Although magma itself seems unlikely to generate flow-induced vibrations, the rapid flow through fractured rock of low-viscosity fluids exsolved from magma appears to be a viable mechanism for volcanic tremor.