A land- and sea-breeze (LSB) circulation under a calm stably stratified environment was simulated in the laboratory using a temperature-controlled water tank. The floor of the tank was divided into two sections representing land and sea. Two heat exchangers, each of them connected to a thermostat, simulated the diurnal thermal cycle typically experienced by the surface in coastal zones. A third heat exchanger positioned at the top of the tank provided a stable thermal stratification. Particle-tracking velocimetry was applied to evaluate the two-dimensional velocity field in the vertical centreline section of the tank orthogonal to the coastline, while a rack of thermocouples measured the vertical temperature profile near the coastline and further inland. It is shown that the overall flow consists of a closed circulation caused by the periodic change of the horizontal temperature difference between land and sea surfaces. Furthermore, the formations of cellular convection during the first phase of warming of the land-side as well as the genesis of the sea-breeze front were detected and analysed. Application of the proper orthogonal decomposition (POD) technique allowed the vortical large-scale structures in the flow to be determined. The results suggest that the energy contained in the first POD eigenmodes rapidly converged with the first mode, associated with the overall LSB circulation, being dominant with 73% of the energy. The other less energetic modes were mainly associated with the cellular convection.

We study experimentally the behaviour of a drop deposited on a conical fibre. It is shown that for wetting liquids, such a drop spontaneously moves towards the region of lower curvature. The driving force is measured and shown to be a gradient of Laplace pressure, which allows us to characterize the dynamics of these self-propelling drops. We conclude by discussing the efficiency of this device for drying a solid initially coated with a liquid film.

The transport of sand by wind results from the equilibrium between the erosion of grains dragged by the flow and the resulting slow down of the wind velocity. The dynamical mechanisms governing the saturation of the sand flux are investigated theoretically. We first demonstrate that previous models, based on the assumption that all the grains have the same trajectory, are either not self-consistent or lead to unstable solutions. A model based on a discrete number of states is derived, which solves these problems. Two well-defined species of grain appear, which correspond to saltons (high-energy grains) and reptons (grains ejected from the sand bed by the impact of saltons). They play specific roles: the negative feedback of the transport on the wind is limited to the reptation layer while most of the transport is due to saltation. The model is further simplified, benefiting from the existence of these two species and the dependencies of the threshold velocity, the saturated flux, the aerodynamic roughness and the saturation length are derived and compared to experimental measurements.

This paper presents experimental measurements of the approach and rebound of a particle colliding obliquely with a wall in a viscous fluid. Steel and glass particles 12.7 mm in diameter were used. The experiments were performed using a thick Zerodur wall (a glass-like material) with various mixtures of glycerol and water. Normal and tangential coefficients of restitution were defined from the ratios of the respective velocity components at the point of contact just prior to and after impact. These coefficients account for losses due to lubrication effects and inelasticity. A third parameter, a coefficient of sliding friction, provides a measure of the tangential force acting on the particle as it slides during a collision.

Oblique collisions in a fluid are qualitatively similar to oblique collisions in a dry system, with a lowered friction coefficient dependent on surface roughness. For smooth surfaces the friction coefficient is drastically reduced due to lubrication effects. A theoretical model that takes into account the dependence of viscosity on pressure is proposed to explain the observed tangential force acting on a smooth sphere during an oblique collision. The model relies on an inferred uniform temperature increase within the lubrication layer, a consequence of viscous heating during impact. The tangential force felt by the particle is expressed as a friction coefficient dependent on the viscosity within the lubrication layer. The viscosity increases owing to pressure effects and decreases owing to thermal effects. For rough surfaces the friction coefficient is comparable to that measured in dry systems, since the surface asperities may interact with each other through the lubrication layer.

The time development of a dense eddy placed on a varying topography in a rotating system is the subject of this paper. It is shown that if the bathymetric variations are comparable with the thickness of the eddy, these will induce a first-order time development in the water mass. Large-amplitude geostrophic theory shows that the water is advected along the depth contours with a speed that is proportional to the slope of the bottom. The results are applied to a laboratory experiment with a rotating parabolic channel. According to theory, an initially circular eddy placed in the centre of the channel becomes elliptical while shifting its axis along the channel. The outcome of the experiment is in accordance with theory, and the importance of topographic advection in the ocean is discussed. It is suggested that the mechanism may be important for moving water from deep-water formation sites and into the global deep-water circulation.

The forced reattachment of flow to an inclined flat surface, simulating a simple flap, was investigated experimentally. The transition from a separated to an attached state of the flow was initiated by an abrupt change in the frequency and the amplitude of periodic perturbations emanating from a slot at the flap shoulder. The excitation parameters determined the total duration of the reattachment process. Minimum reattachment time occurred at an optimal excitation frequency of $F_{\hbox{\scriptsize{\it opt}}}^{+} \approx 1.5$, which was independent of amplitude and flap inclination. The control over the process was achieved by enhancing large spanwise vortices in the flow. Spatial amplification of consecutive vortices induces mean transport of fluid away from the flap surface which causes the main stream to reattach. The time scales of the excitation are at least an order of magnitude smaller than the typical reattachment times.

The controlled separation of flow from an inclined straight flap at high inclination angles was investigated experimentally. The separation process was initiated by an abrupt change in the excitation emanating from a slot at the flap shoulder. A complete cessation of the actuation resulted in formation of a large vortex above the flap akin to the familiar ‘dynamic stall vortex’ (DSV) seen over oscillating airfoils in pitch. The DSV temporarily increased the aerodynamic load over the flap before it dropped to its low separated value. The duration of this overload decreased as the flap inclination increased. The use of periodic excitation during separation slowed down the rate of separation and changed its character depending on the amplitude and the frequency used. Forcing separation by switching the excitation to a high frequency ($3\,{<}\,F^{+}\,{<}\,8$) reduced or even eliminated the increase in flap loading that is associated with the DSV. A switch to low frequencies ($F^{+}\,{<}\,1$) extended the duration of separation and increased the transient overload during the initial stage of the process.

We present an experimental study of the emptying of an ideal vertical bottle under gravity $g$. The idealization reduces the bottle to a cylinder of diameter $D_{0}$, length $L$, closed at the top and open at the bottom through a circular thin-walled hole of diameter $d$, on the axis of the cylinder. The study is performed in the low-viscosity limit. The oscillatory emptying of the ‘bottle’ is referred to as the glug-glug, and is characterized by its period $T$, whereas the whole emptying process is characterized by a time $T_{e}$. Concerning the long time scale $T_{e}$, we show that: \[ \frac{T_{e}}{T_{e0}}=\left(\frac{D_{0}}{d}\right)^{5/2}, \] where $T_{e0}\,{\approx}\, 3.0 L/\sqrt{gD_{0}}$ is the emptying time of an unrestricted cylinder. On the short time scale $T$, we show that the physical origin of the oscillations lies in the compressibility of the surrounding gas. The period can be written as: \[ T\,{=}\,\frac{L}{\sqrt{\gamma P_{0}/\rho}}\Phi(\skew1\bar{z}_{i}/L), \] where $\gamma$ is the ratio of specific heats of the gas, $P_{0}$ its pressure and $\rho$ stands for the density of the liquid. The function $\Phi$ is dimensionless and changes with the relative position of the liquid interface $\skew1\bar{z}_{i}/L$. Finally, this analysis of time scales involved in the emptying of vertical cylinders is applied to other liquid–gas oscillators.

We study the linear and nonlinear stability of a thick surfactant deposition spreading on a thin liquid film using transient growth analysis (TGA) and direct numerical simulations (DNS) of the two-dimensional lubrication equations, respectively. Results of the TGA of the one-dimensional spatially and temporally evolving base state reveal disturbance growth and the selection of a perturbation of intermediate wavenumber. This perturbation targets the ‘contact region’ between the deposition and the underlying thin liquid film and grows despite the absence of intermolecular forces. Increasing the initial thickness ratio of the deposition to the thin film and decreasing the relative magnitude of capillarity and surface diffusion further amplify perturbation growth. The DNS results clearly show the formation of fingers in the contact region behind the surfactant leading edge and provide further confirmation of the TGA findings.

Motions of fluid particles advected by a vortex soliton are studied. In a reference frame which moves with the vortex soliton, particle motions are confined in a torus near the loop part of the vortex soliton for a wide range of three parameters that characterize the shape and strength of the vortex soliton. The transported volume is calculated numerically as a function of these parameters. The product of the volume and the translational velocity of the soliton provides the rate of transport. Using this quantity, the optimized shape of the soliton for the maximum rate of transport is considered. The torus is composed of groups of invariant surfaces around periodic trajectories. Similar phenomena are observed with the KAM tori for non-integrable Hamiltonian systems. To extract the essential mechanism of the transport properties, an ordinary differential equation model is proposed, which is named the ‘chopsticks model’. This model successfully explains the qualitative features of the transport.

The flow passing over a trapezoidal tab mounted on a flat plate is studied using direct numerical simulation (DNS). Such a tab has been used to generate hairpin-like vortices to enhance cross-stream mixing. We attempt to provide a detailed account of the three-dimensional topology and dynamics of the hairpin vortices in the tab wake. Simulations are conducted for three tab inclination angles at Reynolds number $\hbox{\it Re}\,{=}\,600$ based on the free-stream velocity and the tab height. A finite-volume discretization scheme involving $2.6\,{\times}\, 10^6$ control volumes is employed for the simulations and the results are compared with PIV experimental data. Simulations captured all the experimentally observed near-field flow features including a pair of streamwise co-rotating vortices and its transition to hairpin vortices. Simulation results provide new insight into the vortex dynamics in the tab wake. It is shown that the hairpin vortex is capable of lifting up and entraining vorticity from the local boundary layer, thereby increasing its strength to counter the vorticity diffusion. It is also observed that the turbulence production is mostly accomplished by the hairpin heads/arches, while the highest kinetic energy is associated with hairpin vortex legs. The topological characteristics of the structures and the statistical characteristics of the flow are discussed in detail.

An experimental and numerical investigation has been carried out into the instability characteristics of natural convection of an ethanol–water solution in a vertical tank with aspect ratio (height/width) of 15. The solution contains 39 wt% ethanol with Prandtl number ${\it Pr}\,{=}\,26$. The density anomaly due to the Soret effect may be safely ignored in the present test configuration. Onset of instability, in the form of multicellular convection located in the mid-height of the tank, occurs at Grashof number $\hbox{\it Gr}\,{\cong}\,13\,500$. These convection cells are unsteady even at low supercritical states, similar to earlier observations for higher Pr fluids. The cause of such unsteadiness of the flow has been determined by studying the streak images constructed by superposing individual frames of a digital movie sequence. New cells are generated in the upper and lower portions of the tank and then migrate toward the centre, causing the convection cells in the mid-section to merge. At higher Gr, even the tertiary cells, which rotate in the opposite direction of the secondary cells, participate in the merging process. Numerical simulations of the two-dimensional natural convection of a Boussinesq fluid with constant thermophysical properties, carried out at low supercritical Gr equivalent to the experimental value, show the same process of cell generation and merging as that observed in the experiments. By analysing the substantial time rate of change of the kinetic energy of the fluid using the mechanical energy equation, it is determined that the energy needed for the cell generation process is supplied by the work of the dynamic pressure. The subsequent migration of the cells toward the middle is caused by the pressure gradient in the tank. The total kinetic energy of the fluid attains a relative maximum right after a merging process due to the reduction of dissipation associated with the region of strong shear between the cells.

The three-dimensional Green's function of water waves in variable-bathymetry regions, associated with the problem of propagation of water waves emitted from a monochromatic point source, is derived and studied. The solution is of interest in its own right but also provides useful information for the formulation and treatment of complex wave–body–seabed interaction problems in variable-bathymetry regions, especially as regards the hydrodynamic characteristics of large structures installed in the nearshore and coastal environment. Assuming a parallel-contour bathymetry, with a continuous depth function of the form $h(x,y) \,{=}\, h(x)$, attaining constant, but possibly different, values at the semi-infinite regions $x \,{<}\, a$ and $x \,{>}\, b$, the problem is reduced to a two-dimensional one, by using Fourier transform. The transformed problem is treated by applying domain decomposition and reformulating it as a transmission problem in the finite domain containing the bottom irregularity. An appropriate decomposition of the wave potential is introduced, permitting the singular part to be solved analytically, and the problem for the regular part to be reformulated as a variational problem. An enhanced local-mode series representation is used for the regular wave potential in the variable-bathymetry region, including the propagating mode, the sloping-bottom mode (see Athanassoulis & Belibassakis 1999), and a number of evanescent modes. Using this representation, in conjunction with the variational principle, a forced system of horizontal coupled-mode equations is derived for the determination of the complex modal-amplitude functions of the regular wave potential. This system is numerically solved by using a second-order central finite-difference scheme. The source-generated water-wave potential is, finally, obtained by an efficient numerical Fourier inversion based on FFT. Numerical results are presented and discussed for various bottom topographies, including smooth but steep underwater trenches and ridges, putting emphasis on the identification of the important features of the near- and far-field patterns on the horizontal plane and on the vertical plane containing the point source. Characteristic patterns of trapped (well-localized) wave propagation over ridges are predicted and discussed.

We explore the three-dimensional interaction of higher acoustic modes with bias-flow perforated liners in cylindrical and annular ducts. Pressure fluctuations in the vicinity of the liners excite the production and shedding of vorticity from the rims of apertures in the liners. An effective liner compliance is used which accounts for this transfer of acoustical into vortical energy. The investigation is facilitated by a Green's function solution of the Helmholtz equation in a lined section of duct, allowing calculation of the amplitudes of exiting wave modes due to incoming acoustic disturbances. A system containing an arbitrary number of concentric liners and the hollow cavities formed between them can be modelled. The results for an incident plane wave are compared with those from our previously developed one-dimensional model, with excellent agreement. We demonstrate that results for all modes that travel parallel to the liner, including higher circumferential modes in narrow annular gaps, exhibit self-similar behaviour, and that liner design rules developed for planar duct modes can be adapted accordingly. The acoustic absorption can be strongly enhanced by downstream duct reflection for wavelengths larger than twice the liner length, but is less affected at higher frequencies that allow persistent pressure minima along the liner. Across larger frequency ranges, the liner systems are shown to permit two types of resonance associated with the duct and the cavities, respectively, and a third of Helmholtz type, associated with the system as a whole. The effect of these resonances on incident modes is demonstrated, and, in particular, we explore their enhancement of acoustic absorption.

We calculate the optimal upper and lower bounds, subject to the assumption of streamwise invariance, on the long-time-averaged mechanical energy dissipation rate $\varepsilon$ within the flow of an incompressible viscous fluid of constant kinematic viscosity $\nu$ and depth $h$ driven by a constant surface stress $\tau=\rho u^2_\star$, where $u_\star$ is the friction velocity. We show that $\varepsilon \leq \varepsilon_{\max}=\tau^2/(\rho^2\nu)$, i.e. the dissipation is bounded above by the dissipation associated with the laminar solution $\bu=\tau(z+h)/(\rho\nu) \xvec$, where $\xvec$ is the unit vector in the streamwise $x$-direction.

By using the variational ‘background method’ (due to Constantin, Doering and Hopf) and numerical continuation, we also generate a rigorous lower bound on the dissipation for arbitrary Grashof numbers $G$, where $G=\tau h^2/(\rho \nu^2)$. Under the assumption of streamwise invariance as $G \rightarrow \infty$, for flows where horizontal mean momentum balance and total power balance are imposed as constraints, we show numerically that the best possible lower bound for the dissipation is $\varepsilon \geq \varepsilon_{\min}=7.531 u_\star^3/h$, a bound that is independent of the flow viscosity. This scaling (though not the best possible numerical coefficient) can also be obtained directly by applying the same imposed constraints and restricting attention to a particular, analytically tractable, class of mean flows.

Water droplets (0.55 or 1.3 mm diameter) were photographed as they impinged on a stainless steel surface. The droplet impact velocity (10–50 m s−1) and the average roughness (0.03 or 0.23 μm) of the test surfaces were varied. The stainless steel substrate was mounted on the end of a rotating arm, giving linear velocities of up to 50 m s−1. Different stages of droplet impact were photographed by synchronizing the ejection of a single droplet with the position of the rotating arm and triggering of a camera. Finger-shape perturbations were observed around the edges of spreading droplets. The maximum diameter to which a droplet spread and the number of fingers formed around it were measured. The size and number of fingers increased with impact velocity and droplet diameter. At sufficiently high velocities, the tips of these fingers detached, producing satellite droplets. By increasing surface roughness, both the number of fingers and the maximum extent of spreading were decreased. At high impact velocities the spreading liquid film became so thin that it ruptured in several places. A mathematical model, based on linear Rayleigh–Taylor instability theory, was used to predict the wavelength of the fastest growing perturbation around a spreading droplet. The corresponding wavenumber agreed reasonably well with the number of fingers around the droplet.