This experimental study, performed under microgravity conditions, focuses on the evaporation dynamics of ethanol drops and the formation and behaviour of the hydrothermal waves that spontaneously develop on the drop surfaces. The aim of this study is to compare our results to a similar study performed under normal gravity conditions to confirm the purely thermocapillary origin of these instabilities. A scaling law predicts with good agreement the number of instabilities that form, regardless of the gravity level.

The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two- and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria. We found that at a critical deflection angle across the incident shock wave, the perturbations related to the turbulent boundary layer cause bi-directional transition processes between regular and irregular shock patterns for a free-stream Mach number of $\mathit{Ma}_{0}=2$. Computational results show that the mean deflection angle across the separation shock is decoupled from the incident shock wave and can be accurately modelled by the generalised free interaction theory. On the basis of these observations, and the von Neumann and detachment criteria for the asymmetric intersection of shock waves, we derive the critical incident shock deflection angles at which the shock pattern may/must become irregular. Numerical data for a free-stream Mach number of $\mathit{Ma}_{0}=3$ confirm the existence of the dual-solution domain predicted by theory.

We present a mesoscale kinetic model for multicomponent flows, augmented with a short range forcing term, aimed at describing the combined effect of surface tension and near-contact interactions operating at the fluid interface level. Such a mesoscale approach is shown to (i) accurately capture the complex dynamics of bouncing colliding droplets for different values of the main governing parameters, (ii) predict quantitatively the effective viscosity of dense emulsions in micro-channels and (iii) simulate the formation of the so-called soft flowing crystals in microfluidic focusers.

The interactions of vortices shed from two coaxially joined cylinders with a diameter ratio of 0.51 have been studied in a water channel, at Reynolds numbers, based on the large cylinder diameter, between 63 and 1100. Spectral and wavelet analyses of streamwise velocity measurements have identified the formation of three distinct spanwise vortex-shedding cells away from the far ends of the two cylinders, including a low-frequency cell, which appeared in a cyclic manner near the step and behind the large cylinder. Analysis of flow-visualization images has identified two distinct types of vortex connection at cell boundaries: some vortices in a cell of lower frequency connected across the boundary to counterparts in the cell of higher frequency, while others formed a half-loop to connect to a vortex shed from the opposite side of the cylinder in the same cell. Additional cross-boundary vortex connections balanced the total vortex strengths. The interactions of two types of streamwise vortices, identified as edge vortices and junction vortices, with spanwise vortices have also been documented.

We investigate theoretically the statics and dynamics of bubbles in fully confined liquids, i.e. in liquids surrounded by solid walls in all directions of space. This situation is found in various natural and technological contexts (geological fluid inclusions, plant cells and vessels, soil tensiometers, etc.), where such bubbles can pre-exist in the trapped liquid or appear by nucleation (cavitation). We focus on volumetric deformations and first establish the potential energy of fully confined bubbles as a function of their radius, including contributions from gas compressibility, surface tension, liquid compressibility and elastic deformation of the surrounding solid. We evaluate how the Blake threshold of unstable bubble growth is modified by confinement and we also obtain an original bubble stability phase diagram with a regime of liquid superstability (spontaneous bubble collapse) for strong confinements. We then calculate the liquid velocity field associated with radial deformations of the bubble and strain in the solid, and we predict large deviations in the kinematics compared to bubbles in extended liquids. Finally, we derive the equations governing the natural oscillation dynamics of fully confined bubbles, extending Minnaert’s formula and the Rayleigh–Plesset equation, and we show that the compressibility of the liquid as well as the elasticity of the walls can result in ultra-fast bubble radial oscillations and unusually quick damping. We find excellent agreement between the predictions of our model and recent experimental results.

This paper revisits the classical problem of convectively driven one-dimensional (parallel) flow along an infinite vertical plate. We consider flows induced by an impulsive (step) change in plate temperature, a sudden application of a plate heat flux, and arbitrary temporal variations in plate temperature or plate heat flux. Provision is made for pressure work and vertical temperature advection in the thermodynamic energy equation, processes that are generally neglected in previous one-dimensional studies of this problem. The pressure work term by itself provides a relatively minor refinement of the Boussinesq model, but can be conveniently combined with the vertical temperature advection term to form a single term for potential temperature advection. Vertical motion of air in a statically stable environment (stable potential temperature stratification) is associated with a simple negative feedback mechanism: warm air rises, expands and cools relative to the environment, whereas cool air subsides, compresses and warms relative to the environment. Exact solutions of the viscous equations of motion are obtained by the method of Laplace transforms for the case where the Prandtl number is unity. Pressure work and vertical temperature advection are found to have a significant impact on the structure of the solutions at later times.

Surface-active impurities may collect as a stationary film on the lowest part of a bubble rising in liquid while the remainder of the surface moves freely. Numerical approximations for the motion are available if the Reynolds number is low, but they fail for small films. We give the steady-state asymptotic solution for that case, and obtain the perturbation of the drag coefficient from its value for a completely free surface. It depends on the amount by which the surface tension is reduced at the rear stagnation point. This reduction has usually been taken to be the maximum possible for the particular impurity; we consider also the case where dilution is so great that that maximum cannot be reached because the impurity would then be diffusing off the surface at the rear faster than onto it elsewhere.

Enhancement of heat transport across a fluid layer is of fundamental interest as well as great technological importance. For decades, Rayleigh–Bénard convection has been a paradigm for the study of convective heat transport, and how to improve its overall heat-transfer efficiency is still an open question. Here, we report an experimental and numerical study that reveals a novel mechanism that leads to much enhanced heat transport. When vertical partitions are inserted into a convection cell with thin gaps left open between the partition walls and the cooling/heating plates, it is found that the convective flow becomes self-organized and more coherent, leading to an unprecedented heat-transport enhancement. In particular, our experiments show that with six partition walls inserted, the heat flux can be increased by approximately 30 %. Numerical simulations show a remarkable heat-flux enhancement of up to 2.3 times (with 28 partition walls) that without any partitions.

Expressions in closed form are derived for a number of local properties of a random, irrotational wave field. They are: (i) the mean potential and kinetic energies per unit projected area; (ii) the energy balance among the processes of energy input from the surface pressure fluctuations, rate of growth of potential and kinetic energy and horizontal energy flux; and (iii) the partition between potential and kinetic energy. These expressions are mainly in terms of quantities measured at the free surface, which are therefore functions of only two spatial variables (x, y) and of time t.

Approximations for these expressions can be found simply by subsequent expansion methods; the fourth order being the highest for which the assumption of irrotational motion is appropriate in a real fluid. It is shown that the mean product of any three first-order quantities is of fourth or higher order in the root-mean-square wave slope, and this result is applied in estimating the magnitude of some higher order effects. In particular, the skewness of the surface displacement is of the order of the root-mean-square surface slope, which has been confirmed observationally by Kinsman (1960).

We study here Green–Naghdi type equations (also called fully nonlinear Boussinesq, or Serre equations) modelling the propagation of large-amplitude waves in shallow water without a smallness assumption on the amplitude of the waves. The novelty here is that we allow for a general vorticity, thereby allowing complex interactions between surface waves and currents. We show that the a priori ($2+1$)-dimensional dynamics of the vorticity can be reduced to a finite cascade of two-dimensional equations. With a mechanism reminiscent of turbulence theory, vorticity effects contribute to the averaged momentum equation through a Reynolds-like tensor that can be determined by a cascade of equations. Closure is obtained at the precision of the model at the second order of this cascade. We also show how to reconstruct the velocity field in the ($2+1$)-dimensional fluid domain from this set of two-dimensional equations and exhibit transfer mechanisms between the horizontal and vertical components of the vorticity, thus opening perspectives for the study of rip currents, for instance.

Direct numerical simulation of flow past a sphere in a stratified fluid is carried out at a subcritical Reynolds number of 3700 and $Fr=U_{\infty }/ND=1,2$ and 3 to understand the dynamics of moderately stratified flows with $Fr=O(1)$. Here, $U_{\infty }$ is the free stream velocity, $N$ is the background buoyancy frequency and $D$ is the sphere diameter. The unstratified flow past the sphere consists of a separated shear layer that transitions to turbulence, a recirculation zone and a wake with a mean centreline deficit velocity, $U_{0}$, that decreases with downstream distance as a power law. With increasing stratification, the separated shear layer plunges inward vertically and its roll up is inhibited, the recirculation zone is shortened and the mean wake decays at a slower rate of $U_{0}\propto (x_{1}/D)^{-0.25}$ in the non-equilibrium (NEQ) region. The transition from the near wake where $U_{0}$ has a decay rate similar to the unstratified case to the NEQ regime occurs as an oscillatory modulation by a steady lee wave pattern with a period of $t=2\unicode[STIX]{x03C0}/N$ that leads to accelerated $U_{0}$ between $Nt=\unicode[STIX]{x03C0}$ and approximately $Nt=2\unicode[STIX]{x03C0}$. Far downstream, the wake is dominated by coherent horizontal motions. The acceleration of $U_{0}$ by the lee wave and the lower turbulence production in the NEQ regime, thereby less loss to turbulence, prolongs the lifetime of the wake relative to its unstratified counterpart. The intensity, temporal spectra and structure of turbulent fluctuations in the wake are assessed. Buoyancy induces significant anisotropy among the velocity components and between their vertical and horizontal profiles. Consequently, the near wake ($x_{1}/D<10$) exhibits significant differences in turbulence profiles relative to its unstratified counterpart. Spectra of vertical velocity show a discrete peak in the near wake that is maintained further downstream. The turbulent kinetic energy (TKE) balance is computed and contributions from pressure transport and buoyancy are found to become increasingly important as stratification increases. The findings of this investigation will be helpful in designing accurate initial conditions for the temporally evolving model of stratified wakes.

Motivated by examples of erosive incision of channels in sand, we investigate the motion of individual grains in a granular bed driven by a laminar fluid to give us new insights into the relationship between hydrodynamic stress and surface granular flow. A closed cell of rectangular cross-section is partially filled with glass beads and a constant fluid flux Q flows through the cell. The refractive indices of the fluid and the glass beads are matched and the cell is illuminated with a laser sheet, allowing us to image individual beads. The bed erodes to a rest height hr which depends on Q. The Shields threshold criterion assumes that the non-dimensional ratio θ of the viscous stress on the bed to the hydrostatic pressure difference across a grain is sufficient to predict the granular flux. Furthermore, the Shields criterion states that the granular flux is non-zero only for θ > θc. We find that the Shields criterion describes the observed relationship hr ∝ Q1/2 when the bed height is offset by approximately half a grain diameter. Introducing this offset in the estimation of θ yields a collapse of the measured Einstein number q* to a power-law function of θ − θc with exponent 1.75 ± 0.25. The dynamics of the bed height relaxation are described well by the power-law relationship between the granular flux and the bed stress.

The relative dispersion framework for the non-reactive and reactive solute flux in aquifers is presented in terms of the first two statistical moments. The solute flux is described as a space–time process where time refers to the solute flux breakthrough and space refers to the transverse displacement distribution at the control plane. The statistics of the solute flux breakthrough and transversal displacement distributions are derived by analysing the motion of particle pairs. The results indicate that the relative dispersion formulation approaches the absolute dispersion results on increasing the source size (e.g. >10 heterogeneity scales). The solute flux statistics, when sampling volume is accounted for, show a flattened distribution for the solute flux variance in the space–time domain. For reactive solutes, the solute flux shows a tailing phenomenon in time while solute flux variance exhibits bi-modality in transverse distribution during the recession stage of the solute breakthrough. The solute flux correlation structure is defined as an integral measure over space and time, providing a potentially useful tool for sampling design in the subsurface.

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show significantly larger density contrast, more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments for large scales, we derive a model that describes this behaviour.

Steady linear three-dimensional disturbances are investigated in a two-dimensional laminar boundary layer. The boundary layer is subject to a streamwise favourable-to-adverse pressure gradient and eventually undergoes separation. The separating flow corresponds to the first part of a pressure-induced laminar-separation bubble on a flat plate. Streamwise disturbance development in such a flow is studied by means of direct numerical simulation, a water-tunnel experiment and an adjoint-based parabolic theory suited to study spatial optimal growth. A complete overview of the disturbance evolution in various areas of the favourable-to-adverse pressure gradient laminar boundary layer is given. Results from all investigation methods show overall good agreement with respect to disturbance growth and shape within the entire domain. In the favourable pressure-gradient region and, again, slightly downstream of separation, transient growth caused by the lift-up effect dominates disturbance behaviour. In the adverse pressure-gradient region, a modal instability is observed. Evidence is presented that this instability is of Görtler type.

In an experimental study the development of transition downstream of Görtler vortices was investigated. With the tellurium method it was possible to distinguish beyond the Görtler vortices to successive instability modes. The first deforms the vortex pattern in a steady way and produces between each vortex pair boundary-layer profiles with two points of inflexion. When this has been established another instability mode starts, consisting of regular three-dimensional oscillations. By detailed flow visualization a nearly complete picture of the different flow patterns can be obtained.

The attenuation of three-dimensional wavepackets of streaks and Tollmien–Schlichting (TS) waves in a transitional boundary layer using feedback control is investigated numerically. Arrays of localized sensors and actuators (about 10–20) with compact spatial support are distributed near the rigid wall equidistantly along the spanwise direction and connected to a low-dimensional (r = 60) linear quadratic Gaussian controller. The control objective is to minimize the disturbance energy in a domain spanned by a number of proper orthogonal decomposition modes. The feedback controller is based on a reduced-order model of the linearized Navier–Stokes equations including the inputs and outputs, computed using a snapshot-based balanced truncation method. To account for the different temporal and spatial behaviour of the two main instabilities of boundary-layer flows, we design two controllers. We demonstrate that the two controllers reduce the energy growth of both TS wavepackets and streak packets substantially and efficiently, using relatively few sensors and actuators. The robustness of the controller is investigated by varying the number of actuators and sensors, the Reynolds number and the pressure gradient. This work constitutes the first experimentally feasible simulation-based control design using localized sensing and acting devices in conjunction with linear control theory in a three-dimensional setting.

It has been demonstrated by many experiments carried out over the last 60 years that in certain liquids a single millimetre-sized bubble will rise within an unstable path, which is sometimes observed to transit from zigzag to spiral. After performing several groups of direct numerical simulations, the present work gives a theoretical explanation to reveal the physical mechanism causing the transition, and the results are presented in two parts. In the first part, in which a freely rising bubble is simulated, equal-strength vortex pairs are observed to shed twice during a period of the pure zigzag path, and this type of motion is triggered by the amounts of streamwise vorticities accumulated on the bubble interface, when a critical value is reached. However, when the balance between the counter-rotating vortices is broken, an angular velocity is induced between the asymmetric vortex pairs, driving the bubble to rise in an opposite spiral path. Therefore, although there is no preference of the spiral direction as observed in experiments, it is actually determined by the sign of the stronger vortex thread. In the second part, external vertical magnetic fields are imposed onto the spirally rising bubble in order to further confirm the relations between the vortex structures and the unstable path patterns. As shown in our previous studies (Zhang & Ni, Phys. Fluids, vol. 26 (10), 2014, 102102), the strength of the double-threaded vortex pairs, as well as the imbalance between them, will be weakened under magnetic fields. Therefore, as the vortex pairs become more symmetric, the rotating radius of the spirally rising bubble is observed to decrease. We try to answer the question, put forward by Shew et al. (2005, Preprint, ENS, Lyon), ‘what caused the bubble to transit from zigzag to spiral naturally?’

This paper reports experimental findings on the flow of sand down a steep chute. Nearly all granular flow models have a maximum value for the friction and therefore predict that flows on steep slopes will accelerate at a constant rate until the interaction with the ambient fluid becomes important. This prediction has not been tested by previous work, which has focused on relatively low slope angles where steady, fully developed flows occur after short distances. We test this by investigating flows over a much greater range of slope angles (30–50) and flow depths (4–130 particle diameters). We examine flows with two basal conditions, one flat and frictional, the other bumpy. The latter imposes a no-slip condition for slow, deep flows, but permits some degree of slip for high flow velocities. The data suggests that friction can be much larger than theories such as the rheology proposed by Jop, Forterre & Pouliquen (Nature, vol. 441, 2006) suggest and that there may be constant velocity states above the angle of vanishing . Although these flows do not vary in time, all but the flows on the bumpy base at low inclinations accelerate down the slope. A recirculation mechanism sustains flows with a maximum mass flux of , allowing observations to be made at multiple points for each flow for an indefinite period. Flows with Froude number in the range 0.1–25 and bulk inertial number 0.1–2.7 were observed in the dense regime, with surface velocities in the range 0.2–5.6 . Previous studies have focused on . We show that a numerical implementation of the rheology does not fully capture the accelerating dynamics or the transverse velocity profile on the bumpy base. We also observe the transverse separation of the flow into a dense core flanked by dilute regions and the formation of longitudinal vortices.

Boussinesq salt-water laboratory experiments of Rayleigh–Taylor instability (RTI) can achieve mixing efficiencies greater than 0.75 when the unstable interface is confined between two stable stratifications. This is much greater than that found when RTI occurs between two homogeneous layers when the mixing efficiency has been found to approach 0.5. Here, the mixing efficiency is defined as the ratio of energy used in mixing compared with the energy available for mixing. If the initial and final states are quiescent then the mixing efficiency can be calculated from experiments by comparison of the corresponding density profiles. Varying the functional form of the confining stratifications has a strong effect on the mixing efficiency. We derive a buoyancy-diffusion model for the rate of growth of the turbulent mixing region, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\dot{h} = 2 \sqrt{\alpha A g h}$ (where $A = A(h)$ is the Atwood number across the mixing region when it extends a height $h$, $g$ is acceleration due to gravity and $\alpha $ is a constant). This model shows good agreement with experiments when the value of the constant $\alpha $ is set to 0.07, the value found in experiments of RTI between two homogeneous layers (where the height of the turbulent mixing region increases as $h =\alpha A g t^2$, an expression which is equivalent to that derived for $\dot{h}$).