Both experimental and theoretical studies of fast and microscale physical phenomena occurring during the growth of vapour bubbles in nucleate pool boiling are reported. The focus is on the liquid film of micrometric thickness (a ‘microlayer’) that can form between the heater and the liquid–vapour interface of a bubble. The microlayer strongly affects the macroscale heat transfer and is thus important to be understood. The microlayer appears as a result of the inertial forces that cause the hemispherical bubble shape. It is shown that the microlayer can be seen as the Landau–Levich film deposited by the bubble foot edge during its receding. Paradoxically, the deposition is controlled by viscosity and surface tension. The microlayer profile measured with white-light interferometry, the temperature distribution over the heater, and the bubble shape are observed with synchronised high-speed cameras. According to the numerical simulations, the microlayer consists of two regions: a dewetting ridge near the contact line, and a longer and flatter bumped part. It is shown that the ridge cannot be measured by interferometry because of its intrinsic limitation on the interface slope. The ridge growth is linked to the contact line receding. The simulated dynamics of both the bumped part and the contact line agrees with the experiment. The physical origin of the bump in the flatter part of microlayer is explained.

It is known that inertial lift forces can lead to particle focusing in channel flows; yet oscillatory straining effects have also been suggested as a mechanism for particle focusing in wavy channels. To explore the synergy between these two mechanisms, we analytically and experimentally investigate the focusing behaviour of rigid neutrally buoyant particles in a wavy channel. We decompose the particle-free channel flow into a primary Poiseuille flow and secondary eddies induced by the waviness. We calculate the perturbation of the particle on the particle-free flow and the resulting lateral lift force exerted on the particle using the method of matched asymptotic expansions. This yields a zeroth-order lift force arising from the Poiseuille flow and a first-order lift force due to the waviness of the channel. We further incorporate the inertial lift force into the Maxey–Riley equation and simulate particle trajectories in wavy channels. The interactions between the zeroth-order lift force and the particle-free flow largely determine the focusing locations. Experiments in wavy channels with varying amplitudes at channel Reynolds numbers ranging from 5 to 250 are consistent with the predictions of the focusing locations, which are mainly governed by the channel Reynolds number as well as the competition between the inertial lift and the oscillatory straining effects.

Motivated by drag-based propulsion of crinoids, the shape reconfiguration of a feather-like elastic structure under both steady and unsteady translational motions is investigated. The simplified elastic structure consists of a centre rod to which numerous side flaps are attached by elastic hinges. These side flaps fold in only one direction to realize a dramatic reduction in the area of the structure during the recovery stroke. Compared with experimental measurements, analytical methods developed to couple the dynamics of the centre rod and the side flaps successfully predict the drag force and three-dimensional reconfiguration of the elastic structure during both power and recovery strokes. A dimensionless speed given by the ratio of inertial fluid force to elastic bending force is proposed for the coupled deflections of the centre rod and side flaps, and is found to determine primarily the reconfiguration of the elastic structure. A reconfiguration number defined specifically for our model provides an appropriate characterization of the effect of side-flap folding on drag force reduction. Moreover, the ratio of drag forces between the power and recovery strokes is evaluated to find model conditions for the optimal force ratio.

An ultrasonic phased array system is introduced to study the three-dimensional (3-D) movement of a single bubble in a GaInSn alloy under a transverse magnetic field (MF), which is verified by bubble experiments in water. The 3-D motion trajectories of individual bubbles in the GaInSn are obtained under a horizontal MF. As the MF becomes stronger, the bubble successively oscillates in random directions (R mode), a direction perpendicular to the MF (V mode), a direction parallel to the MF (P mode) and finally it rises straight (S mode). The significant anisotropy of the oscillation directions at a moderate MF intensity may be due to the anisotropy of the vortex structure around the bubble. Furthermore, the oscillation amplitude gradually declines with increasing MF intensity until the bubble trajectory finally becomes a straight line. Our measurements allow us to specify the characteristic regions for the observed bubble modes in the $N-Eo-Re$ parameter space (N is the magnetic interaction parameter, Eo is the Eötvös number and Re is the Reynolds number). In addition, more detailed characteristics of bubble terminal velocity are revealed, showing that the bubble velocities are closely related to the motion modes. The increase in bubble velocity at a moderate MF intensity is caused by the weakening oscillation. At a high strength, the MF monotonically suppresses the rise velocity of the bubble with a fixed scaling law.

A solid body in a viscous fluid undergoing oscillatory motion naturally produces a steady secondary flow due to convective inertia. This phenomenon is embodied in the streaming flow generated by a sphere in an unbounded fluid executing rectilinear oscillations. We review the considerable literature on this canonical problem and summarise exact and asymptotic formulas in the small-amplitude limit. These analytical formulas are used to explore the characteristic flow structure of this problem and clarify previously unreported features. A single, toroidal-shaped vortex exists in each hemisphere regardless of the oscillation frequency, which can drive a counter-flow away from the sphere. The vortex centre moves monotonically away from the sphere with decreasing oscillation frequency, and engulfs the entire flow domain for $\beta \equiv \omega R^2/\nu < 16.317$, where $\omega$ is the angular oscillation frequency, $R$ the sphere radius, and $\nu$ the fluid kinematic viscosity. This seemingly abrupt change in flow structure at the critical frequency $\beta _{critical} =16.317$, and its quantification, appear to have not been reported previously. We perform a direct numerical simulation of the Navier–Stokes equations, to (1) confirm existence of this critical frequency at finite amplitude, and (2) examine its variation with amplitude. This reveals a universal relationship between the critical frequency and oscillation amplitude, clarifying previous reports on the structure of this streaming flow. The critical frequency is shown to be identical for the streaming flow and the cycle-averaged particle paths, establishing that the critical frequency is accessible directly using standard measurements.

Shock-tube experiments on Richtmyer–Meshkov (RM) instability at a perturbed SF$_6$ layer surrounded by air, induced by a cylindrical divergent shock, are reported. To explore the effects of reverberating waves and interface coupling on instability growth, gas layers with various shapes are created: unperturbed inner interface and sinusoidal outer interface (case US); sinusoidal inner and outer interfaces that have identical phase (case IP); sinusoidal inner and outer interfaces that have opposite phase (case AP). For each case, three thicknesses are considered. Results show that reverberating waves inside the layer dominate the early-stage instability growth, while interface coupling dominates the late-stage growth. The influences of waves on divergent RM instability are more pronounced than the planar and convergent counterparts, which are estimated accurately based on gas dynamics theory. Both the wave influence and interface coupling depend heavily on the layer shape, leading to diverse growth rates: the quickest growth for case AP, medium growth for case US, the slowest growth for case IP. In particular, for the IP case, there exists a critical thickness below which the instability growth is suppressed by both the reverberating waves and interface coupling. This provides an efficient way to modulate the growth of divergent RM instability. It is found that divergent RM instability involves weak nonlinearity and strong interface coupling such that the linear theory of Mikaelian (Phys. Fluids, vol. 17, 2005, 094105) can well reproduce the instability growth at late stages for all cases. This constitutes the first experimental confirmation of the Mikaelian theory.

Direct numerical simulations of turbulent channel flow subjected to spanwise wall oscillations in the form of streamwise travelling waves (STW) were performed in an effort to elucidate the mechanism responsible for the observed drag reduction. We imposed large amplitudes to identify the proper effects of STW, while keeping the angular frequency and wavenumber fixed at a particular values. We primarily focus on the vorticity transport mechanism, to better understand the influence of STW actuation on the near-wall turbulence. We identify key terms appearing in the turbulent enstrophy transport equations that are directly linked to the STW actuation. The analysis reveals that the primary effect of the STW forcing is to attenuate the spanwise turbulent enstrophy at the wall, which is linked to the fluctuating wall shear stress. The suppression of the wall-normal turbulent enstrophy is deemed to be subordinate. To strengthen this point, we performed numerical experiments, where the streamwise fluctuating velocity, and consequently the spanwise vorticity, is artificially suppressed next to the wall. The anisotropic invariant maps show striking resemblance for large amplitude STW actuation and artificially forced cases. Detailed analysis of various structural features is provided, which includes the response of the near-wall streaks and shear layers of spanwise fluctuating velocity field. The quasistreamwise vortices, which play a key role in the regeneration mechanism, are shown to be pushed away from the wall, resulting in their weakened signature at the wall.

We present results from direct numerical simulations of flows in spherical and oblate spheroidal shells, driven both by precession and thermal convection, with Ekman number $Ek=10^{-4}$, non-diffusive Rayleigh numbers from $Ra=0.1$ to $Ra=10$ and unity Prandtl number. The applied precessional forcing spans seven orders of magnitude. Our experiments show a clear transition between a convective state and a precessing flow that can be approximated by a reduced dynamical model. The change in the flow is apparent in visualizations and a decomposition of the velocity into symmetric and antisymmetric components. For the flow dominated by precession, some parameter combinations show two stable solutions that can be realized by a hysteresis or a strong thermal forcing. An increase of the Rayleigh number at a constant precession rate exhibits established scaling properties for the heat transfer, with exponents $2/7$ and $6/5$.

When a liquid jet plunges into a pool, it can generate a bubble-laden jet flow underneath the surface. This common and simple phenomenon is investigated experimentally for circular jets to illustrate and quantify the role played by the net gas/liquid void fraction on the maximum bubble penetration depth. It is first shown that an increase in either the impact diameter or the jet fall height to diameter ratio at constant impact momentum leads to a reduction in the bubble cloud size. By measuring systematically the local void fraction using optical probes in the biphasic jet, it is then demonstrated that this effect is a direct consequence of the increase in air content within the cloud. A simple momentum balance model, including only inertia and the buoyancy force, is shown to predict the bubble cloud depth without any fitting parameters. Finally, a Froude number based on the bubble terminal velocity, the cloud depth and also the net void fraction is introduced to propose a simple criterion for the threshold between the inertia-dominated and buoyancy-dominated regimes.

We study the stationary Navier–Stokes equations in the region between two rotating concentric cylinders. We first prove that, for a small Reynolds number, if the fluid flow is axisymmetric and if its velocity is sufficiently small in the $L^\infty$-norm, then it is necessarily the Taylor–Couette–Poiseuille flow. If, in addition, the associated pressure is bounded or periodic in the $z$ axis, then it coincides with the well-known canonical Taylor–Couette flow. We discuss the relation between uniqueness and stability of such a flow in terms of the Taylor number in the case of narrow gap of two cylinders. The investigation in comparison with two Reynolds numbers based on inner and outer cylinder rotational velocities is also conducted. Next, we give a certain bound of the Reynolds number and the $L^\infty$-norm of the velocity such that the fluid is, indeed, necessarily axisymmetric. As a result, it is clarified that smallness of Reynolds number of the fluid in the two rotating concentric cylinders governs both axisymmetry and the Taylor–Couette–Poiseuille flow with the exact form of the pressure.

The nexus between turbulence, particle interaction and interfacial tension is virtually unexplored, despite being highly relevant to a wealth of industrial and environmental settings. Here we investigate it by conducting experiments on non-Brownian spherical particles at the interface of turbulent liquid layers. The latter are electromagnetically stirred in a quasi-two-dimensional apparatus, while the particles are individually tracked. By systematically varying interfacial conditions, turbulence intensity, particle size and concentration from dilute to dense, we map the system behaviour over a wide parameter space. We reveal how the dynamics is governed by the balance of drag, capillarity and lubrication. Based on their scaling, we propose a phase diagram comprising three distinct regimes, characterized by widely different levels of clustering and fluctuating energy of the particles. This is quantitatively confirmed by the experimental results.

Direct numerical simulations of turbulent flows over highly permeable porous walls were performed at various Reynolds numbers to examine the effects of the Reynolds number on permeable wall turbulence. The porous medium consisted of Kelvin cell arrays with porosity $0.95$, and the permeability Reynolds number $Re_K$ ranged from approximately 7 to 50. Simulations with thin and thick porous walls were performed to investigate the effects of spanwise roller vortices associated with the Kelvin–Helmholtz instability. The results show that the effect of the Kelvin–Helmholtz instability becomes more significant with increasing the permeability Reynolds number, and spanwise rollers, for which length scale is an order of channel height, dominate turbulence when $Re_K \gtrsim 30$. Spanwise rollers reinforce the negative correlation between the wall-normal and streamwise velocity fluctuations close to the porous/fluid interface, and intensify the turbulent velocity fluctuations away from the porous walls, leading to increased frictional resistance. An investigation of the Reynolds number dependence of the modified logarithmic law indicates that the zero-plane displacement and equivalent roughness height are proportional to the square root of permeability, whereas the von Kármán constant increases with the permeability Reynolds number because of the increased mixing length resulting from the relatively large-scale velocity fluctuations induced by spanwise rollers. We developed a model for the modified log law for permeable wall turbulence based on permeability, and confirmed that the skin friction coefficient obtained from the model reasonably predicts the skin friction coefficient for several types of high-porosity porous media. Hence, permeability is a key parameter that characterizes the logarithmic mean velocity profiles over a variety of porous media with high porosity.

We explore the transition to chaos in a prototypical hydrodynamic oscillator, namely a globally unstable low-density jet subjected to external time-periodic forcing. As the forcing strengthens at an off-resonant frequency, we find that the jet exhibits a sequence of nonlinear states: period-1 limit cycle $\rightarrow $ quasiperiodicity $\rightarrow$ intermittency $\rightarrow$ low-dimensional chaos. We show that the intermittency obeys type-II Pomeau–Manneville dynamics by analysing the first return map and the scaling properties of the quasiperiodic lifetimes between successive chaotic epochs. By providing experimental evidence of the type-II intermittency route to chaos in a globally unstable jet, this study reinforces the idea that strange attractors emerge via universal mechanisms in open self-excited flows, facilitating the development of instability control strategies based on chaos theory.

A variational principle is proposed to derive the governing equations for the problem of ocean wave interactions with a floating ice shelf, where the ice shelf is modelled by the full linear equations of elasticity and has an Archimedean draught. The variational principle is used to form a thin-plate approximation for the ice shelf, which includes water–ice coupling at the shelf front and extensional waves in the shelf, in contrast to the benchmark thin-plate approximation for ocean wave interactions with an ice shelf. The thin-plate approximation is combined with a single-mode approximation in the water, where the vertical motion is constrained to the eigenfunction that supports propagating waves. The new terms in the approximation are shown to have a major impact on predictions of ice shelf strains for wave periods in the swell regime.

This paper examines the shape of a steady jet with a swirling component, ejected from a circular orifice at an angle to the horizontal. Assuming the Froude number to be large, we derive a set of asymptotic equations for a slender jet. In the inviscid limit, the solutions of the set predict that, if the swirling velocity of the flow exceeds a certain threshold, the jet bends against gravity and rises until the initial supply of the liquid's kinetic energy is used up. This effect is due to the fact that the contributions of the swirl and streamwise velocities to the centrifugal force are of opposite signs, with their sum to be balanced by gravity. As a result, swirl- and streamwise-dominated jets bend in opposite directions. Downward-bending jets also exhibit counter-intuitive behaviour. If the swirling velocity is strong enough (but is still below the above threshold), the streamwise velocity on the jet's axis may decrease with the distance from the orifice, despite the acceleration due to gravity. Eventually, a stagnation point emerges due to this effect, arguably destabilising the jet. Also paradoxically, viscosity-dominated jets can reach higher (if they bend upwards) and farther (in all cases) than their inviscid counterparts, due to the fact that viscosity suppresses formation of stagnation points.

Understanding the mechanism of thermal instability in nanofluids is of fundamental importance to explore the reasons behind the enhancement of heat transfer efficiency. Since Buongiorno (ASME J. Heat Transfer, vol. 128, 2006, pp. 240–250) proposed his theoretical model of nanofluids, most studies focusing on the thermal instability analysis exclusively considered Brownian motion and thermophoresis as the main diffusion mechanisms of nanoparticles. All the analyses concluded that a nanofluid layer is much more unstable than its pure counterpart as it is heated from below. However, a recent experimental observation on Rayleigh–Bénard convection appears to contradict the theoretical prediction, implying that some mechanisms neglected in the previous model may have a significant impact on the onset of thermal convection. In the present study, we revise the convective transport model of nanofluids proposed by Buongiorno and find that the gravitational settling of nanoparticles is a crucial factor influencing the thermal instability behaviour of nanofluids. By performing a linear stability analysis based on the novel model, the effect of gravity settling exhibits a stabilizing mechanism to resist the destabilizing effect of thermophoresis. Furthermore, the onset of instability can be delayed once the nanoparticle diameter exceeds a certain threshold, which explains the phenomenon observed in experiments. Particularly, the oscillatory mode is found to emerge and dominate the flow instability when the gravity settling effect is competitive with the effect of thermophoresis.