Odd viscosity is associated with a number of striking physical phenomena: a disk rotating in a viscous liquid experiences a normal compressive or tensile stress depending on its sense of rotation; chiral active matter interfacial deformations level off in a manner akin to surface tension; and unstable thermocapillary films become stabilized. In this article we show that odd viscosity decreases the size and intensity of Moffatt vortices in a corner formed by a solid substrate and a free interface. The effect is present because odd viscosity creates a normal-stress-induced shear stress at the liquid–gas interface. The new shear stress is out of phase and oppositely directed with respect to the interfacial liquid velocity. It squeezes the vortices and damps their rotation. As a consequence, Moffatt vortices can now be observed with greater facility in an experiment. Odd viscosity also increases the range of corner angles over which Moffatt vortices can be observed, and, in general, it shows a tendency to moderate singular behaviour.

This paper studies numerically the convection of water vapour in snowpacks using an Eulerian–Eulerian two-phase approach. The convective water vapour transport in snow and its effects on snow density are often invoked to explain observed density profiles, e.g. of thin Arctic snow covers, but this process has never been numerically simulated and analysed in a systematic manner. Here, the impact of convection on the thermal and phase change regimes as a function of different snowpack depths, thermal boundary conditions and Rayleigh numbers is analysed. We find considerable impact of natural convection on the snow density distribution with a layer of significantly lower density at the bottom of the snowpack and a layer of higher density located higher in the snowpack or at the surface. We find that emergent heterogeneity in the snow porosity results in a feedback effect on the spatial organization of convection cells causing their horizontal displacement. Regions where the snowpack is most impacted by phase changes are found to be horizontally extended and vertically thin, ‘pancake’-like layers at the top and bottom of the snowpack. We further demonstrate that among the parameters important for natural convection, the snowpack depth has the strongest influence on the heat and mass transfer. Despite our simplifying assumptions, our study represents a significant improvement over the state of the art and a first step to accurately simulate snowpack dynamics in diverse regions of the cryosphere.

For the dispersion of soluble matter in solvent flowing through a tube as investigated originally by G.I. Taylor, a streamwise dispersion theory is developed from a Lagrangian perspective for the whole process with multi-scale effects. By means of a convected coordinate system to decouple convection from diffusion, a diffusion-type governing equation is presented to reflect superposable diffusion processes with a multi-scale time-dependent anisotropic diffusivity tensor. A short-time benchmark, complementing the existing Taylor–Aris solution, is obtained to reveal novel statistical and physical features of mean concentration for an initial phase with isotropic molecular diffusion. For long times, effective streamwise diffusion prevails asymptotically corresponding to the overall enhanced diffusion in Taylor's classical theory. By inverse integral expansions of local concentration moments, a general streamwise dispersion model is devised to match the short- and long-time asymptotic solutions. Analytical solutions are provided for most typical cases of point and area sources in a Poiseuille tube flow, predicting persistent long tails and skewed platforms. The theoretical findings are substantiated through Monte Carlo simulations, from the initial release to the Taylor dispersion regime. Asymmetries of concentration distribution in a circular tube are certified as originated from (a) initial non-uniformity, (b) unidirectional flow convection, and (c) non-penetration boundary effect. Peculiar peaks in the concentration cloud, enhanced streamwise dispersivity and asymmetric collective phenomena of concentration distributions are illustrated heuristically and characterised to depict the non-equilibrium dispersion. The streamwise perspective could advance our understanding of macro-transport processes of both passive solutes and active suspensions.

The kinetic energy spectrum in the atmospheric mesoscale has a - 5/3 slope, which suggests an energy cascade. But the underlying dynamics of this cascade is still not fully understood. Is it driven by inertia–gravity waves, vortices or something else? To answer these questions, it is necessary to decompose the spectrum into contributions from waves and vortices. Linear decompositions are straightforward, but can lead to ambiguous results. A recent paper by Wang & Bühler (J. Fluid Mech., vol. 882, 2020, A16) addresses this problem by presenting a nonlinear decomposition of the energy spectrum into waves and vortices using the omega equation. They adapt this method for one-dimensional aircraft data and apply it to two datasets. In the lower stratosphere, the results show a mesoscale spectrum dominated by waves. The situation in the upper troposphere is different: here vortices are just as important, or possibly more than important, as waves, although the limitations of the one-dimensional data preclude a definitive answer.

We explore the strong stratification regime of stably stratified turbulence and the intermediate regime towards the viscosity-affected stratified state. Three-dimensional velocity-density fields from direct numerical simulations are decomposed into internal gravity waves (IGWs) and eddy motion based on Riley's decomposition (Riley et al., AIP Conf. Proc., vol. 76, issue 1, 1981, pp. 79–112) extended to account for the space–time properties of waves, their modification by vertically sheared horizontal flow and the vertical mixing by eddies (Lam et al., Atmosphere, vol. 11, issue 4, 2020, p. 420). We establish the evolution equations for the IGW and eddy parts separately. Up to buoyancy Reynolds number ${Re}_b\sim 1$, we observe a large exchange of energy that pumps energy from the IGW to eddy. For ${Re}_b>1$, the IGW and eddy dynamics seem to be separate and no global exchange is observed. Our decomposition enables computation of the contributions to the mixing coefficient in terms of the IGW and eddy. At the largest ${Re}_b$ considered, the mixing due to eddies is four times that due to waves.

The direct numerical simulation database from Shin et al. (J. Fluid Mech., vol. 823, 2017, pp. 1–25) is used to study three-dimensional vortical and very-large-scale coherent structures in a turbulent round jet at a Reynolds number of $7300$. In particular, horseshoe vortices and their role in the formation of very-large-scale coherent structures in the jet near and intermediate fields are assessed. The swirling strength criterion together with conditional averaging are used to visualize volumetric vortical structures. It is shown that, similar to wall-bounded turbulent flows, the turbulent jet is populated with symmetric and asymmetric horseshoe-like vortices, which induce high-momentum and low-momentum regions in the flow. However, unlike what is found for wall-bounded flows, inverse horseshoe-like vortices are common in the turbulent jet. They prevail in the shear region around the potential core in the jet near field and contribute to the mixing of the potential core in the jet. In the jet near field, groups of axially aligned horseshoe structures induce long streaky structures, which are periodic in the azimuthal and streamwise directions. In the jet intermediate field, very-large-scale motions (VLSMs) consisting of high-momentum regions, flanked on either side by low-momentum regions, are found to be associated with groups of horseshoe vortices. Instantaneous three-dimensional flow fields suggest that horseshoe vortices tend to concatenate and form organized spiral as well as axially aligned coherent VLSMs. A detection scheme is introduced to identify and average over these VLSMs. This conditional averaging reveals that spiral VLSMs and axially aligned VLSMs constitute $72\,\%$ and $28\,\%$ of the total VLSMs, respectively.

There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of theoretical controllability, which investigate whether or not refined and precise control is indeed possible in a given system. In this work, seeking to highlight the utility and broad applicability of such rigorous analysis, we recount and illustrate key concepts of geometric control theory in the context of multiple particles in Stokesian fluids interacting with each other, such that they may be readily and widely applied in this largely unexplored fluid-dynamical setting. Motivated both by experimental and abstract questions of control, we exemplify these techniques by explicit and detailed application to multiple problems concerning the control of two particles, such as the motion of tracers in flow and the guidance of one sphere by another. Further, we showcase how this analysis of controllability can directly lead to the construction of schemes for control, in addition to facilitating explorations of mechanical efficiency and contributing to our overall understanding of non-local hydrodynamic interactions in the Stokes limit.

We derive the upper limit for power extraction from an open-channel flow with lateral bypass representing tidal power or run-of-river plants for the complete range of blockage $\unicode[STIX]{x1D70E}$, Froude number $Fr_{2}$ and turbine head $H_{T}$. For this, a generic turbine model is used: a momentum and energy sink distributed over the geometric blocking $\unicode[STIX]{x1D70E}$ of the channel allowing lateral bypass. It is indicated that existing models neglect important aspects of the free-surface deformation due to the energy extraction, yielding unphysical behaviour at high blockage, high Froude number or high turbine head. The asymptotic validity of existing theories for $\unicode[STIX]{x1D70E}\rightarrow 0$, $Fr_{2}\rightarrow 0$, $H_{T}\rightarrow 0$ becomes evident: firstly, by comparing existing theories with the presented general theory; and secondly, by the experimental validation of the existing and presented theories. The accompanying systematic experimental study comprises a wide range of blockage ratios, $0.25\leqslant \unicode[STIX]{x1D70E}\leqslant 1.0$, of downstream Froude numbers, $0.2\leqslant Fr_{2}\leqslant 0.5$, and of different turbine heads, $H_{T}$, measured in multiples of the specific energy $E_{0}$ of the undisturbed flow. The subsequent model-based optimisation allows an indication of the optimal turbine head $H_{T,opt}/E_{0}$ as well as the maximal obtainable coefficient of performance $C_{P,opt}$ as a function of $\unicode[STIX]{x1D70E}$ and $Fr_{2}$ or downstream water depth $h_{2}/E_{0}$, respectively. The theory reveals points of operation in which there is a surge wave in the tailwater. The new physical insight and optimisation results may serve for plant design and operation, as well as for investment decisions.

We study the two-dimensional Rayleigh–Bénard instability subject to the combined effects of a solid–liquid phase boundary and shear using linear stability theory and energy analysis. We consider two thermal states of the solid (isothermal and conducting), and two types of shear that can arise in different contexts. When the melting temperature is equal to that held at the top boundary, three instability modes can arise with the increase of Reynolds number Re that characterizes the shear intensity: a boundary mode, a mixed boundary–bulk mode and a bulk flow mode. When the melting temperature lies between the top and the bottom boundaries, the introduction of Couette flow, independent of its intensity, always leads to the mixed mode, whereas the instability with Poiseuille flow is dominated by the bulk flow mode once Re exceeds a critical value, below which the mixed mode dominates. The energy analysis suggests that there exist two mechanisms by which the shear flow affects the system: one is by inhibiting the upward heat flux and another is by absorbing energy from the perturbed hydrodynamic field. These two mechanisms can play totally different roles in different cases. Results in the high-Re regime indicate that, when Re exceeds its classical threshold, i.e. Re = 5772.2 for Poiseuille flow, the Tollmien–Schlichting instability will be dominant in the present system.

We report a new interferometric method to study the interactions between two gas bubbles undergoing small-amplitude oscillations in a liquid, based on the extension of a previously developed one-bubble set-up. Nanometric oscillations of millimetre-sized supported bubbles are excited acoustically; the response of each bubble is recorded interferometrically, as a function of the mutual distance (from quasi-contact to greater than the bubbles radii). The interferometric nature of the technique and the resonant nature of the vibration modes enable the accurate measurement of the amplitude (with sub-nanometric sensitivity), frequency and mutual phase of oscillation, whose variations over the bubble–bubble distance range allow the interactions to be probed. The bubbles oscillate at the same frequencies, exhibiting a low-frequency, in-phase and a high-frequency, out-of-phase resonance peak, whose separation is a function of distance, in good agreement with the theory for free interacting bubbles. The technique, here demonstrated for the volume modes of air bubbles in water, can be extended to other gas–liquid and liquid–liquid interfaces, bare or adsorbate-covered, as well as to shape oscillations.

In this paper we study finite particle Reynolds number effects up to $Re_p=50$ on the dynamics of small spherical bubbles and solid particles in an isotropic turbulent flow. We consider direct numerical simulations of light pointwise particles with various expressions of the drag force to account for finite $Re_p$ and the type of particle. Namely, we consider the Stokes drag law, the Schiller and Neumann relation and the Mei law. We show that an effective Stokes number, based on the mean value of the drag coefficient to account for the inertial effects involved in the drag law, gives a quasi-self-similar evolution of the variances of the bubble acceleration and of the forces exerted on the particle. This allows us to provide a satisfactory prediction of these quantities using Tchen's theory at finite particle Reynolds number. Based on these relations, we can specify the conditions under which the total inertial force (sum of the added mass and the Tchen contributions) is negligible compared with the drag force. Thus, for particles of very small dimensions, the fluid inertia force is negligible, provided the density ratio is of order 1 or larger. However, when the particle inertia becomes consequential, the threshold value of the density ratio increases significantly. Although this corresponds to the limit of the validity of the model, this draws attention to the fact that, for large Stokes numbers, the added mass and fluid inertia forces could play a more important role than is usually attributed to them.

Instability of collapsible tubes is studied theoretically and experimentally in many papers in the context of biological applications. Up to the present day, only Newtonian fluid flows in elastic tubes have been studied. However, there are circumstances when blood, bile and other biological fluids show essentially non-Newtonian behaviour. In this paper, we re-investigate theoretically axisymmetric stability of elastic tubes conveying power-law fluids. It is shown that for the power-law index $n=1$, i.e. for the Newtonian case, axisymmetric disturbances in infinite-length tubes are damped, which is in accordance with experimental and theoretical observations, where the oscillations always involve non-axisymmetric motion of the tube walls. However, for $n<0.611$, the axisymmetric disturbances can be growing, which predicts a new type of instability of elastic tubes conveying pseudoplastic (shear-thinning) fluids. For $n<1/3$, local instability of axisymmetric perturbations becomes absolute in infinite tubes, while finite-length tubes become globally unstable. The effects of the axial tension, elastic tube length and, if present, lengths of inlet and outlet rigid tubes on the stability of finite-length tubes are analysed.

When the top of a sessile droplet is contacted by an opposing solid surface, the droplet can transfer depending on the wettabilities and relative velocity of the surfaces. What if the surface receiving the liquid was porous? High-speed imaging was used to capture the transfer of a droplet from a solid substrate to an opposing porous surface. The parameters that were varied include the wettability of the donor substrate, the pore size of the receiving surface and the droplet's volume and working fluid. Generally, the transfer process is split into two sequential regimes, wetting and wicking, with wicking being three orders of magnitude longer than wetting on average. The wetting regime is split into two sub-regimes, the donor-independent and donor-dependent regimes. The donor-independent regime follows the dynamics of droplet coalescence, starting in a mass-limited viscous regime followed by a capillary–inertial regime. The donor-dependent regime is driven by a global change in Laplace pressure across the liquid bridge, with the viscous wedge of the receding contact line being the rate-limiting factor. The wicking regime is governed by Darcy's law, completing the transfer process of the droplet.

The wake flow past an axisymmetric body of revolution at a diameter-based Reynolds number $Re=u_{\infty }D/\nu =5000$ is investigated via a direct numerical simulation. The study is focused on identification of coherent vortical motions and the dominant frequencies in this flow. Three dominant coherent motions are identified in the wake: the vortex shedding motion with the frequency of $St=fD/u_{\infty }=0.27$, the bubble pumping motion with $St=0.02$, and the very-low-frequency (VLF) motion originated in the very near wake of the body with the frequency $St=0.002$–$0.005$. The vortex shedding pattern is demonstrated to follow a reflectional symmetry breaking mode, whereas the vortex loops are shed alternatingly from each side of the vortex shedding plane, but are subsequently twisted and tangled, giving the resulting wake structure a helical spiraling pattern. The bubble pumping motion is confined to the recirculation region and is a result of a Görtler instability. The VLF motion is related to a stochastic destabilisation of a steady symmetric mode in the near wake and manifests itself as a slow, precessional motion of the wake barycentre. The VLF mode with $St=0.005$ is also detectable in the intermediate wake and may be associated with a low-frequency radial flapping of the shear layer.

The propagation speed, shape and stability of the rim generated by a liquid-curtain breakup are studied. In the experiment, a liquid curtain surrounded by a slot die, edge guides and the surface of a roller breaks at the contact point between the edge guide and roller in a low-Weber-number range, and the rim propagates in the horizontal direction. Except for the initial time, the rim is almost straight and has a nearly constant propagation speed. For an Ohnesorge number much smaller than 1, unevenness occurs on the rim and the droplets separate from it. When the Ohnesorge number is of the order of unity, the rim becomes convex vertically downward, and the liquid lump flows down. The shape, propagation speed and surface stability of the rim are discussed by analysing the equation proposed by Entov & Yarin (J. Fluid Mech., vol. 140, 1984, pp. 91–111). It is shown that the volume flow rate condition at the slot die exit is important to explain the propagation of the rim. Additionally, in the initial stage of the curtain breakup, the Plateau–Rayleigh instability causes unevenness on the rim surface, and after the rim reaches the slot die exit, the Rayleigh–Taylor instability generates a liquid lump on the rim, which grows into droplets when the Ohnesorge number is much less than 1.