We study unstable waves in gas–liquid two-layer channel flows driven by a pressure gradient, under stable stratification, not assumed to be set in motion impulsively. The basis of the study is direct numerical simulation (DNS) of the two-phase Navier–Stokes equations in two and three dimensions for moderately large Reynolds numbers, accompanied by a theoretical description of the dynamics in the linear regime (Orr–Sommerfeld–Squire equations). The results are compared and contrasted across a range of density ratios $r=\unicode[STIX]{x1D70C}_{liquid}/\unicode[STIX]{x1D70C}_{gas}$. Linear theory indicates that the growth rate of small-amplitude interfacial disturbances generally decreases with increasing $r$; at the same time, the cutoff wavenumbers in both streamwise and spanwise directions increase, leading to an ever-increasing range of unstable wavenumbers, albeit with diminished growth rates. The analysis also demonstrates that the most dangerous mode is two-dimensional in all cases considered. The results of a comparison between the DNS and linear theory demonstrate a consistency between the two approaches: as such, the route to a three-dimensional flow pattern is direct in these cases, i.e. through the strong influence of the linear instability. We also characterize the nonlinear behaviour of the system, and we establish that the disturbance vorticity field in two-dimensional systems is consistent with a mechanism proposed previously by Hinch (J. Fluid Mech., vol. 144, 1984, p. 463) for weakly inertial flows. A flow-pattern map constructed from two-dimensional numerical simulations is used to describe the various flow regimes observed as a function of density ratio, Reynolds number and Weber number. Corresponding simulations in three dimensions confirm that the flow-pattern map can be used to infer the fate of the interface there also, and show strong three-dimensionality in cases that exhibit violent behaviour in two dimensions, or otherwise the development of behaviour that is nearly two-dimensional behaviour possibly with the formation of a capillary ridge. The three-dimensional vorticity field is also analysed, thereby demonstrating how streamwise vorticity arises from the growth of otherwise two-dimensional modes.

We propose a body-fitted mesh approach based on a semi-Lagrangian streaming step combined with an entropy-based collision model. After determining the order of convergence of the method, we analyse the flow past a circular cylinder in the lower subcritical regime, at a Reynolds number $Re=3900$, in order to assess the numerical performances for wall-bounded turbulence. The results are compared to experimental and numerical data available in the literature. Overall, the agreement is satisfactory. By adopting an efficient local refinement strategy together with the enhanced stability features of the entropic model, this method extends the range of applicability of the lattice Boltzmann approach to the solution of realistic fluid dynamics problems, at high Reynolds numbers, involving complex geometries.

Recent experiments have demonstrated that small-scale rotary devices installed in a microfluidic channel can be driven passively by the underlying flow alone without resorting to conventionally applied magnetic or electric fields. In this work, we conduct a theoretical and numerical study on such a flow-driven ‘watermill’ at low Reynolds number, focusing on its hydrodynamic features. We model the watermill by a collection of equally spaced rigid rods. Based on the classical resistive force (RF) theory and direct numerical simulations, we compute the watermill’s instantaneous rotational velocity as a function of its rod number $N$, position and orientation. When $N\geqslant 4$, the RF theory predicts that the watermill’s rotational velocity is independent of $N$ and its orientation, implying the full rotational symmetry (of infinite order), even though the geometrical configuration exhibits a lower-fold rotational symmetry; the numerical solutions including hydrodynamic interactions show a weak dependence on $N$ and the orientation. In addition, we adopt a dynamical system approach to identify the equilibrium positions of the watermill and analyse their stability. We further compare the theoretically and numerically derived rotational velocities, which agree with each other in general, while considerable discrepancy arises in certain configurations owing to the hydrodynamic interactions neglected by the RF theory. We confirm this conclusion by employing the RF-based asymptotic framework incorporating hydrodynamic interactions for a simpler watermill consisting of two or three rods and we show that accounting for hydrodynamic interactions can significantly enhance the accuracy of the theoretical predictions.

Hairpin vortices are widely studied as an important structural aspect of wall turbulence. The present work describes, for the first time, nonlinear travelling wave solutions to the Navier–Stokes equations in the channel flow geometry – exact coherent states (ECS) – that display hairpin-like vortex structure. This solution family comes into existence at a saddle-node bifurcation at Reynolds number $Re=666$. At the bifurcation, the solution has a highly symmetric quasi-streamwise vortex structure similar to that reported for previously studied ECS. With increasing distance from the bifurcation, however, both the upper and lower branch solutions develop a vortical structure characteristic of hairpins: a spanwise-oriented ‘head’ near the channel centreplane where the mean shear vanishes connected to counter-rotating quasi-streamwise ‘legs’ that extend toward the channel wall. At $Re=1800$, the upper branch solution has mean and Reynolds shear-stress profiles that closely resemble those of turbulent mean profiles in the same domain.

A small water channel network is proposed for designing shallow water fields, and the network is applied to attain water wave cloaking. The design formula is derived from an analogy between waves in a water channel and in an electric circuit; an approach of a transmission line metamaterial is extended to water waves and the water channel is used as an alternative of the transmission line. The size of the water channel is sufficiently smaller than the wavelength and a number of the channels are periodically connected as a network. This small water channel network makes artificial wave fields, and it works for a wide band of frequencies. First, we make an isotropic network equivalent to a shallow water space with constant depth in order to validate the proposed design method. It shows no wave reflection at the interface due to impedance matching. After that, the proposed theory is applied to designing an anisotropic small water channel network for demonstrating shallow water cloaking. A cylinder is cloaked from waves by the network surrounding the cylinder. Both cases are confirmed with numerical computations by solving the boundary-value problem based on linear potential theory.

The steady-state interaction of acoustic–gravity waves in an ocean of uniform depth is researched theoretically by means of the homotopy analysis method (HAM), an analytic approximation method for nonlinear problems. Considering compressibility, a hydroacoustic wave can be produced by the interaction of two progressive gravity waves with the same wavelength travelling in opposite directions, which contains an infinite number of small denominators in the framework of the classical analytic approximation methods, like perturbation methods. Using the HAM, the infinite number of small denominators are avoided once and for all by means of choosing a proper auxiliary linear operator. Besides, by choosing a proper ‘convergence-control parameter’, convergent series solutions of the steady-state acoustic–gravity waves are obtained in cases of both non-resonance and exact resonance. It is found, for the first time, that the steady-state resonant acoustic–gravity waves widely exist. In addition, the two primary wave components and the resonant hydroacoustic wave component might occupy most of wave energy. It is found that the dynamic pressure on the sea bottom caused by the resonant hydroacoustic wave component is much larger than that in the case of non-resonance, which might even trigger microseisms of the ocean floor. All of these might deepen our understanding and enrich our knowledge of acoustic–gravity waves.

We computationally study the motion of an initially spherical capsule flowing through a straight channel with an orthogonal lateral branch, using a three-dimensional immersed-boundary lattice-Boltzmann method. The capsule is enclosed by a strain-hardening membrane and contains an internal fluid of the same viscosity as the fluid in which it is suspended. Our primary focus is to study the influence of the geometry of the side branch on the capsule path selection. Specifically, we consider the case where the side branch cross-section is half that of the straight channel and study various bifurcation configurations, where the branch is rectangular or square, centred or not on the straight channel axis. The capsule is initially centred on the axis of the straight channel. We impose the flow rate split ratio between the two downstream branches of the bifurcation. We summarise the results obtained for different capsule-to-channel size ratios, flow Reynolds number $Re$ (based on the parent channel size and average flow speed) and capsule mechanical deformability (as measured by the capillary number) in phase diagrams giving the critical flow rate split ratio above which the capsule flows into the side branch. A major finding is that, at equal flow rate split between the two downstream branches, the capsule will enter a branch which is narrow in the spanwise direction, but will not enter a branch which is narrow in the flow direction. For $Re\leqslant 5$, this novel intriguing phenomenon primarily results from the background flow, which is strongly influenced by the side branch geometry. For higher values of $Re$, the capsule relative size and deformability also play specific roles in the path selection. The capsule trajectory does not always obey the classical Fung’s bifurcation law, which stipulates that a particle (in Fung’s case, a red blood cell) enters the bifurcation branch with the highest flow rate. We also consider the same branched channels operating under constant pressure drop conditions and show that such systems are difficult to control due to the transient additional pressure drop caused by the capsule. The present results obtained for dilute systems open new perspectives on the design of microfluidic systems, with optimal channel geometries and flow conditions to enrich cell and particle suspensions.

We study the viscous-fingering instability in a radial Hele-Shaw cell in which the top boundary has been replaced by a thin elastic sheet. The introduction of wall elasticity delays the onset of the fingering instability to much larger values of the injection flow rate. Furthermore, when the instability develops, the fingers that form on the expanding air–liquid interface are short and stubby, in contrast with the highly branched patterns observed in rigid-walled cells (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108, 2012, 074502). We report the outcome of a comprehensive experimental study of this problem and compare the experimental observations to the predictions from a theoretical model that is based on the solution of the Reynolds lubrication equations, coupled to the Föppl–von-Kármán equations which describe the deformation of the elastic sheet. We perform a linear stability analysis to study the evolution of small-amplitude non-axisymmetric perturbations to the time-evolving base flow. We then derive a simplified model by exploiting the observations (i) that the non-axisymmetric perturbations to the sheet are very small and (ii) that perturbations to the flow occur predominantly in a small wedge-shaped region ahead of the air–liquid interface. This allows us to identify the various physical mechanisms by which viscous fingering is weakened (or even suppressed) by the presence of wall elasticity. We show that the theoretical predictions for the growth rate of small-amplitude perturbations are in good agreement with experimental observations for injection flow rates that are slightly larger than the critical flow rate required for the onset of the instability. We also characterize the large-amplitude fingering patterns that develop at larger injection flow rates. We show that the wavenumber of these patterns is still well predicted by the linear stability analysis, and that the length of the fingers is set by the local geometry of the compliant cell.

Turbulence characteristics of an asymmetric oscillatory boundary layer flow are analysed through two-component laser-Doppler measurements carried out in a large oscillatory flow tunnel and direct numerical simulation (DNS). Five different Reynolds numbers, $R_{\unicode[STIX]{x1D6FF}}$, in the range 846–2057 have been investigated experimentally, where $R_{\unicode[STIX]{x1D6FF}}=\tilde{u} _{0max}\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D708}$ with $\tilde{u} _{0max}$ the maximum oscillatory velocity in the irrotational region, $\unicode[STIX]{x1D6FF}$ the Stokes length and $\unicode[STIX]{x1D708}$ the fluid kinematic viscosity. DNS has been carried out for the lowest three $R_{\unicode[STIX]{x1D6FF}}$ equal to 846, 1155 and 1475. Both experimental and numerical results show that the flow statistics increase during accelerating phases of the flow and especially at times of transition to turbulent flow. Once turbulence is fully developed, the near-wall statistics remain almost constant until the late half-cycle, with values close to those reported for steady wall-bounded flows. The higher-order statistics reach large values within a normalized wall distance of approximately $y/\unicode[STIX]{x1D6FF}=0.2$ at phases corresponding to the onset of low-speed streak breaking, because of the intermittency of the velocity fluctuations at these times. In particular, the flatness of the streamwise velocity fluctuations reaches values of the order of ten, while the flatness of the wall-normal velocity fluctuations reaches values of several hundreds. Far from the wall, at locations where the vertical gradient of the streamwise velocity is zero, the skewness is approximately zero and the flatness is approximately equal to 3, representative of a normal distribution. At lower elevations the distribution of the fluctuations deviate substantially from a normal distribution, but are found to be well described by other standard theoretical probability distributions.

The Richtmyer–Meshkov instability on a three-dimensional single-mode light/heavy interface is experimentally studied in a converging shock tube. The converging shock tube has a slender test section so that the non-uniform feature of the shocked flow is amply exhibited in a long testing time. A deceleration phenomenon is evident in the unperturbed interface subjected to a converging shock. The single-mode interface presents three-dimensional characteristics because of its minimum surface feature, which leads to the stratified evolution of the shocked interface. For the symmetry interface, it is quantitatively found that the perturbation amplitude experiences a rapid growth to a maximum value after shock compression and finally drops quickly before the reshock. This quick reduction of the interface amplitude is ascribed to a significant Rayleigh–Taylor stabilization effect caused by the deceleration of the light/heavy interface. The long-term effect of the Rayleigh–Taylor stabilization even leads to a phase inversion on the interface before the reshock when the initial interface has sufficiently small perturbations. It is also found that the amplitude growth is strongly suppressed by the three-dimensional effect, which facilitates the occurrence of the phase inversion.

Localized turbulence bounded by non-turbulent flow in a uniformly stratified environment is studied with direct numerical simulations of stably stratified shear layers. Of particular interest is the turbulent/non-turbulent interfacial (TNTI) layer, which is detected by identifying the turbulent region in terms of its potential vorticity. Fluid near the outer edge of the turbulent region gains potential vorticity and becomes turbulent by diffusion arising from both viscous and molecular effects. The flow properties near the TNTI layer change depending on the buoyancy Reynolds number near the interface, $Re_{bI}$. The TNTI layer thickness is approximately 13 times the Kolmogorov length scale for large $Re_{bI}$ ($Re_{bI}\gtrsim 30$), consistent with non-stratified flows, whereas it is almost equal to the vertical length scale of the stratified flow, $l_{vI}=l_{hI}Re^{-1/2}$ (here $l_{hI}$ is the horizontal length scale near the TNTI layer, and $Re$ is the Reynolds number), in the low-$Re_{bI}$ regime ($Re_{bI}\lesssim 2$). Turbulent fluid is vertically transported towards the TNTI layer when $Re_{bI}$ is large, sustaining the thin TNTI layer with large buoyancy frequency and mean shear. This sharpening effect is weakened as $Re_{bI}$ decreases and eventually becomes negligible for very low $Re_{bI}$. Overturning motions occur near the TNTI layer for large $Re_{bI}$. The dependence on buoyancy Reynolds number is related to the value of $Re_{bI}$ near the TNTI layer, which is smaller than the value deep inside the turbulent core region. An imprint of the internal gravity waves propagating in the non-turbulent region is found for vorticity within the TNTI layer, inferring an interaction between turbulence and internal gravity waves. The wave energy flux causes a net loss of the kinetic energy in the turbulent core region bounded to the TNTI layer, and the amount of kinetic energy extracted from the turbulent region by internal gravity waves is comparable to the amount dissipated in the turbulent region.

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the combined effect of electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, the Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in the internal flow pattern. Such effects further result in retardation of the drop settling velocity, which would have otherwise increased due to the influence of charge convection. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the ‘tip-stretching’ effect on the flow field. As a result, the drop deformation gets intensified with an increase in sensitivity of the surface tension to the local surfactant concentration. Consequently, for an oblate type of deformation the elevated drag force causes a further reduction in velocity. For similar reasons, prolate drops experience less drag and settle faster than the surfactant-free case. In addition to this, with increased sensitivity of the interfacial tension to the surfactant concentration, the asymmetric deformation about the equator gets suppressed. These findings may turn out to be of fundamental significance towards designing electrohydrodynamically actuated droplet-based microfluidic systems that are intrinsically tunable by varying the surfactant concentration.

Although the vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusion appears to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in the previous studies, a vortex cannot be fully described by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part to represent the rotation and the shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and the direction of the local fluid rotation axis. The direction and the strength of local fluid rotation are examined by investigating the kinematics of the fluid element in two- and three-dimensional flows. A new vector quantity, which is called the vortex vector in this paper, is defined to describe the local fluid rotation and it is the rotational part of the vorticity. This can be understood as that the direction of the vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation. With these new revelations, a vortex is defined as a connected region where the vortex vector is not zero. In addition, through direct numerical simulation (DNS) and large eddy simulation (LES) examples, it is demonstrated that the newly defined vortex vector can fully describe the complex vertical structures of turbulence.

The results of experiments on the flow through a circular sudden expansion pipe at moderate Reynolds numbers are presented. At five diameters upstream of the expansion, laminar flow was disturbed by a (constant) cross-flow jet, a suction or a (periodic in–out) synthetic jet from a hole in the wall. When the disturbance exceeded a critical value of the control parameter depending on the Reynolds number, localised turbulent patches formed downstream of the expansion at fixed axial positions. For the cross-flow jet, the onset of turbulent patches is related to the velocity ratio of the mean jet velocity to the mean pipe velocity. At low velocity ratio, turbulent patches formed intermittently. For the suction disturbance, the flow experienced a strong asymmetry of the recirculation region and required a larger velocity ratio before the turbulent patch formed. For the synthetic jet, the amplification of wavy disturbances into turbulent patches and their axial positions are controlled by the driving frequency. Overall, these results suggest the existence of different mechanisms for the development of localised turbulent patches.

The influence of tilt on flow reversals in two-dimensional thermal convection in rectangular cells with two typical aspect ratios, $\unicode[STIX]{x1D6E4}=\text{width/height}=1$ and 2, are investigated by means of direct numerical simulations. For $\unicode[STIX]{x1D6E4}=1$, tilt tends to suppress flow reversals. However, it is found that flow reversals characterized by two main rolls are promoted by tilt for $\unicode[STIX]{x1D6E4}=2$, which are even observed for some cases of small Prandtl numbers ($Pr$) and large tilt angles ($\unicode[STIX]{x1D6FD}$). Different from level cases where the four corner rolls all have opportunities to grow and trigger a flow reversal, the reversals in an anticlockwise tilted cell with $\unicode[STIX]{x1D6E4}=2$ are always led by the growth of the bottom-right or the top-left corner roll. Tilt is favourable for the growth of the bottom-right or the top-left corner roll and thus for breaking the balance between the two main rolls and triggering a flow reversal. The mode decomposition analysis shows that the appearance of the intermediate single-roll mode is crucial for reversals, and flow reversals in a tilted cell with $\unicode[STIX]{x1D6E4}=2$ can be viewed as a mode competition process between single-roll mode and horizontally adjacent double-roll mode. They can only occur in a limited range of $\unicode[STIX]{x1D6FD}$ where the two modes have comparable strength. Furthermore, the Nusselt numbers at the hot plate $Nu_{h}$ and at the cold plate $Nu_{c}$ behave differently during a flow reversal for $\unicode[STIX]{x1D6E4}=2$ due to the preference of single corner roll growth.

The irreversible mixing efficiency is studied using large-eddy simulations (LES) of stratified turbulence, where three different subgrid-scale (SGS) parameterizations are employed. For comparison, direct numerical simulations (DNS) and hyperviscosity simulations are also performed. In the regime of stratified turbulence where $Fr_{v}\sim 1$, the irreversible mixing efficiency $\unicode[STIX]{x1D6FE}_{i}$ in LES scales like $1/(1+2Pr_{t})$, where $Fr_{v}$ and $Pr_{t}$ are the vertical Froude number and turbulent Prandtl number, respectively. Assuming a unit scaling coefficient and $Pr_{t}=1$, $\unicode[STIX]{x1D6FE}_{i}$ goes to a constant value $1/3$, in agreement with DNS results. In addition, our results show that the irreversible mixing efficiency in LES, while consistent with this prediction, depends on SGS parameterizations and the grid spacing $\unicode[STIX]{x1D6E5}$. Overall, the LES approach can reproduce mixing efficiency results similar to those from the DNS approach if $\unicode[STIX]{x1D6E5}\lesssim L_{o}$, where $L_{o}$ is the Ozmidov scale. In this situation, the computational costs of numerical simulations are significantly reduced because LES runs require much smaller computational resources in comparison with expensive DNS runs.

In this work, we discuss experiments and discrete element simulations of wall-bounded shear flows of slightly polydisperse spheres under gravity. Experiments were performed in an annular shear cell in which the bottom bumpy wall rotates at fixed velocity, while a pressure is applied at the top bumpy wall. The coaxial cylinders delimiting the flow are flat, frictional and transparent, allowing visualization of the flow. Velocity profiles were obtained by particle image velocimetry, and are characterized by an exponential profile, the decay length of which depends on the applied load, but not on the wall velocity. A force sensor was installed at different vertical positions on the outer sidewall in order to measure wall forces. The effective streamwise and transverse wall friction coefficients were thus estimated, showing wall friction weakening in creep zones. In order to better understand these results, contact dynamics simulations were carried out in a simplified configuration (Artoni & Richard, Phys. Rev. Lett., vol. 115 (15), 2015, 158001). In this case, profiting from the possibility of varying the particle–wall friction coefficient, different flow regimes were observed. In particular, shear can either be localized (1) at the bottom or (2) at the top of the shear cell, or (3) it can be quite evenly distributed in the vertical direction. Through an averaging technique that explicitly takes into account gradient effects (Artoni & Richard, Phys. Rev. E, vol. 91 (3), 2015, 032202), relevant, coarse-grained, continuum fields (solid fraction, velocity, stresses, velocity fluctuations) were obtained. They allow a discussion of the relevance of velocity fluctuations (i.e. granular temperature) for describing non-locality in granular flow. The case of solid-like fluctuations is also addressed. Finally, a simplified stress analysis is devoted to explain the emergence of complex shear localization patterns by the heterogeneity of effective bulk friction, which is due to the joint effect of gravity and wall friction.

The characteristics of a turbulent core-annular flow with water-lubricated high viscosity oil in a vertical pipe are investigated using direct numerical simulation, in conjunction with a level-set method to track the phase interface between oil and water. At a given mean wall friction ($Re_{\unicode[STIX]{x1D70F}}=u_{\unicode[STIX]{x1D70F}}R/\unicode[STIX]{x1D708}_{w}=720$, where $u_{\unicode[STIX]{x1D70F}}$ is the friction velocity, $R$ is the pipe radius and $\unicode[STIX]{x1D708}_{w}$ is the kinematic viscosity of water), the total volume flow rate of a core-annular flow is similar to that of a turbulent single-phase pipe flow of water, indicating that water lubrication is an effective tool to transport high viscosity oil in a pipe. The high viscosity oil flow in the core region is almost a plug flow due to its high viscosity, and the water flow in the annular region is turbulent except for the case of large oil volume fraction (e.g. 0.91 in the present study). With decreasing oil volume fraction, the mean velocity profile in the annulus becomes more like that of turbulent pipe flow, but the streamwise evolution of vortical structures is obstructed by the phase interface wave. In a reference frame moving with the core velocity, water is observed to be trapped inside the wave valley in the annulus, and only a small amount of water runs through the wave crest. The phase interface of the core-annular flow consists of different streamwise and azimuthal wavenumber components for different oil holdups. The azimuthal wavenumber spectra of the phase interface amplitude have largest power at the smallest wavenumber whose corresponding wavelength is the pipe circumference, while the streamwise wavenumber having the largest power decreases with decreasing oil volume fraction. The overall convection velocity of the phase interface is slightly lower than the core velocity. Finally, we suggest a predictive oil holdup model by defining the displacement thickness in the annulus and considering the boundary layer characteristics of water flow. This model predicts the variation of the oil holdup with the superficial velocity ratio very well.

This paper presents an analytic solution for aerodynamic noise generated by an unsteady wall pressure gust interacting with a spanwise-variable trailing edge in a background steady uniform flow. Viscous and nonlinear effects are neglected. The Wiener–Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a tailored modal expansion in the spanwise coordinate; however, only finitely many modes are cut-on, therefore the far-field noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated trailing edges compared to those with straight edges. The two mechanisms behind the noise reduction are an increased destructive interference in the far field, and a redistribution of acoustic energy from low cut-on modes to higher cut-off modes. Five different test-case trailing-edge geometries are considered. The analytic solution identifies which geometries are most effective in different frequency ranges: geometries which promote destructive interference are best at low frequencies, whilst geometries which promote a redistribution of energy are better at high frequencies.

We present, in this paper, numerical simulations of bubble sloshing in a spherical tank, resulting from a tank rotation around a fixed axis in microgravity conditions. This configuration is of great interest in space applications where sloshing can have harmful effects on the stability of satellites. Depending on the dimensionless numbers characterising this phenomenon, our study is focused on the motion and the deformation of a bubble, initially at rest, which is set in motion when the manoeuvre is starting until it reaches a constant rotation speed around the axis. It is shown in this article that, during the first stage of the manoeuvre, the motion of the bubble is essentially driven by the inertial force that depends on the angular acceleration. Next, when the angular velocity is increasing, the centrifugal force being dominant, the trajectory of the bubble is pushed towards the direction between the centre of the tank and the axis of rotation. Finally, when the angular velocity becomes constant, the bubble, reaching a quasi-steady position, is deformed and pressed against the solid boundary of the tank. A quantified description of these phenomena is proposed through a parametric study varying the essential dimensionless numbers, i.e. the Bond number based on the angular velocity, and another Bond number based on the angular acceleration. As the temporal evolution of the forces acting on the satellite wall is of utmost importance for designing satellites and manoeuvres, we also present an analysis characterising the latter. We also detail the first comparisons between the numerical simulations and the Fluidics experiment performed in the International Space Station (ISS) in microgravity conditions. Thanks to these comparisons, we can validate the simulations in configurations of interest.