Gas volumes with an equivalent spherical diameter greater than that of the tube in which they rise by buoyancy – so-called Taylor bubbles – assume a characteristic bullet shape and ascend with a velocity that is dependent primarily on the tube diameter, and also on the physical properties of the liquid, but, remarkably, is mostly independent of the gas volume. The requirement of liquid volume conservation suggests a plausible explanation of this paradoxical feature in that the space vacated under the rising bubble must be replenished by the liquid film falling along the bubble surface. It is demonstrated by numerical means that, by limiting the bubble diameter, a cylindrical ‘cage’ of thin vertical rods coaxial with the tube permits the flow rate of this film to increase, with the result that the bubble is able to ascend with a significantly higher velocity than in an empty tube with the same diameter.

Owing to the Taylor–Proudman theorem, it is generally believed that rotating flows should have two-dimensional dynamics for rapid background rotation. Yet, we show that two infinitely long counter-rotating vertical vortices always remain unstable to three-dimensional perturbations even for large rotation rate about the vertical axis. The dominant instability consists of quasi-antisymmetric displacements of the two vortices. Its growth rate is independent of the rotation rate when it is sufficiently large, while the most amplified vertical wavelength scales like the rotation rate. Direct numerical simulations show that the instability leads ultimately to a full three-dimensional breakdown of the vortex pair. In other words, a two-dimensional vortex pair will spontaneously develop three-dimensional variations even in the limit of infinite rotation rate but the wavelength will tend to infinity. This implies that the Taylor–Proudman theorem can be strictly valid only in vertically bounded flows. The scaling for the wavelength is next generalized by showing that the typical vertical scale in rapidly rotating unbounded flows is $L_v \sim L_h/Ro$, where $L_h$ is the horizontal scale and $Ro$ the Rossby number. This scaling law is shown to derive from a self-similarity of the Navier–Stokes equations for $Ro \ll 1$. The resulting reduced equations are identical to those obtained first by Julien et al. (Theor. Comput. Fluid Dyn., vol. 11, issue 3–4, 1998, pp. 251–261) and Nazarenko & Schekochihin (J. Fluid Mech., vol. 677, 2011, pp. 134–153) by means of multiscale analyses in the cases of rotating convection or turbulence. The self-similarity demonstrated herein suggests that these reduced equations are valid for any rapidly rotating unbounded flow.

Tsunami waves induced by landslides are a threat to human activities and safety along coastal areas. In this paper, we characterize experimentally the waves generated by the gravity-driven collapse of a dry granular column into water. Three nonlinear wave regimes are identified depending on the Froude number ${Fr}_f$ based on the ratio of the velocity of the advancing granular front and the velocity of linear gravity waves in shallow water: transient bores for large ${Fr}_f$, solitary waves for intermediate values of ${Fr}_f$, and nonlinear transition waves at small ${Fr}_f$. The wave amplitude relative to the water depth increases with ${Fr}_f$ in the three regimes but with different nonlinear scalings, and the relative wavelength is an increasing or decreasing function of ${Fr}_f$ depending on the wave regime. Two of these wave regimes are rationalized by considering that the advancing granular front acts as a vertical piston pushing the water, while the last one is found to be a transition from shallow- to deep-water conditions. The present modelling contributes to a better understanding of the rich hydrodynamics of the generated waves, with coastal risk assessment as practical applications.

Abrupt depth transitions (ADTs) have recently been identified as potential causes of ‘rogue’ ocean waves. When stationary and (close-to-) normally distributed waves travel into shallower water over an ADT, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show, by comparing to new experiments and numerical simulations, that the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the ADT, and new second-order free waves generated due to the ADT.

An analytical solution of the impulsive impact of a cylindrical body submerged below a calm water surface is obtained by solving a free boundary problem. The shape of the cross-section of the body is arbitrary. The integral hodograph method is applied to derive the complex velocity potential defined in a parameter plane. The boundary-value problem is reduced to a Fredholm integral equation of the first kind in the velocity magnitude on the free surface. The velocity field, the impulsive pressure on the body surface and the added mass are determined in a wide range of depths of submergence for various cross-sectional shapes, such as a flat plate, a circular cylinder and a rectangle.

Turbulent convection plays a crucial role in many natural environments and engineering applications. One of the most fundamental questions is how the heat flux depends on the thermal driving and fluid property. It has been proposed that when the fluid layer experiences extremely strong thermal driving, the boundary layers will become fully turbulent and the so-called ultimate regime will emerge. In this work we proposed a numerical experiment in which the thermal boundary layer can be spatially decoupled with the viscous one. We demonstrate that, once the thermal boundary layer is fully decoupled from the viscous boundary layer and locates entirely inside the turbulent bulk, the scaling laws corresponding to the ultimate regime can be obtained, namely $Nu \sim Ra^{1/2}Pr^{1/2}$ and $Re \sim Ra^{1/2} Pr^{-1/2}$ with $Nu$ being the Nusselt number, $Re$ the Reynolds number, $Ra$ the Rayleigh number and $Pr$ the Prandtl number, respectively. Therefore, our results support the physical conjecture of the ultimate regime for the turbulent convection.

The effect of a counter-current gas flow on the linear stability of an inclined falling liquid film switches from destabilizing to stabilizing, as the flow confinement is increased. We confront this linear effect with the response of nonlinear surface waves resulting from long-wave interfacial instability. For the strongest confinement studied, the gas flow damps both the linear growth rate and the amplitude of nonlinear travelling waves, and this holds for waves of the most-amplified frequency and for low-frequency solitary waves. In the latter case, waves are shaped into elongated humps with a flat top that resist secondary instabilities. For intermediate confinement, the linear and nonlinear responses are opposed and can be non-monotonic. The linear growth rate of the most-amplified waves first decreases and then increases as the gas velocity is increased, whereas their nonlinear amplitude is first amplified and then damped. Conversely, solitary waves are amplified linearly but damped nonlinearly. For the weakest confinement, solitary waves are prone to two secondary instability modes that are not observed in unconfined falling films. The first involves waves of diminishing amplitude slipstreaming towards their growing leading neighbours. The second causes wave splitting events that lead to a train of smaller, shorter waves.

Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground-effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically relevant Strouhal numbers, dimensionless amplitudes and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn (AIAA J., 2018, pp. 1–15)) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake-vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement.

A Boussinesq fluid inside a stably thermally stratified square container whose walls are inclined ${45}^{\circ }$ with respect to gravity, with two opposite walls kept at constant temperatures and the other two insulated is nearly isothermal in the regions above and below the horizontal diagonal. The flow is concentrated in the wall boundary layers and a shear layer centred about the horizontal diagonal. The equilibrium is maintained by the balance between dissipation in the shear and boundary layers, the heat fluxes at the constant temperature walls, and the induced flow resulting from the no-flux condition at the inclined insulated walls. The dynamical response of the fluid to vertical oscillations of the container is studied over a range of forcing frequencies. For a small forcing amplitude and below a viscosity-dependent cutoff forcing frequency, this response exhibits a modal cellular structure localized about the shear layer. With increasing forcing amplitude, the response experiences instabilities, studied here numerically at a forcing frequency above the cutoff frequency, that are similar to those encountered in the Faraday wave problem, such as parametric subharmonic instability, triadic resonance and resonant collapse.

The ability of vortices to induce aerodynamic loads on proximal surfaces plays a significant role in a wide variety of flows. However, most studies of vortex-induced effects primarily focus on analysing the influence of the rotation-dominated cores of vortices. In this work, we show that not only are vortices in viscous flows surrounded by strain-dominated regions, but these regions are dynamically important and can sometimes even dictate the induced aerodynamic loads. We demonstrate this for a pitching airfoil, which exhibits dynamic stall and generates several force-inducing vortices. Using a data-driven force partitioning method (FPM), we quantify the influence of vortices as well as vortex-associated strain to show that our current understanding of vortex-dominated phenomena, such as dynamic stall, is incomplete without considering the substantial effect of strain-dominated regions that are associated with vortices.

We investigate evanescent inertial waves, both theoretically and experimentally, in a fluid subject to a background rotation of $\varOmega$. We predict that there is a smooth transition from conventional inertial waves to evanescent disturbances at a frequency of $\varpi = 2\varOmega$, and that at this cross-over frequency the evanescent disturbances are spatially extensive, having a horizontal extent which is limited only by viscosity, or by the size of the domain. These findings are confirmed by our experiments, which, to the best of our knowledge, represent the first quantitative experimental investigation of evanescent inertial waves.

The reshocked turbulent Richtmyer–Meshkov (RM) mixing of two media is the most representative problem of more general and complex turbulent mixing induced by interfacial instabilities, broadly occurring in both nature and engineering applications. An accurate prediction of its evolving of spatial structure and mixing width (MW) is of fundamental importance. However, satisfactory prediction with the large-eddy simulation (LES) has not yet been achieved, even for the most important MW. In this paper, we innovatively solve this problem by combining the idea of the constrained large-eddy simulation (CLES), which succeeded previously only in classical single-medium turbulence, and our recently developed Reynolds averaged Navier–Stokes (RANS) model, which realized a satisfactory prediction of MW. Specifically, in our currently developed CLES model, with the aid of Reynolds decomposition, the unclosed subgrid scale (SGS) LES model is decomposed into two parts, i.e. the averaged and the fluctuating. The averaged part is dominated and modelled by the counterpart of our recently developed RANS model to accurately predict the MW, while the fluctuating part is modelled with the classical Smagorinsky model. Consequently, besides successfully capturing the three-dimensional large-scale structure of turbulence and the evolution of the (normalized) mixed mass, our newly proposed CLES also predicts a satisfactory MW with a very coarse grid. To the best of our knowledge, this is the first time that the LES can yield such a comparable result with experiment.

We consider the evolution of the bulk bubble-size distribution $N(a,t)$ of large bubbles (Weber number ${\textit {We}}\gg 1$) under free-surface entrainment described generally by an entrainment size distribution $I(a)$ with power-law slope $\gamma$ and large-radius cutoff $a_{max}$. Our main focus is the interaction between turbulence-driven fragmentation and free-surface entrainment, and, for simplicity, we ignore other mechanisms such as degassing, coalescence and dissolution. Of special interest are the equilibrium bulk distribution $N_{eq}(a)$, with local power-law slope $\tilde {\beta }_{eq}(a)$, and the time scale $\tau _c$ to reach this equilibrium after initiation of entrainment. For bubble radii $a\ll a_{max}$, we find two regimes for the dependence of $N_{eq}(a)$ on the entrainment distribution. There is a weak injection regime for $\gamma \ge -4$, where $\tilde {\beta }_{eq}(a)=-10/3$ independent of the entrainment distribution; and a strong injection regime for $\gamma <-4$, where the power-law slope depends on $\gamma$ and is given by $\tilde {\beta }_{eq}(a)=\gamma +2/3$. The weak regime provides a general explanation for the commonly observed $-10/3$ power law originally proposed by Garrett et al. (J. Phys. Oceanogr., vol. 30 (9), 2000, pp. 2163–2171), and suggests that different weak entrainment mechanisms can all lead to this result. For $a\sim a_{max}$, we find that $N_{eq}(a)$ exhibits a steepening deviation from a power law due to fragmentation and entrainment, similar to what has been observed, but here absent other mechanisms such as degassing. The evolution of $N(a,t)$ to $N_{eq}(a)$ is characterised by the critical time $\tau _c \propto C_f \varepsilon ^{-1/3} {a_{max}}^{2/3}$, where $\varepsilon$ is the turbulence dissipation rate and $C_f$ is a new constant that quantifies the dependence on the daughter size distribution in a fragmentation event. For typical breaking waves, $\tau _c$ can be quite small, limiting the time $t\lesssim \tau _c$ when direct measurement of $N(a,t)$ might provide information about the underlying entrainment size distribution.

In a sheared suspension, the chaotic motion of the particles disperses the suspending liquid and drives an exponential and broadly distributed growth of the elongation of its material lines. This paper addresses experimentally and theoretically the consequences of this complex advection on the mixing of an initially segregated blob of diffusive dye, at large Péclet number and down to the finest scales of mixing. As the suspension is sheared, the combined action of the mean and fluctuating components of the flow stretches and folds the blob into a multi-scale lamellar structure. At short time, overlaps between the lamellae are scarce and the probability distribution concentration can be understood from the local stretching statistics only. At intermediate times, dispersion limits the volume within which lamellae deploy; overlaps become abundant and their statistics determine the concentration distribution. At longer times, the dye becomes homogeneous at the particle scale and the concentration distribution is set by dispersion only. Predictions for both the concentration distribution and the transitions between these successive stages of mixing are provided and compared to the experimental results.

Oscillatory flow features are common in the unstart of hypersonic mixed-compression intakes and can be classified as low-amplitude or high-amplitude oscillatory unstarted flows. The low-amplitude oscillatory unstarted flow is driven by the shear layer from shock interactions ahead of the cowl, while the high-amplitude oscillatory unstarted flow is driven by the separation caused by shock–boundary-layer interaction on the ramp. While previous studies have observed these flow features and reported their associated frequency, there is no simple criterion available for predicting which mode will occur, and there is a lack of consensus on the appropriate frequency scaling parameter. We study a mixed-compression hypersonic intake in a hypersonic wind tunnel by varying the internal contraction ratio and the throttling ratio to observe various kinds of unstart regimes. Two significant conclusions emerge from considering the results for high-throttling-ratio conditions $(TR > 0.55)$ from the current as well as previous studies. Firstly, the actual shock-on-lip condition at the cowl corresponding to the unthrottled condition, as observed from schlieren images, demarcates the boundary between the two modes of oscillatory unstart flows upon throttling. Secondly, a suitable length scale $(l^*)$, defined as the extent of the subsonic region in the unstarted flow (as observed from the experimental schlieren images), gives the appropriate frequency scaling parameter ($f^* = a_0/4l^*$ where $a_0$ is the stagnation acoustic speed).

The vortex-induced vibration of a flexible filament attached behind a stationary cylinder is studied in the two-dimensional, laminar flow regime. We explore the response of the filament for a wide range of flexibility and inertia. Lock-in with a large number of normal modes of the filament, each in a different regime of reduced speed, is observed. Reduced speed is the free-stream speed of the incoming flow non-dimensionalized with the first natural frequency of the structure and the diameter of the cylinder. Several branches, based on response of the filament, are identified and the contributions of various structural modes along these branches are quantified. Contribution from a particular structural mode increases significantly during lock-in, accompanied by a large amplitude of vibration. The transition between different branches is found to be hysteretic and intermittent. The flow exhibits a variety of vortex-shedding patterns, including the $\mathsf {2P+2S}$ mode. The modes of shedding show a systematic variation with amplitude and frequency. The map of vortex-shedding patterns in the amplitude–frequency plane resembles the corresponding map for forced vibration of a rigid cylinder. The transformation of wake from one mode of shedding to another is explained phenomenologically. Variation of rate of energy transfer between the fluid and filament with space and time is analysed to determine optimal placement of transducers for harvesting energy.

This study performs global stability/receptivity analyses of hypersonic flows over a swept blunt body with infinite span. For the first time, we obtain the characteristics of the leading attachment-line mode to the variation of sweep angles from $20^{\circ }$ to $70^{\circ }$. The global eigenfunctions exhibit the characteristics of the attachment-line instability at the leading edge. At the same time, cross-flow (at small sweep angles) or second Mack mode (at larger sweep angles) dominates further downstream. We establish an adjoint-based bi-orthogonal eigenfunction system to address the receptivity problem of such flows to any external forces and boundary perturbations. The receptivity analyses indicate that the global modes are the most responsive to external forces and surface perturbations applied in the vicinity of the attachment line, regardless of the sweep angles. It is also proven that the present global extension of the bi-orthogonal eigenfunction system can be successfully applied to complex hypersonic flows.

Liquid-infused surfaces (LISs) are a promising technique for reducing friction, fouling and icing in both laminar and turbulent flows. Previous work has demonstrated that these surfaces are susceptible to shear-driven drainage. Here, we report a different failure mode using direct numerical simulations of a turbulent channel flow with liquid-infused longitudinal grooves. When the liquid–liquid surface tension is small and/or grooves are wide, we observe travelling-wave perturbations on the interface with amplitudes larger than the viscous sublayer of the turbulent flow. These capillary waves induce a roughness effect that increases drag. The generation mechanism of these waves is explained using the theory developed by Miles for gravity waves. Energy is transferred from the turbulent flow to the LIS provided that there is a negative curvature of the mean flow at the critical layer. Given the groove width, the Weber number and an estimate of the friction Reynolds number, we provide relations to determine whether a LIS behaves as a smooth or rough surface in a turbulent flow.

Instability and transition in the boundary layer on a slender cone ($60^{\circ }$ apex angle) rotating in still fluid are investigated using hot-wire anemometry as well as through linear stability analysis. In contrast to broad cones (including the disk), where a cross-flow instability dominates the transition and different studies report similar transition Reynolds numbers, the reported transition Reynolds numbers on slender cones are scattered. The present experiments provide quantitative experimental datasets and the stability and transition are evaluated based on both the Reynolds number and a Görtler number. The results consistently show that the instability development depends on the Görtler number rather than the Reynolds number and that transition starts at a well-defined Görtler number, whereas the transition Reynolds number depends on the rotational rate. The measured disturbance that first grows in the laminar region has a frequency approximately the same as or twice the rotational rate of the cone, which according to the stability analysis corresponds to the critical frequency of a slightly inclined vortex structure with respect to the cone axis or an axisymmetric vortex structure. These structures are similar to those observed in the flow visualisations of Kobayashi & Izumi (J. Fluid Mech., vol. 127, 1983, pp. 353–364) and considered as being due to a centrifugal instability.

We present experimentally obtained time-averaged vertical temperature profiles $\theta (z)$ in horizontal convection (HC) in water (Prandtl number $Pr \simeq 6$), which were measured near the heating and cooling plates that are embedded in the bottom of HC samples. Three HC rectangular samples of different sizes but the same aspect ratio $\varGamma \equiv L:W:H = 10:1:1$ ($L$, $W$ and $H$ are the length, width and height of the sample, respectively) were used in the experiments, which allowed us to study HC in a Rayleigh-number range $2 \times 10^{10} \lesssim {Ra} \lesssim 9 \times 10^{12}$. The measurements revealed that above the cooling plate, the mean temperature profiles have a universal scaling form $\theta (z/\lambda _c)$ with $\lambda _c$ being a $Ra$-dependent thickness of the cold thermal boundary layer (BL). The $\theta (z/\lambda _c)$-profiles agree well with solutions to a laminar BL equation in HC, which is derived under assumption that the large-scale horizontal velocity achieves its maximum near the plate and vanishes in the bulk. Above the heating plate, the mean temperature field has a double-layer structure: in the lower layer, the $\theta$ profiles scale with the hot thermal BL thickness $\lambda _h$, while in the upper layer, they again scale with $\lambda _c$. Both scaling forms are in good agreement with the solutions to the BL equation with a proper parameter choice.