The present work aims at exploring the scale-by-scale kinetic energy exchanges in multiphase turbulence. For this purpose, we derive the Kármán–Howarth–Monin equation which accounts for the variations of density and viscosity across the two phases together with the effect of surface tension. We consider both conventional and phase conditional averaging operators. This framework is applied to numerical data from detailed simulations of forced homogeneous and isotropic turbulence covering different values for the liquid volume fraction, the liquid–gas density ratio, the Reynolds number and the Weber number. We confirm the existence of an additional transfer term due to surface tension. Part of the kinetic energy injected at large scales is transferred into kinetic energy at smaller scales by classical nonlinear transport while another part is transferred to surface energy before being released back into kinetic energy, but at smaller scales. The overall kinetic energy transfer rate is larger than in single-phase flows. Kinetic energy budgets conditioned in a given phase show that the scale-by-scale transport of turbulent kinetic energy due to pressure is a gain (loss) of kinetic energy for the lighter (heavier) phase. Its contribution can be dominant when the gas volume fraction becomes small or when the density ratio increases. Building on previous work, we hypothesise the existence of a pivotal scale above which kinetic energy is stored into surface deformation and below which the kinetic energy is released by interface restoration. Some phenomenological predictions for this scale are discussed.

The present study focuses on the influence of gas swirl on the spray behaviour from a two-fluid coaxial atomiser with high gas-to-liquid dynamic pressure ratios $M$ by varying both the liquid Reynolds number ${\textit{Re}}_l$ and the gas Weber number ${\textit{We}}_g$. The investigations identify the deviations of the carrier phase velocity fields, droplet distribution, and dispersion when swirl is introduced to the gas phase compared with the non-swirling conditions. The changes in the axial, radial and tangential velocities of the continuous phase due to the introduction of swirl are highlighted while retaining a self-similar behaviour. The slip velocity of the large droplets in swirling sprays is negative, unlike the known positive value for non-swirling sprays. The shape of the radial profiles of the mean drop size is investigated along ${\textit{We}}_g$, notably revealing an inflection point for swirling sprays at high-${\textit{We}}_g$ values. A global assessment of the drop size uncovered that swirl leads to its increase for low $M$ while assisting spray formation at high $M$. Additionally, the radial profiles of axial fluxes for swirling sprays have a wider bell-shaped curve compared with non-swirling sprays at high $M$, unlike the off-centre maxima found for low $M$. However, the mentioned dependencies of drop sizes and fluxes cannot be determined by $M$ solely for intermediate gas-to-liquid momentum ratios ($23\lt M\lt 46$), and vary with ${\textit{Re}}_l$ and ${\textit{We}}_g$. In addition, the response of at least the mean droplets at the edge of the spray to the large gas eddies shows a linear relation with swirl intensity.

Direct numerical simulations of two-phase, free-surface flow past a fully submerged, fixed circular cylinder are conducted for transitional Reynolds numbers $400 \leqslant {\textit{Re}} \leqslant 2000$, with Weber number ${\textit{We}} = 1000$, Froude number ${\textit{Fr}} = 1$ and a fixed gap ratio $G = 0.5$. This parameter combination corresponds to the gas entrainment regime characterised by the production of multiscale gas bubbles through interface breakup in the wake, which is of particular interest for its implications in enhancing gas transfer and mixing in environmental and engineering flows, such as air–water gas exchange processes in rivers and oceans, and the design and performance of naval and offshore structures. For ${\textit{Re}}= 400$, the jet forced through the $0.5D$ gap where $D$ is the diameter of the cylinder, efficiently convects opposite-signed vorticity downstream, suppressing the classical von Kármán instability and yielding a quasisteady recirculation bubble. The jet’s stabilising influence, however, breaks down once ${\textit{Re}} \approx 500$: periodic vortex shedding re-emerges and the wake becomes unsteady in spite of the continuing jet. The corresponding dimensionless shedding frequency Strouhal number $St$ grows with ${\textit{Re}}$ as $0.52-72.7{\textit{Re}}^{-1}$. The onset of unsteadiness first shortens the mean separation length but then drives it towards a saturation plateau for higher ${\textit{Re}}$ values. Surface rupture in the turbulent wake fragments entrained air into a multiscale bubble population whose number density follows $S_b(R_{\textit{eff}}) \propto R_{\textit{eff}}^{-6}$, consistent with gravity–capillary breakup in breaking waves, where $R_{\textit{eff}}$ represents the effective radii of the bubbles. Intermittency in entrainment corresponding to vortex shedding contrasts sharply with the finger-like structures observed under laminar conditions, underscoring the role of turbulent mixing. The coupled analysis of vorticity transport, shear-layer instability and bubble statistics elucidates how momentum exchange and air entrainment over a submerged body are governed under non-turbulent and turbulent conditions.

Amphibious unmanned vehicles promise next-generation water-based missions by eliminating the need for multiple vehicles to traverse water and air separately. Existing research-grade quadrotors can navigate in water and air and cross the water–air boundary, but it remains unclear how their transition is affected by rotor kinematics and geometry. We present here experimental results from isolated small rotors (diameters $\sim 10\,\mathrm{cm}$) dynamically transitioning from water to air. We discovered that rotors experience an abrupt change in frequency, lift and torque before reaching the interface, and the change is linked to the surface depression caused by a free surface vortex. We explored how the surface dynamics are affected by advance ratio, rotor diameter, number of rotor blades and input throttle. Free surface vortices above rotating objects have been studied in the context of unbaffled stirred tanks, but not in the field of small amphibious rotorcraft. We show that existing free surface vortex models can be adapted to explain water-to-air rotor performance. A better understanding of water–air rotor transitions helps to (i) assess the amphibious capability of existing aerial rotors, and (ii) suggest efficient water–air transition strategies for next-generation amphibious vehicles.

The breakup and coalescence of particle aggregates confined at the interface of turbulent liquid layers are investigated experimentally and theoretically. In particular, we consider conductive fluid layers driven by Lorentz forces and laden with millimetre-scale floating particles. These form aggregates held together by capillary attraction and disrupted by the turbulent motion. The process is fully characterised by imaging at high spatio-temporal resolution. The breakup frequency $\varOmega$ is proportional to the mean strain rate and follows a power-law scaling $\varOmega \sim D^{3\text{/}2}$, where $D$ is the size of the aggregate, attributed to the juxtaposition of particle-scale strain cells. The daughter aggregate size distribution exhibits a robust U-shape, which implies erosion of small fragments as opposed to even splitting. The coalescence kernel $\varGamma$ between pairs of aggregates of size $D_{1}$ and $D_{2}$ scales as $\varGamma \sim ( D_{1} + D_{2} )^{2}$, which is consistent with gas-kinetic dynamics. These relations, which apply to regimes dominated both by capillary-driven aggregation and by drag-driven breakup, are implemented into the population balance equation for the evolution of the aggregate number density. Comparison with the experiments shows that the framework captures the observed distribution for aggregates smaller than the forcing length scale.

This study quantitatively investigates the two-dimensional pseudosteady shock refraction at an inclined air–water interface, referred to as the water wedge, in the weak and strong incident shock strength groups. Numerical simulations are employed to validate the predicted refraction sequences from a previous study (Anbu Serene Raj et al. 2024 J. Fluid Mech. 998, A49). A distinctive irregular refraction pattern, referred to as the bound precursor refraction with a Mach reflection, is numerically validated in the weak shock group. Based on the numerical simulations, an enhanced formulation is proposed to determine the sonic line of the incident flow Mach number ($M_b$) in water, thereby providing an appropriate transition condition for an irregular refraction with a Mach reflection to a free precursor refraction with a Mach reflection transition. Furthermore, comparative studies on solid and water wedges of wedge angle $20^\circ$ reveal discernible differences in the shock reflection patterns. The interplay of the energy dissipation due to the transmitted shock wave and the Richtmyer–Meshkov instability at the air–water interface results in the variation of the triple-point trajectory and transition angles between single Mach reflection (SMR) to transitional Mach reflection (TMR) occurring in air.

The present article investigates the stability of Rayleigh–Bénard convection in a composite system consisting of a horizontal fluid layer overlying a fluid-saturated Darcy porous layer subjected to a time-periodic temperature distribution. The bottom surface is heated periodically with time, whereas a Biot number-dependent thermal boundary condition represents the heat transfer at the upper surface. The Beavers–Joseph–Saffman–Jones condition describes the ‘slip’ at the interface of the domains, and the Lions interface condition governs the normal force balance, incorporating a dynamic pressure term. The Chebyshev tau method and Fourier analysis are utilised to obtain linear instability bounds, which are compared with strong global and asymptotic limits derived from the nonlinear analysis using the energy method. Four deliberately chosen configurations of superposed fluid- and porous-layer systems are investigated. Two configurations validate the analysis through the limiting cases of the classical Darcy–Bénard and Rayleigh–Bénard systems obtained by setting the fluid-to-porous depth ratio $(\hat {d})$ to zero and infinity, respectively. The other two configurations involve layers with equal depths $(\hat {d} =1)$ and a shallow fluid layer overlying a porous layer $(\hat {d} \sim 0.1)$. For these cases, modulation substantially influences the onset of convection. In the last case, the linear theory points out that modulation parameters can control the dominant convective mode (fluid/porous). Furthermore, unlike the previously reported studies, the nonlinear stability bounds are found to be significantly lower than the linear instability bounds, indicating the possibility of subcritical instabilities in the presence of modulation. The region of subcritical instabilities increases with modulation amplitude.

Pendant drops appear in many engineering applications, such as inkjet printing and optical tensiometry, and they have also been the subject of studies of droplet–particle interaction. While the hydrostatics of pendant drops has been studied extensively, the influence of external flow disturbances has received limited attention. This research aims to incorporate aerodynamic factors into the understanding of pendant drop behaviour. Employing a simplified model, an irrotational flow aligned with the drop’s axis is derived from a distribution of singularity elements within the drop. The drop’s equilibrium shape is then determined using a numerical model that couples the flow field with the Young–Laplace equation. The model’s predictions are compared to droplet images captured via high-speed shadowgraph in a vertical wind tunnel, showing good agreement with the experimentally observed shapes. Additionally, under certain flow conditions, the drop exhibits instability in the form of periodic pendulum-like motion. This instability was linked to two distinct critical drop heights, and the corresponding stability criterion was mathematically derived from the numerical model. Our theoretical and experimental findings provide the first quantitative description of the equilibrium shape and stability criterion of pendant drops under the influence of external flow.

In air-entraining flows, there is often strong turbulence beneath the free surface. We consider the entrainment of bubbles at the free surface by this strong free-surface turbulence (FST). Our interest is the entrainment size distribution (per unit free surface area) $I(a)/A_{\textit{FS}}$, for bubbles with radius $a$ greater than the capillary scale ($\approx 1.3\ \mathrm{mm}$ for air–water on Earth), where gravity dominates surface tension. We develop a mechanistic model based on entrained bubble size being proportional to the minimum radius of curvature of the initial surface deformation. Using direct numerical simulation of a flow that isolates entrainment by FST, we show that, consistent with our mechanism, $I(a)/A_{\textit{FS}} = C_I \, g^{-3} \varepsilon ^{7/3} (2 a)^{-14/3}$, where $g$ is gravity, and $\varepsilon$ is the turbulence dissipation rate. In the limit of negligible surface tension, $C_I\approx 3.62$, and we describe how $C_I$ decreases with increasing surface tension. This scaling holds for sufficiently strong FST such that near-surface turbulence is nearly isotropic, which we show is true for turbulent Froude number ${\textit{Fr}}^2_T = \varepsilon /u_{\textit{rms}} g \gt 0.1$. While we study FST entrainment in isolation, our model corroborates previous numerical results from shear-driven flow, and experimental results from open-channel flow, showing that the FST entrainment mechanism that we elucidate can be important in broad classes of air-entraining flows.

In this paper, a phase-change model based on a geometric volume-of-fluid (VOF) framework is extended to simulate nucleate boiling with a resolved microlayer and conjugate heat transfer. Heat conduction in both the fluid and solid domains is simultaneously solved, with interfacial heat-transfer resistance (IHTR) imposed. The present model is implemented in the open-source software Basilisk with adaptive mesh refinement (AMR), which significantly improves computational efficiency. However, the approximate projection method required for AMR introduces strong oscillations within the microlayer due to intense heat and mass transfer. This issue is addressed using a ghost fluid method, allowing nucleate boiling experiments to be successfully replicated. Compared with previous literature studies, the computational cost is reduced by three orders of magnitude. We investigated the impact of contact angle on nucleate boiling through direct numerical simulation (DNS). The results show that the contact angle primarily influences the bubble growth by altering the hydrodynamic behaviour within the microlayer, rather than the thermal effect. An increase in contact angle enhances contact line mobility, resulting in a slower bubble growth, while maintaining an approximately constant total average mass flux. Furthermore, the sensitivity of bubble dynamics to the contact angle diminishes as the angle decreases. Finally, a complete bubble cycle from nucleation to detachment is simulated, which, to our knowledge, has not been reported in the open literature. Reasonable agreement with experimental data is achieved, enabling key factors affecting nucleate boiling simulations in the microlayer regime to be identified, which were previously obscured by limited simulation time.

Interface-resolved direct numerical simulations are performed to investigate bubble-induced transition from a laminar to elasto-inertial turbulent (EIT) state in a pressure-driven viscoelastic square channel flow. The Giesekus model is used to account for the viscoelasticity of the continuous phase, while the dispersed phase is Newtonian. Simulations are performed for both single- and two-phase flows for a wide range of Reynolds (${Re}$) and Weissenberg (${\textit{Wi}}$) numbers. In the absence of any discrete external perturbations, single-phase viscoelastic flow is transitioned to an EIT regime at a critical Weissenberg number ($Wi_{cr})$ that decreases with increasing ${Re}$. It is demonstrated that injection of bubbles into a laminar viscoelastic flow introduces streamline curvature that is sufficient to trigger an elastic instability leading to a transition to an EIT regime. The temporal turbulent kinetic energy spectrum shows a scaling of $-2$ for this multiphase EIT regime, and this scaling is found to be independent of size and number of bubbles injected into the flow. It is also observed that bubbles move towards the channel centreline and form a string-shaped alignment pattern in the core region at the lower values of ${Re}=10$ and ${\textit{Wi}}=1$. In this regime, there are disturbances in the core region in the vicinity of bubbles while flow remains essentially laminar. Unlike the solid particles, it is found that increasing shear-thinning effect breaks up the alignment of bubbles.

In this study we focus on the collision rate and contact time of finite-sized droplets in homogeneous, isotropic turbulence. Additionally, we concentrate on sub-Hinze–Kolmogorov droplet sizes to prevent fragmentation events. After reviewing previous studies, we theoretically establish the equivalence of spherical and cylindrical formulations of the collision rate. We also obtained a closed-form expression for the collision rate of inertial droplets under the assumption of inviscid interactions. We then perform droplet-resolved simulations using the Basilisk solver with a multi-field volume-of-fluid method to prevent numerical droplet coalescence, ensuring a constant number of droplets of the same size within the domain, thereby allowing for the accumulation of collision statistics. The collision statistics are studied from numerical simulations, varying parameters such as droplet volume fraction, droplet size relative to the dissipative scale, density ratio and viscosity ratio. Our results show that the contact time is finite, leading to non-binary droplet interactions at high volume fractions. Additionally, the contact duration is well predicted by the eddy turnover time. We also find that the radial distribution at contact is significantly smaller than that predicted by the hard-sphere model due to droplet deformation in close proximity. Furthermore, we show that for neutrally buoyant droplets, the mean relative velocity is similar to the mean relative velocity of the continuous phase, except when the droplets are close. Finally, we demonstrate that the collision rate obeys the appropriate theoretical law, although a numerical prefactor weakly varies as a function of the dimensionless parameters, which differs from the constant prefactor from theory.

Riparian vegetation along riverbanks and seagrass along coastlines interact with water currents, significantly altering their flow. To characterise the turbulent fluid motion along the streamwise-edge of a region covered by submerged vegetation (canopy), we perform direct numerical simulations of a half-channel partially obstructed by flexible stems, vertically clamped to the bottom wall. An intense streamwise vortex forms along the canopy edge, drawing high-momentum fluid into the side of the canopy and ejecting low-momentum fluid from the canopy tip, in an upwelling close to the canopy edge. This mechanism has a profound impact on the mean flow and on the exchange of momentum between the fluid and the structure, which we thoroughly characterise. The signature of the canopy-edge vortex is also found in the dynamical response of the stems, assessed for two different values of their flexibility. Varying the flexibility of the stems, we observe how different turbulent structures over the canopy are affected, while the canopy-edge vortex does not exhibit major modifications. Our results provide a better understanding of the flow in fluvial and coastal environments, informing engineering solutions aimed at containing the water flow and protecting banks and coasts from erosion.

The interaction between deep oceanic currents and an ice base is critical to accurately predict global ice melting rates, yet predictions are often affected by inaccuracies due to inadequate dynamical modelling of the ice–water interface morphology. To improve current predictive models, we numerically investigate the evolution of the ice–water interface under a subsurface turbulent shear-dominated flow, focusing on the time and length scales that govern both global and local morphological features. Based on our previous work (Perissutti, Marchioli & Soldati 2024 Intl J. Multiphase Flow 181, 105007), where we confirmed the existence of a threshold Reynolds number below which only streamwise-oriented topography forms and above which a larger-scale spanwise topography emerges and coexists with the streamwise structures, we explore three orders of magnitude for the Stefan number (the ratio of sensible heat to latent heat). We examine its impact on ice melting and its role in shaping the interface across the two distinct morphodynamic regimes. We identify characteristic time scales of ice melting and demonstrate that the key features of ice morphodynamics scale consistently with the Stefan number and the Péclet number (the ratio of heat advection to diffusion) in both regimes. These scaling relationships can be leveraged to infer the main morphodynamic characteristics of the ice–water interface from direct numerical simulation datasets generated at computationally feasible values of Péclet and Stefan numbers, enabling the incorporation of morphodynamics into geophysical melting models and thereby enhancing their predictive accuracy.

The presence of salt in seawater significantly affects the melt rate and morphological evolution of ice. This study investigates the melting process of a vertical cylinder in saline water using a combination of laboratory experiments and direct numerical simulations. The two-dimensional (2-D) direct numerical simulations and three-dimensional (3-D) experiments achieve thermal Rayleigh numbers up to $\textit{Ra}_{T}= \mathcal{O} (10^{9} )$ and saline Rayleigh numbers up to $\textit{Ra}_{S}=\mathcal{O} (10^{12} )$. Some 3-D simulations of the vertical ice cylinder are conducted at $\textit{Ra}_{T}= \mathcal{O} (10^{5} )$ to confirm that the results in 2-D simulations are qualitatively similar to those in 3-D simulations. The mean melt rate exhibits a non-monotonic relationship with ambient salinity. With increasing salinity, the mean melt rate initially decreases towards the point where thermal and saline effects balance, after which it increases again. Based on the ambient salinity, the flow can be categorised into three regimes: temperature-driven flow, salinity-driven flow and thermal-saline competing flow. In the temperature-driven and competing flow regimes, we find that the mean melt rate follows a $\textit{Ra}_{T_d}^{1/4}$ scaling, where the subscript $d$ denotes a response parameter. In contrast, in the salinity-driven flow regime, we see a transition from a $\textit{Ra}_{T_d}^{1/4}$ to a $\textit{Ra}_{T_d}^{1/3}$ scaling. Additionally, the mean melt rate follows a $\textit{Ra}_{S_d}^{1/3}$ scaling in this regime. The ice cylinder develops distinct morphologies in different flow regimes. In the thermal-saline competing flow regime, distinctive scallop (dimpled) patterns emerge along the ice cylinder due to the competition between thermal buoyancy and saline buoyancy. We observe these scallop patterns to migrate downwards over time, due to local differences in the melt rate, for which we provide a qualitative explanation.

Direct numerical simulations of a uniform flow past a fixed spherical droplet are performed to determine the parameter range within which the axisymmetric flow becomes unstable. The problem is governed by three dimensionless parameters: the drop-to-fluid dynamic viscosity ratio, $\mu ^\ast$, and the external and internal Reynolds numbers, ${\textit{Re}}^e$ and ${\textit{Re}}^i$, which are defined using the kinematic viscosities of the external and internal fluids, respectively. The present study confirms the existence of a regime at low-to-moderate viscosity ratio where the axisymmetric flow breaks down due to an internal flow instability. In the initial stages of this bifurcation, the external flow remains axisymmetric, while the asymmetry is generated and grows only inside the droplet. As the disturbance propagates outward, the entire flow first transits to a biplanar-symmetric flow, characterised by two pairs of counter-rotating streamwise vortices in the wake. A detailed examination of the flow field reveals that the vorticity on the internal side of the droplet interface is driving the flow instability. Specifically, the bifurcation sets in once the maximum internal vorticity exceeds a critical value that decreases with increasing ${\textit{Re}}^i$. For sufficiently large ${\textit{Re}}^i$, internal flow bifurcation may occur at viscosity ratios of $\mu ^\ast = {\mathcal{O}}(10)$, an order of magnitude higher than previously reported values. Finally, we demonstrate that the internal flow bifurcation in the configuration of a fixed droplet in a uniform fluid stream is closely related to the first path instability experienced by a buoyant, deformable droplet of low-to-moderate $\mu ^\ast$ freely rising in a stagnant liquid.

By incorporating leading-edge (L-E) protuberances inspired by humpback whale flippers, this study enhances hydrodynamic performance, mitigates cavitation effects and develops efficient models to minimise noise emissions in aquatic systems. Experimental and numerical simulations are conducted on four semi-elliptical NACA 16020 three-dimensional (3-D) hydrofoils, including a baseline hydrofoil and three modified versions featuring sinusoidal L-E alterations. These alterations encompass amplitudes of 2 %, wavelengths of 8.33 % and 4.1667 % of the mean chord length (C), and wavenumbers of 12 and 6. Experimental analysis encompassing both cavitational and non-cavitational regimes at varying attack angles revealed significant relationships between the hydrodynamic performance and partial sheet cavitation. Hydrodynamic force analysis shows that hydrofoils with L-E protuberances generate elevated lift at moderate and high angles of attack (AOA) in cavitating and non-cavitating conditions. Under lower-severity cavitating conditions, models with L-E protuberances exhibit no significant reduction in sound pressure level. In contrast, at higher severity, the presence of L-E protuberances effectively reduces the flow-induced noise, with partial cavities covering 30 %–50 % of the chord. Numerical simulations were conducted to investigate the turbulent kinetic energy (TKE) distribution and the presence of counter-rotating vortices on each protuberance. The results reveal a significantly enhanced TKE around the trough area and the presence of counter-rotating vortices at each protuberance peak. The more realistic asymmetric design performed better than the other modifications regarding hydrodynamic force, whereas the symmetric model with wavelengths of 8.33 % excelled at cavitation and noise suppression. Therefore, this study offers promising avenues for advancing hydrofoil design in diverse engineering domains.

This study investigates the fluid mechanisms underlying the interaction between ventilated shoulder and tail cavities under vertical launching conditions. It is found that expansion and contraction coexist within the tail cavity. When the expansion rate exceeds the contraction rate, the volume of the tail cavity increases; conversely, it decreases. Through this process, the cavity undergoes cyclic pulsation during its vertical evolution, including expansion, over-expansion, contraction and over-contraction. Before the shoulder cavity extends to the position of the tail cavity, wall confinement restricts the tail cavity from expanding towards the vehicle’s lateral wall. After the encounter between the shoulder and tail cavities, the re-entrant flow at the end of the shoulder cavity induces the tail cavity to overcome wall confinement and expand towards the lateral wall, initiating their fusion. As a result, a supercavity forms and attaches to the surface of the vehicle. Moreover, after the fusion, the pressure driving mode at the vehicle’s bottom wall shifts from the tail cavity pulsation to the re-entrant flow. In addition, an increase in the ventilation rate induces progressive expansion of the shoulder cavity’s radial dimension, and accelerates its downstream propagation. The fusion mode between the shoulder and tail cavities transitions from progressive fusion to coverage fusion.

Developing reduced-order models for the transport of solid particles in turbulence typically requires a statistical description of the particle–turbulence interactions. In this work, we utilize a statistical framework to derive continuum equations for the moments of the slip velocity of inertial, settling Lagrangian particles in a turbulent boundary layer. Using coupled Eulerian–Lagrangian direct numerical simulations, we then identify the dominant mechanisms controlling the slip velocity variance, and find that for a range of Stokes number ${S{\kern-0.5pt}t}^+$, Settling number ${S{\kern-0.5pt}v}^+$ and Reynolds number $\textit{Re}_\tau$ (based on frictional scales),the slip variance is primarily controlled by local differences between the ‘seen’ variance and the particle velocity variance, while terms appearing due to the inhomogeneity of the turbulence are subleading until ${S{\kern-0.5pt}v}^+$ becomes large. We also consider several comparative metrics to assess the relative magnitudes of the fluctuating slip velocity and the mean slip velocity, and we find that the vertical mean slip increases rapidly with ${S{\kern-0.5pt}v}^+$, rendering the variance relatively small – an effect found to be most substantial for ${S{\kern-0.5pt}v}^+\gt 1$. Finally, we compare the results with a model of the acceleration variance (Berk & Coletti 2021 J. Fluid Mech. 917, A47) based the concept of a response function described in Csanady (1963 J. Atmos. Sci. 20, 201–208), highlighting the role of the crossing trajectories mechanism. We find that while there is good agreement for low ${S{\kern-0.5pt}v}^+$, systematic errors remain, possibly due to implicit non-local effects arising from rapid particle settling and inhomogeneous turbulence. We conclude with a discussion of the implications of this work for modelling the transport of coarse dust grains in the atmospheric surface layer.

This study investigated the cylindrically divergent Rayleigh–Taylor instability (RTI) on a liquid–gas interface and its dependence on initial conditions. A novel hydrophobic technique was developed to generate a two-dimensional water–air interface with controlled initial conditions. The experimental configuration utilised high-pressure air injection to produce uniform circumferential acceleration. Amplitude measurements over time revealed that the cylindrical RTI growth depends strongly on the azimuthal wavenumber. Experimental results demonstrated that surface tension significantly suppresses the liquid–gas cylindrical RTI, even inducing a freeze-out and oscillatory perturbation growth – a phenomenon observed for the first time. Spectrum analysis of the interface contours demonstrated that the cylindrical RTI evolves in a weakly nonlinear regime. Linear and weakly nonlinear models were derived to accurately predict the time-varying interface amplitudes and high-order modes. The linear model was further used to determine conditions for unstable, freeze-out and oscillatory solutions of the cylindrically divergent RTI. These findings offer valuable insights into manipulating hydrodynamic instabilities in contracting/expanding geometries using surface tension.