We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

Flow through sudden expansion finds its application in several engineering and biological processes. Though the stability of flow through steady sudden expansion has garnered much attention, little to none is given to the pulsatile flow through sudden expansion. Hence, in the present work we study the influence of inflow pulsatility on flow characteristics in a sudden expansion. The inflow velocity is a sinusoidal waveform that is modulated to encompass a wide range of amplitudes, ${{a}}$, and reduced velocities, ${{U_{r}}}$. We report four different modes, namely, synchronized growth of the recirculation region (at high ${{U_{r}}}$), necking and diffusion of the recirculation region (at moderately high ${{U_{r}}}$), splitting and convection of the recirculation region (at moderate ${{U_{r}}}$) and inverse growth of the recirculation region (at low ${{U_{r}}}$). In each mode, the symmetry-breaking critical Reynolds number is obtained through numerical experiments and compared with those of Floquet stability analysis. We found that diffusion and the convection mode of the recirculation region increases the stability of the flow while the inverse growth mode of the recirculation region decreases the same. The effect of the expansion ratio, ${{ER}}$, is also explored, and we found that as ${{ER}}$ increases, the absolute stability of flow decreases, but relative stability between the modes remains similar. Finally, we explain the dynamics of the modes by using terms involving the vorticity transport equation.

Two common definitions of the spatially local rate of kinetic energy cascade at some scale $\ell$ in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ $R>0$, $Q>0$ quadrant, where $R$ and $Q$ are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when $R$ is large.

The rupture of the thin film at the top of a bubble at a liquid–gas interface leads to an axisymmetric collapse of the bubble cavity. We present scaling laws for such a cavity collapse, established from experiments conducted with bubbles spanning a wide range of Bond (${10^{-3}< Bo\leq 1}$) and Ohnesorge numbers (${10^{-3}< Oh<10^{-1}}$), defined with the bubble radius $R$. The cavity collapse is a capillary-driven process, with a dependency on viscosity and gravity, affecting respectively, precursory capillary waves on the cavity boundary and the static bubble shape. The collapse is characterised by the normal interface velocity ($U_n$) and by the tangential wave propagation velocity of the kink ($U_t$), defined by the intersection of the concave cavity boundary formed after the rupture of the thin film with the convex boundary of the bubble cavity. During the collapse, $U_t$ remains constant and is shown to be $U_t=4.5U_c{\mathcal {W}}_R$, where $U_c$ is the capillary velocity and ${\mathcal {W}}_R(Oh,Bo)={(1-\sqrt {Oh {\mathscr {L}}} )^{-1/2}}$ is the wave resistance factor due to the precursory capillary waves, with $\mathscr {L}(Bo)$ being the path correction of the kink motion. The movement of the kink in the normal direction is part of the inward shrinkage of the whole cavity due to the sudden reduction of gas pressure inside the bubble cavity after the thin film rupture. This normal velocity is shown to scale as $U_c$ in the equatorial plane, while at the bottom of the cavity $\bar {U}_{nb}=U_c(Z_c/R)({\mathcal {W}_R}/ {\mathscr {L}})$, where $Z_c(Bo)$ is the static cavity depth. The filling rate of the cavity, which remains a constant throughout the collapse, is shown to be entirely determined by the shrinking velocity and scales as ${Q_T\simeq 2{\rm \pi} R Z_c U_c}$. From $Q_T$ we recover the jet velocity scaling, thereby relating the cavity collapse with the jet velocity scaling.

This study gives insights into the interfacial instabilities of a ventilation cavity by injecting gas vertically into the horizontal liquid crossflow through both numerical and experimental investigations. We identified four distinct regimes of the ventilation cavity based on their topological characteristics: (I) discrete bubble, (II) continuous cavity, (III) bifurcated cavity, and (IV) bubble plume. The boundaries for these regimes are delineated within the parameter space of crossflow velocity and jet speed. A comprehensive analysis of the flow characteristics associated with each regime is presented, encompassing the phase mixing properties, the dominant frequency of pulsation, and the time-averaged profile of the cavity. This study conducted a detailed investigation of the periodic pulsation at the leading-edge interface of the cavity, also known as the ‘puffing phenomenon’. The results of local spectral analysis and dynamic mode decomposition indicate that the high-frequency instability in the near-field region exhibits the most significant growth rate. In contrast, the low-frequency mode with the largest amplitude spans a broader region from the orifice to the cavity branches. A conceptual model has been proposed to elucidate the mechanism behind the pulsation phenomenon observed along the cavity interface: the pulsation results from the alternate intrusion of the crossflow and the cavity recovery at the leading edge, being governed mainly by the periodic oscillating imbalance between the static pressure of gas near the orifice and the stagnation pressure of crossflow at the leading edge.

Field observations of debris flows often show that a deep dry granular front is followed by a progressively thinner and increasingly watery tail. These features have been captured in recent laboratory flume experiments (Taylor-Noonan et al., J. Geophys. Res.: Earth Surf., vol. 127, 2022, e2022JF006622). In these experiments different initial release volumes were used to investigate the dynamics of an undersaturated monodisperse grain–water mixture as it flowed downslope onto a horizontal run-out pad. Corresponding dry granular flows, with the same particle release volumes, were also studied to show the effect of the interstitial fluid. The inclusion of water makes debris flows much more mobile than equivalent volumes of dry grains. In the wet flows, the formation of a dry front is crucially dependent on the heterogeneous vertical structure of the flow and the velocity shear. These effects are included in the depth-averaged theory of Meng et al. (J. Fluid Mech., vol. 943, 2022, A19), which is used in this paper to quantitatively simulate both the wet and dry experimental flows using a high-resolution shock-capturing scheme. The results show that velocity shear causes dry grains (located near the free surface) to migrate forwards to create a dry front. The front is more resistant to motion than the more watery material behind, which reduces the overall computed run-out distance compared with debris-flow models that assume plug flow and develop only small dry snouts. Velocity shear also implies that there is a net transport of water to the back of the flow. This creates a thin oversaturated tail that is unstable to roll waves in agreement with experimental observations.

Adding moving boundaries to convective fluids is known to result in non-trivial and surprising dynamics, leading to spectacular geoformations ranging from kilometre-scale karst terrains to planetary-scale plate tectonics. On the one hand, the moving solid alters the surrounding flow field, but on the other hand, the flow modifies the motion and shape of the solid. This leads to a two-way coupling that is significant in the study of fluid–structure interactions and in the understanding of geomorphologies. In this work, we investigate the coupling between a floating plate and the convective fluid below it. Through numerical experiments, we show that the motion of this plate is driven by the flow beneath. However, the flow structure is also modified by the presence of the plate, leading to the ‘thermal blanket’ effect where the trapped heat beneath the plate results in buoyant and upwelling flows that in turn push the plate away. By analysing this two-way coupling between moving boundary and fluid, we are able to capture the dynamical behaviours of this plate through a low-dimensional stochastic model. Geophysically, the thermal blanket effect is believed to drive the continental drift, therefore understanding this mechanism has significance beyond fluid dynamics.

Supergranule aggregation, i.e. the gradual aggregation of convection cells to horizontally extended networks of flow structures, is a unique feature of constant heat flux-driven turbulent convection. In the present study, we address the question if this mechanism of self-organisation of the flow is present for any fluid. Therefore, we analyse three-dimensional Rayleigh–Bénard convection at a fixed Rayleigh number ${Ra} \approx 2.0 \times 10^{5}$ across $4$ orders of Prandtl numbers ${Pr} \in [10^{-2}, 10^{2}]$ by means of direct numerical simulations in horizontally extended periodic domains with aspect ratio $\varGamma = 60$. Our study confirms the omnipresence of the mechanism of supergranule aggregation for the entire range of investigated fluids. Moreover, we analyse the effect of ${Pr}$ on the global heat and momentum transport, and clarify the role of a potential stable stratification in the bulk of the fluid layer. The ubiquity of the investigated mechanism of flow self-organisation underlines its relevance for pattern formation in geophysical and astrophysical convection flows, the latter of which are often driven by prescribed heat fluxes.

The dipole–multipole transition in rapidly rotating dynamos is investigated through the analysis of forced magnetohydrodynamic waves in an unstably stratified fluid. The focus of this study is on the inertia-free limit applicable to planetary cores, where the Rossby number is small not only on the core depth but also on the length scale of columnar convection. By progressively increasing the buoyant forcing in a linear magnetoconvection model, the slow magnetic–Archimedean–Coriolis (MAC) waves are significantly attenuated so that their kinetic helicity decreases to zero; the fast MAC wave helicity, on the other hand, is practically unaffected. In turn, polarity reversals in low-inertia spherical dynamos are shown to occur when the slow MAC waves disappear under strong forcing. Two dynamically similar regimes are identified – the suppression of slow waves in a strongly forced dynamo and the excitation of slow waves in a moderately forced dynamo starting from a small seed field. While the former regime results in polarity reversals, the latter regime produces the axial dipole from a chaotic multipolar state. For either polarity transition, a local Rayleigh number based on the mean wavenumber of the energy-containing scales bears the same linear relationship with the square of the peak magnetic field measured at the transition. The self-similarity of the dipole–multipole transition can place a constraint on the Rayleigh number for polarity reversals in the Earth.

The electrohydrodynamic processes taking place in a cone jet cause ohmic and viscous dissipation, and ultimately self-heating of the liquid. Despite this, previous analyses have modelled cone jets as isothermal systems. To investigate the validity of this assumption, this work applies the leaky-dielectric model to cone jets, while also requiring conservation of energy to reproduce the variation of temperature caused by dissipation and temperature-dependent liquid properties. The main goals are to determine whether there exist electrospraying conditions for which the isothermal assumption is inaccurate, and quantify the temperature field under such conditions. The work confirms that self-heating and thermal effects are important in liquids with sufficiently high conductivities, which is a significant limit because these electrical conductivities are needed to produce jets and droplets with radii of tens of nanometres or smaller. The numerical solution provides accurate expressions for evaluating the dissipation and the temperature increase in cone jets, and confirms that thermal effects cause the apparent breakdown of the traditional scaling law for the current of cone jets of highly conducting liquids.

The axisymmetric problem of a conical shell impact onto an inviscid and incompressible liquid of infinite depth is studied. The shell is thin, and its deadrise angle is small. The problem is inertia dominated. Gravity, surface tension and viscous effects are not taken into account. The hydrodynamic loads acting on the shell and the shell displacements are determined at the same time. The model by Scolan (J. Sound Vib., vol. 277, issue 1–2, 2004, pp. 163–203) is used to find the flow and hydrodynamic pressure caused by the shell impact. This model is based on the Wagner theory of water impact, which was generalised to axisymmetric problems of hydroelastic slamming. Dry and wet modes of the conical shell, as well as the corresponding frequencies, are calculated. It is shown that a conical shell can be approximated by a circular plate only for a very small deadrise angle. Deflections and strains in the conical shell during the impact stage, when the wetted part of the shell increases at high rate, as well as the hydrodynamic loads, are determined and analysed.

Three different porous substrates (with different pore sizes, $s$, and permeabilities, $K$) are used to examine their effect on the structure of boundary layer flow over them. The flow is characterised with single-point hot-wire measurements as well as planar particle image velocimetry. In order to elucidate differences in shallow and deep flows past porous substrates, foams with two different thicknesses ($h$) are used (for all three substrates). A wide range of friction Reynolds numbers ($2000< Re_\tau <13\,500$) and permeability-based Reynolds numbers ($1< Re_K< 50$) are attained. For substrates with $Re_K \sim 1$, the flow behaviour remains similar to flow over impermeable smooth walls and as such Townsend's hypothesis remains valid. Very large-scale motions are observed over permeable foams even when the $Re_K > 1$. In contrast, a substantial reduction in velocity disturbances and associated length scales is achieved for permeable foams with intermediate values of pore density and relative foam thickness ($h/s$), which affects outer-layer similarity. As permeability is increased by increasing pore size, the foam becomes sparse relative to viscous scales at high Reynolds numbers. For such foams, the flow conforms to outer-layer similarity and is more akin to flow over rough surfaces. Permeability attenuates the wavelengths associated with the outer-layer peak.

In magnetoconvection, the flow of an electromagnetically conductive fluid is driven by a combination of buoyancy forces, which create the fluid motion due to thermal expansion and contraction, and Lorentz forces, which distort the convective flow structure in the presence of a magnetic field. The differences in the global flow structures in the buoyancy-dominated and Lorentz-force-dominated regimes lead to different heat transport properties in these regimes, reflected in distinct dimensionless scaling relations of the global heat flux (Nusselt number $Nu$) versus the strength of buoyancy (Rayleigh number $Ra$) and electromagnetic forces (Hartmann number $Ha$). Here, we propose a theoretical model for the transition between these two regimes for the case of a static vertical magnetic field applied across a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. The model suggests that the scaling exponents $\gamma$ in the buoyancy-dominated regime, $Nu\sim Ra ^\gamma$, and $\xi$ in the Lorentz-force-dominated regime, $Nu\sim (Ha^{-2}Ra)^\xi$, are related as $\xi =\gamma /(1-2\gamma )$, and the onset of the transition scales with $Ha^{-1/\gamma }Ra$. These theoretical results are supported by our direct numerical simulations for $10\leq Ha\leq 2000$, Prandtl number $Pr=0.025$ and $Ra$ up to $10^9$ and data from the literature.

We report numerical simulations confirming the predictions in Gordillo & Riboux (J. Fluid Mech., vol. 941, 2022, A10), where we elucidated the lubrication mechanism by which a drop of a low-viscosity liquid impacting over a smooth solid substrate skates over a thin gas film that prevents contact with the wall. Moreover, with the purpose of explaining the so-called lift-off mechanism reported in Kolinski et al. (Phys. Rev. Lett., vol. 112, issue 13, 2014, 134501), we extend our previous findings and derive expressions for the time-varying thickness of the gas layer at the region where the distance to the wall is minimum, finding good agreement with the numerical results. In addition, we report that our predictions for the minimum thickness of the gas film separating a falling drop from a wall at room temperature follow closely the experimental values when gas kinetic effects are retained in the analysis, and also report that the analogous equation for the minimum thickness of the vapour layer formed after a drop impacts a superheated wall predicts well the experimental measurements.

We show that a heating pattern applied to a surface with a corrugation pattern generates a propulsive effect. The same heating pattern applied to a smooth surface creates propulsion through nonlinear thermal streaming associated with pitchfork bifurcation. The combination of groove and heating patterns generates thermal drift, representing a forced response whose magnitude changes with the relative position of both patterns. Thermal drift is always present, while thermal streaming requires sufficiently intense heating. When both effects are active, a change in the relative position of these patterns produces rapid changes in the magnitude of propulsion, resulting in the formation of limit points. The strength of propulsion increases with a decrease in the Prandtl number and with an addition of uniform heating.

The preference for particles to accumulate at specific regions in the near-wall part is a widely observed phenomenon in wall-bounded turbulence. Unlike small particles more frequently found in low-speed streaks, finite-size particles can accumulate in either low-speed or high-speed streaks. However, mechanisms and influencing factors leading to the different preferential concentration locations still need to be clarified. The present study conducts particle-resolved direct numerical simulations of particle-laden turbulent channel flows to provide a better understanding of this seemingly puzzling behaviour of preferential accumulation. These simulations cover different particle-to-fluid density ratios, particle volume fractions, particle sizes and degrees of sedimentation intensity. We find that the large particle size is the crucial factor that results in particles accumulating in high-speed streaks. Large particles not only are difficult to be conveyed by the quasi-streamwise vortices to low-speed streaks but also can escape from the near-wall region before moving spanwisely out from high-speed streaks. The sedimentation effect allows particles to gather closer to the channel wall and stay longer in the near-wall regions, reinforcing the sweeping mechanism of quasi-streamwise vortices that transport particles from high- to low-speed streaks. As a result, sedimenting particles tend to accumulate in the low-speed streaks.