The early stage of a gravity-driven flow resulting from the sudden removal of a floating body is investigated. Initially, the fluid is at rest, with a rigid, symmetric wedge floating on its surface. The study focuses on the initial evolution of the wedge-shaped depression formed on the water’s free surface. The fluid has finite depth, and the resulting flow is assumed to be governed by potential theory. The initial flow is described by a linear boundary-value problem, which is solved using conformal mapping and the theory of complex analytic functions. The behaviour of the flow velocity near the corner points of the fluid domain is analysed in detail. It is shown that the linear theory predicts a power-law singularity in the flow velocity at the vertex of the wedge-shaped depression, with the exponent depending on the wedge angle. As the cavity extends toward the bottom, the flow singularity at the vertex becomes stronger. The local flow near the vertex is shown to be self-similar at leading order in the short-time limit. At the other two corner points – where the initial free surface intersects the surface of the wedge – the linear theory predicts continuous velocities with singular velocity gradients. Theoretical predictions are compared with numerical results obtained using OpenFOAM. Good agreement is observed at short times, except in small vicinities of the corner points, where inner solutions are required. In practical applications, understanding the short-time behaviour of the depressions is important for predicting jet formation in regions of high surface curvature.

A model for galloping detonations is conceived as a sequence of very fast re-ignitions followed by long periods of evolution with quenched reactions. Numerical simulations of the one-dimensional Euler equations are conducted in this limit. While the mean speed and structure is found in reasonable agreement with Chapman–Jouguet theory, very strong pulsations of the lead shock appear, along with a train of rear-facing N-waves. These dynamics are analysed using characteristics. A closed-form solution for the lead shock dynamics is formulated, which is found in excellent agreement with numerics. The model relies on the presence of a single time scale of the process, the pulsation period, which controls the shock dynamics via the shock change equations and establishes a shock decay with a single time constant. These long periods of shock decay with known dynamics are punctuated by energy release events, with ‘kicks’ in the shocked speed controlled by the pressure increase and resulting lead shock amplification. Model predictions are found in excellent agreement with previous numerical results of pulsating detonations far from the stability limit.

This numerical investigation focuses on the mechanisms, flow topology and onset of Kelvin–Helmholtz instabilities (KHIs), that drive the leading-edge shear-layer destabilisation in the wake of wall-mounted long prisms. Large-eddy simulations are performed at ${\textit{Re}} = 2.5\times 10^3, 5\times 10^3$ and $1\times 10^4$ for prisms with a range of aspect ratio (AR, height-to-width) between $0.25$ and $1.5$, and depth ratios (DR, length-to-width) of $1{-}4$. Results show that shear-layer instabilities enhance flow irregularity and modulate spanwise vortex structures. The onset of KHI is strongly influenced by depth ratio, such that long prisms (${\textit{DR}}= 4$) experience earlier initiation compared with shorter ones (${\textit{DR}}= 1$). At higher Reynolds numbers, the onset of KHI shifts upstream towards the leading-edge, intensifying turbulence kinetic energy and increasing flow irregularity, especially for long prisms. The results further show that in this configuration, energy transfer from the secondary recirculation region contributes to the destabilisation of the leading-edge shear layer by reinforcing low-frequency modes. A feedback mechanism is identified wherein energetic flow structures propagate upstream through reverse boundary-layer flow, re-energising the leading-edge shear layer. Quantification using probability density functions reveals rare, intense upstream energy convection events, driven by this feedback mechanism. These facilitate the destabilisation process regardless of Reynolds number. This study provides a comprehensive understanding of the destabilisation mechanisms for leading-edge shear layers in the wake of wall-mounted long prisms.

Undulatory slender objects have been a central theme in the hydrodynamics of swimming at low Reynolds number, where the slender body is usually assumed to be inextensible, although some microorganisms and artificial microrobots largely deform with compression and extension. Here, we theoretically study the coupling between the bending and compression/extension shape modes, using a geometrical formulation of kinematic microswimmer hydrodynamics to deal with the non-commutative effects between translation and rotation. By means of a coarse-grained minimal model and systematic perturbation expansions for small bending and compression/extension, we analytically derive the swimming velocities and report three main findings. First, we revisit the role of anisotropy in the drag ratio of the resistive force theory, and generally demonstrate that no motion is possible for uniform compression with isotropic drag. We then find that the bending–compression/extension coupling generates lateral and rotational motion, which enhances the swimmer’s manoeuvrability, as well as changes in progressive velocity at a higher order of expansion, while the coupling effects depend on the phase difference between the two modes. Finally, we demonstrate the importance of often-overlooked Lie bracket contributions in computing net locomotion from a deformation gait. Our study sheds light on compression as a forgotten degree of freedom in swimmer locomotion, with important implications for microswimmer hydrodynamics, including understanding of biological locomotion mechanisms and design of microrobots.

We study the dynamics of salt fingers in the regime of slow salinity diffusion (small inverse Lewis number) and strong stratification (large density ratio), focusing on regimes relevant to Earth’s oceans. Using three-dimensional direct numerical simulations in periodic domains, we show that salt fingers exhibit rich, multiscale dynamics in this regime, with vertically elongated fingers that are twisted into helical shapes at large scales by mean flows and disrupted at small scales by isotropic eddies. We use a multiscale asymptotic analysis to motivate a reduced set of partial differential equations that filters internal gravity waves and removes inertia from all parts of the momentum equation except for the Reynolds stress that drives the helical mean flow. When simulated numerically, the reduced equations capture the same dynamics and fluxes as the full equations in the appropriate regime. The reduced equations enforce zero helicity in all fluctuations about the mean flow, implying that the symmetry-breaking helical flow is generated spontaneously by strictly non-helical fluctuations.

Cross-shelf transport in the inner continental shelf is governed by wind, wave and tidal interactions, but the role of Langmuir circulation (LC), induced by wave–current interaction and modulated by tides, has remained under-studied in this setting. We develop a Reynolds-averaged Navier–Stokes (RANS) model incorporating the Craik–Leibovich vortex force to resolve LC, coupled with a mass-conserving undertow and oscillating along-shelf tidal currents, and compare results against field data from the Martha’s Vineyard Coastal Observatory (MVCO). Under strong wave forcing (significant wave height $H_{\textit{sig}} = 2.12\,\mathrm{m}$ and significant wave period $T_w = 5.8\,\mathrm{s}$), LC persists throughout the tidal cycle, reducing vertical shear in the tidally averaged cross-shelf velocity profile compared with simulations excluding LC. During peak tidal velocity (reaching $25\,\mathrm{cm\,s^{-1}}$ with period of $ 12.42\,\mathrm{h}$), LC is temporarily suppressed but reforms rapidly as tidal energy declines, sustaining high vertical mixing. Conversely, under weak wave forcing ( $H_{\textit{sig}} = 0.837\,\mathrm{m}$, $T_w = 4.3\,\mathrm{s}$), tidal currents persistently suppress LC, resulting in a cross-shelf undertow profile with greater vertical shear compared with strong-wave conditions. Model–observation comparisons show that only simulations including both the Craik–Leibovich vortex force and tidal forcing reproduce the observed undertow structure at MVCO. These results demonstrate that accurate prediction of cross-shelf transport at tidal and subtidal time scales requires resolving both the generation and disruption of LC by tides.

A Lagrangian description of bubble swarms has largely eluded both experimental and numerical efforts. Now, in a tour de force of deep-learning-enabled optical tracking measurements, Huang et al. (2025 J. Fluid. Mech. 1014, R1) have managed to follow the three-dimensional trajectories of $10^5$ deforming and overlapping bubbles within a swarm, perhaps for long enough to witness their approach to the diffusive limit. Their results reveal that bubble swarms exhibit a dispersion law strikingly reminiscent of classical Taylor dispersion in isotropic turbulence, but with an earlier, undulatory transition from the ballistic-to-diffusive regime. Huang et al. (2025 J. Fluid Mech. 1014, R1), have helped close the loop on our understanding of Lagrangian bubble dispersion – from self-stirring swarms to bubbles in isotropic turbulence.

This work combines Navier–Stokes–Korteweg dynamics and rare event techniques to investigate the transition pathways and times of vapour bubble nucleation in metastable liquids under homogeneous and heterogeneous conditions. The nucleation pathways deviate from classical theory, showing that bubble volume alone is an inadequate reaction coordinate. The nucleation mechanism is driven by long-wavelength fluctuations with densities slightly different from the metastable liquid. We propose a new strategy to evaluate the typical nucleation times by inferring the diffusion coefficients from hydrodynamics. The methodology is validated against state-of-the-art nucleation theories in homogeneous conditions, revealing non-trivial, significant effects of surface wettability on heterogeneous nucleation. Notably, homogeneous nucleation is detected at moderate hydrophilic wettabilities despite the presence of a wall, an effect not captured by classical theories but consistent with atomistic simulations. Hydrophobic surfaces, instead, anticipate the spinodal. The proposed approach is fairly general and, despite the paper discussing results for a prototypical fluid, it can be easily extended, also in complex geometries, to any real fluid provided the equation of state is available, paving the way to model complex nucleation problems in real systems.

The paper uses three-dimensional large eddy simulation (LES) to investigate the structure and propagation of dam break waves of non-Newtonian fluids described by a power-law rheology. Simulations are also conducted for the limiting case of a dam-break wave of Newtonian fluid (water). Turbulent dam-break waves are found to have a two-layer structure and to generate velocity streaks beneath the region in which the flow is strongly turbulent and lobes at the front. The bottom part of the wave resembles a boundary layer and contains a log-law sublayer, while the streamwise velocity is close to constant inside the top layer. The value of the von Kármán constant is found to reach the standard value (i.e. $\kappa$ ≈ 0.4) associated with turbulent boundary layers of Newtonian fluids only inside the strongly turbulent region near the front of Newtonian dam-break waves. Much higher values of the slope of the log law are predicted for non-Newtonian dam-break waves (i.e. $\kappa$ ≈ 0.28) and in the regions of weak turbulence of Newtonian waves. LES shows that a power-law relationship can well describe the temporal evolution of the front position during the acceleration and deceleration phases, and that increasing the shear-thinning behaviour of the fluid increases the speed of the front. The numerical experiments are then used to investigate the predictive abilities of shallow water equation (SWE) models. The paper also proposes a novel one-dimensional (1-D) SWE model which accounts for the bottom friction by employing a friction coefficient regression valid for power-law fluids in the turbulent regime. An analytical approximate solution is provided by splitting the current into an outer region, where the flow is considered inviscid and friction is neglected, and an inner turbulent flow region, close to the wave front. The SWE numerical and analytical solutions using a turbulent friction factor are found to be in better agreement with LES compared with the agreement shown by an SWE numerical model using a laminar friction coefficient. The paper shows that inclusion of turbulence effects in SWE models used to predict high-Reynolds-number Newtonian and non-Newtonian dam break flows results is more accurate predictions.

In typical nature and engineering scenarios, such as supernova explosion and inertial confinement fusion, mixing flows induced by hydrodynamic interfacial instabilities are essentially compressible. Despite their significance, accurate predictive tools for these compressible flows remain scarce. For engineering applications, the Reynolds-averaged Navier–Stokes (RANS) simulation stands out as the most practical approach due to its outstanding computational efficiency. However, existing RANS studies focus primarily on cases where the compressible effect plays an insignificant role in mixing development, with quite limited attention given to scenarios with significant compressibility influence. Moreover, most of the existing RANS mixing models demonstrate significantly inaccurate predictions for the latter. This study develops a novel compressible RANS mixing model by incorporating physical compressibility corrections into the $K$–$L$–$\gamma$ mixing transition model recently proposed by Xie et al. (J. Fluid Mech. 1002, 2025, A31). Specifically, taking the density-stratified Rayleigh–Taylor mixing flows as representative compressible cases, we first analyse the limitations of the existing model for compressible flows, based on high-fidelity data and local instability criteria. Subsequently, the equation of state for a perfect gas is employed to derive comprehensive compressibility corrections. The crucial turbulent composition and heat fluxes are integrated into the closure of the key turbulent mass flux term of the turbulent kinetic energy equation. These corrections enable the model to accurately depict compressible mixing flows. Systematic validations confirm the efficacy of the proposed modelling scheme. This study offers a promising strategy for modelling compressible mixing flows, paving the way for more accurate predictions in complex scenarios.

We consider the efficiency of turbulence, a dimensionless parameter that characterises the fraction of the input energy stored in a turbulent flow field. We first show that the inverse of the efficiency provides an upper bound for the dimensionless energy injection in a turbulent flow. We analyse the efficiency of turbulence for different flows using numerical and experimental data. Our analysis suggests that efficiency is bounded from above, and, in some cases, saturates following a power law reminiscent of phase transitions and bifurcations. We show that for the von Kármán flow the efficiency saturation is insensitive to the details of the forcing impellers. In the case of Rayleigh–Bénard convection, we show that within the Grossmann and Lohse model, the efficiency saturates in the inviscid limit, while the dimensionless kinetic energy injection/dissipation goes to zero. In the case of pipe flow, we show that saturation of the efficiency cannot be excluded, but would be incompatible with the Prandtl law of the drag friction coefficient. Furthermore, if the power-law behaviour holds for the efficiency saturation, it can explain the kinetic energy and the energy dissipation defect laws proposed for shear flows. Efficiency saturation is an interesting empirical property of turbulence that may help in evaluating the ‘closeness’ of experimental and numerical data to the true turbulent regime, wherein the kinetic energy saturates to its inviscid limit.

The interface shape near a moving contact line is described by the Cox–Voinov theory, which contains a constant term that is not trivially obtained. In this work, an approximate expression of this term in explicit form is derived under the condition of a Navier slip. Introducing the approximation of a local slippery wedge flow, we first propose a novel form of the generalised lubrication equation. A matched asymptotic analysis of this equation yields the Cox–Voinov relation with the constant term expressed in elementary functions. For various viscosity ratios and contact angles, the theoretical predictions are rigorously validated against full numerical solutions of the Stokes equations and available asymptotic results.

The dynamics of self-propelled colloidal particles is strongly influenced by their environment through hydrodynamic and, in many cases, chemical interactions. We develop a theoretical framework to describe the motion of confined active particles by combining the Lorentz reciprocal theorem with a Galerkin discretisation of surface fields, yielding an equation of motion that efficiently captures self-propulsion without requiring an explicit solution for the bulk fluid flow. Applying this framework, we identify and characterise the long-time behaviours of a Janus particle near rigid, permeable and fluid–fluid interfaces, revealing distinct motility regimes, including surface-bound skating, stable hovering and chemo-hydrodynamic reflection. Our results demonstrate how the solute permeability and the viscosity contrast of the surface influence a particle’s dynamics, providing valuable insights into experimentally relevant guidance mechanisms for autophoretic particles. The computational efficiency of our method makes it particularly well suited for systematic parameter sweeps, offering a powerful tool for mapping the phase space of confined active particles and informing high-fidelity numerical simulations.

Interactions of turbulent boundary layers with a compliant surface are investigated experimentally at Reτ = 3300–8900. Integrating tomographic particle tracking with Mach–Zehnder interferometry enables simultaneous mapping of the compliant wall deformation and the three-dimensional velocity and pressure fields. Our initial study (J. Fluid. Mech. vol. 980, R2) shows that the flow–deformation correlations decrease with increasing Reτ, despite an order of magnitude increase in deformation amplitude. To elucidate the mechanisms involved, the same velocity, pressure and kinetic energy fields are decomposed to ‘wave-coherent’ and ‘stochastic’ parts using a Hilbert projection method. The phase dependent coherent variables, especially the pressure, are highly correlated with the wave, but decrease with increasing Reτ. While the coherent energy is 6 %–10 % of the stochastic level, the pressure root mean square is comparable near the wall. The energy flux between the coherent and stochastic parts and the pressure diffusion reverse sign at the critical layer. To explain the Reτ dependence, the characteristic deformation wavelength (three times the thickness) is compared with the scales of the energy-containing eddies in the boundary layer represented by the k−1 range in the energy spectrum. When the deformation wavelength is matched with the kxEuu peak at the present lowest Reτ, the flow–deformation correlations and coherent pressure become strong, even for submicron deformations. In this case, the flow and wall motion become phase locked, suggesting resonant behaviours. As Reτ increases, the wall wavelengths and spectral range of attached eddies are no longer matched, resulting in reduced correlations and lower coherent energy and pressure, despite larger deformation.