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.