This paper discusses the propagation of coastal currents generated by a river outflow using a 1 ${1}/{2}$-layer, quasigeostrophic model, following Johnson et al. (2017) (JSM17). The model incorporates two key physical processes: Kelvin-wave-generated flow and vortical advection along the coast. We extend JSM17 by deriving a fully nonlinear, long-wave, dispersive equation governing the evolution of the coastal current width. Numerical solutions show that, at large times, the flow behaviour divides naturally into three regimes: a steady outflow region, intermediate regions consisting of constant-width steady currents and unsteady propagating fronts leading the current. The widths of the steady currents depend strongly on dispersion when the constant outflow potential-vorticity anomaly is negative. Simulations using contour dynamics show that the dispersive equation captures the full quasigeostrophic behaviour more closely than JSM17 and give accurate bounds on the widths of the steady currents.

We study the evaporation dynamics of non-thin non-spherical-cap (i.e. wavy) droplets. These droplets exhibit surface curvature that varies periodically with the polar angle, which profoundly influences their evaporation flux, internal flow dynamics, and the resultant deposition patterns upon complete evaporation. The droplet is considered quasi-static throughout its entire lifetime. The asymptotic expansions of the evaporation flux in the diffusion-limited model, and the induced internal inviscid flow of the droplets, are derived through asymptotic analysis. Under the assumption of small deformation amplitudes, the accuracies of these two expansions are validated numerically. Expanding upon these asymptotic results, we also investigate the surface density profile of the droplet deposition after it dries up. The results indicate that the freely moving contact line of the droplet leads to the deposited stain exhibiting a mountain-like morphology. The internal inviscid flow along with the non-spherical-cap shape eliminates the divergence of the deposited surface density profile at droplet’s centre. This work provides a theoretical basis for geometrically controlled sessile droplet evaporation, which may have practical applications in industry.

Measurements in high-speed flows are difficult to acquire. To maximise their utility, it is important to quantify the preceding events that can influence a sensor signal. Flow perturbations that are invisible to a sensor may prevent the detection of key physics. Conversely, perturbations that originate away from a sensor may impact its signal at the measurement time. The collection of the latter perturbations defines the domain of dependence (DOD) of the sensor, which can be evaluated efficiently using adjoint-variational methods. For Mach 4.5 transitional flat-plate boundary layers, we consider the DOD of an instantaneous and localised wall-pressure observation, akin to that by a piezoelectric probe. At progressively earlier times prior to the measurement, the DOD retreats upstream from the probe, and the sensitivity to flow perturbations expands spatially and is amplified. The expansion corresponds to a wider region where initial disturbances can influence the measurement, and the amplification is because these perturbations grow during their forward evolution before reaching the probe. The sensitivity has a wavepacket structure concentrated near the boundary-layer edge, and a portion that radiates into the free stream. The DOD is further interpreted as the optimal initial perturbation with unit energy that maximises the norm of the measurement, establishing a link to transient-growth analysis. We test this formulation for a laminar condition and contrast the sensor dependence on different components of the state vector. When the boundary layer is transitional, we adopt the general formulation to assess the impact of sensor placement within the transition and turbulent zones on the DOD, and we characterise the flow disturbances that most effectively influence the measurement in each regime.

The attachment-line boundary layer is critical in hypersonic flows because of its significant impact on heat transfer and aerodynamic performance. In this study, high-fidelity numerical simulations are conducted to analyse the subcritical roughness-induced laminar–turbulent transition at the leading-edge attachment-line boundary layer of a blunt swept body under hypersonic conditions. This simulation represents a significant advancement by successfully reproducing the complete leading-edge contamination process induced by a surface roughness element in a realistic configuration, thereby providing previously unattainable insights. Two roughness elements of different heights are examined. For the lower-height roughness element, additional unsteady perturbations are required to trigger a transition in the wake, suggesting that the flow field around the roughness element acts as a perturbation amplifier for upstream perturbations. Conversely, a higher roughness element can independently induce the transition. A low-frequency absolute instability is detected behind the roughness, leading to the formation of streaks. The secondary instabilities of these streaks are identified as the direct cause of the final transition.

We perform direct numerical simulations of sub-Kolmogorov, inertial spheroids settling under gravity in homogeneous, isotropic turbulence, and find that small-scale clustering, measured via the correlation dimension, depends sensitively on the spheroid aspect ratio. In particular, such spheroids are shown to cluster more as their anisotropy increases. Further, the approach rate for pairs of spheroids is calculated and found to deviate significantly from the spherical-particle limit. Our study, spanning a range of Stokes numbers and aspect ratios, provides critical inputs for developing collision models to understand the dynamics of sedimenting, anisotropic particles in general, and ice crystals in clouds in particular.

Recent experimental studies reveal that the near-wake region of a circular cylinder at hypersonic Mach numbers exhibits self-sustained flow oscillations. The oscillation frequency was found to have a universal behaviour. These oscillations are of a fundamentally different nature in comparison with flow oscillations caused due to vortex shedding, which are commonly observed in cylinder wakes at low-subsonic Mach numbers. The experimental observations suggest an aeroacoustic feedback loop to be the driving mechanism of the oscillations at high Mach numbers. An analytical aeroacoustic model that successfully predicts the experimentally observed frequencies and explains the universal behaviour is presented here. The model provides physical insights into and informs us of flow regimes where deviations from universal behaviour are to be expected. These findings hold relevance for a wider class of non-canonical wake flows at high Mach numbers.

The on-body flow and near-to-intermediate wake of a 6:1 prolate spheroid at a pitch angle of $\alpha = 10^{\circ }$ and a length-based Reynolds number, ${Re}_L = U_\infty L / \nu = 3 \times 10^4$, are investigated using large eddy simulation (LES) across four stratification levels: ${\textit {Fr}} = U_{\infty }/ND = \infty , 6, 1.9$ and $1$. A streamwise vortex pair, characteristic of non-zero $\alpha$ in unstratified flow over both slender and blunt bodies, is observed. At ${\textit {Fr}} = \infty$ (unstratified) and $6$, the vortex pair has a lateral left–right asymmetry as has been reported in several previous studies of unstratified flow. However, at higher stratification levels of ${\textit {Fr}} = 1.9$ and $1$, this asymmetry disappears and there is a complex combination of body-shed vorticity that is affected by baroclinicity and vorticity associated with internal gravity waves. Even at the relatively weak stratification of ${\textit {Fr}} = 6$, the wake is strongly influenced by buoyancy from the outset: (a) the vertical drift of the wake is more constrained at ${\textit {Fr}} = 6$ than at ${\textit {Fr}} = \infty$ throughout the domain; and (b) the streamwise vortex pair loses coherence by $x/D = 10$ in the ${\textit {Fr}} = 6$ wake, unlike the ${\textit {Fr}} = \infty$ case. For the ${\textit {Fr}} = 1$ wake, flow separation characteristics differ significantly from those at ${\textit {Fr}} = \infty$ and $6$, resulting in a double-lobed wake topology that persists throughout the domain.

In marine and offshore engineering, the presence of air in the water plays a significant role in influencing impact pressures during water entry events. Owing to limited research on the impact loads of aerated water entry, this study aims to explore the effect of aeration on water entry impact pressures. A comprehensive experimental investigation on pure and aerated water entry of a wedge with a 20° deadrise angle was presented. The wire-mesh sensor (WMS) technology was proposed to accurately quantify the spatial and temporal distributions of void fractions in multiphase environments. The WMS provides reliable and consistent measurements at varying void fractions, as validated against image-based methods. The results indicated that the aeration reduced peak impact pressures by up to 33 %, and extended pressure duration, with a linear relationship between impact pressure and void fraction. Furthermore, the probability distribution of peak pressures conformed well to both the generalised extreme value and Weibull distributions, with the void fraction exerting a strong influence on pressure distribution parameters. These findings suggest that controlled aeration can effectively mitigate impact loads, offering practical implications for marine structure design.

We study the near-wall behaviour of pressure spectra and associated variances in canonical wall-bounded flows, with a special focus on pipe flow. Analysis of the pressure spectra reveals the universality of small and large scales, supporting the establishment of $ k^{-1}$ spectral layers as predicted by fundamental physical theories. However, this universality does not extend to the velocity spectra (Pirozzoli, J. Fluid Mech., vol. 989, 2024, A5), which show a lack of universality at the large-scale end and systematic deviations from the $ k^{-1}$ behaviour. We attribute this fundamental difference to the limited influence of direct viscous effects on pressure, with implied large differences in the near-wall behaviour. Consequently, the inner-scaled pressure variances continue to increase logarithmically with the friction Reynolds number as we also infer from a refined version of the attached-eddy model, while the growth of the velocity variance tends to saturate. Extrapolated distributions of the pressure variance at extremely high Reynolds numbers are inferred.

Recent studies focusing on the response of turbulent boundary layers (TBLs) to a step change in roughness have provided insight into the scaling and characterisation of TBLs and the development of the internal layer. Although various step-change combinations have been investigated, ranging from smooth-to-rough to rough-to-smooth, the minimum required roughness fetch length over which the TBL returns to its homogeneously rough behaviour remains unclear. Moreover, the relationship between a finite- and infinite-fetch roughness function (and the equivalent sand-grain roughness) is also unknown. In this study, we determine the minimum ‘equilibrium fetch length’ for a TBL developing over a smooth-to-rough step change as well as the expected error in local skin friction if the fetch length is under this minimum threshold. An experimental study is carried out where the flow is initially developed over a smooth wall, and then a step change is introduced using patches of P24 sandpaper. Twelve roughness fetch lengths are tested in this study, systematically increasing from $L = 1\delta _2$ up to $L = 39\delta _2$ (where L is the roughness fetch length and $\delta _2$ is the TBL thickness of the longest fetch case), measured over a range of Reynolds numbers ($4\times 10^3 \leqslant Re_\tau \leqslant 2\times 10^4$). Results show that the minimum fetch length needed to achieve full equilibrium recovery is around $20\delta _2$. Furthermore, we observe that the local friction coefficient, $C_{\! f}$, recovers to within 10 % of its recovered value for fetch lengths $\geqslant 10\delta _2$. This information allows us to incorporate the effects of roughness fetch length on the skin friction and roughness function.

The linear and nonlinear dynamics of centrifugal instability in Taylor–Couette flow are investigated when fluids are stably stratified and highly diffusive. One-dimensional local linear stability analysis (LSA) of cylindrical Couette flow confirms that the stabilising role of stratification in centrifugal instability is suppressed by strong thermal diffusion (i.e. low Prandtl number $Pr$). For $Pr\ll 1$, it is verified that the instability dependence on thermal diffusion and stratification with the non-dimensional Brunt–Väisälä frequency $N$ can be prescribed by a single rescaled parameter $P_{N}=N^{2}Pr$. From direct numerical simulation (DNS), various nonlinear features such as axisymmetric Taylor vortices at saturation, secondary instability leading to non-axisymmetric patterns or transition to chaotic states are investigated for various values of $Pr\leqslant 1$ and Reynolds number $Re_{i}$. Two-dimensional bi-global LSA of axisymmetric Taylor vortices, which appear as primary centrifugal instability saturates nonlinearly, is also performed to find the secondary critical Reynolds number $Re_{i,2}$ at which the Taylor vortices become unstable by non-axisymmetric perturbation. The bi-global LSA reveals that $Re_{i,2}$ increases (i.e. the onset of secondary instability is delayed) in the range $10^{-3}\lt Pr\lt 1$ at $N=1$ or as $N$ increases at $Pr=0.01$. Secondary instability leading to highly non-axisymmetric or irregular chaotic patterns is further investigated by three-dimensional DNS. The Nusselt number $Nu$ is also computed from the torque at the inner cylinder for various $Pr$ and $Re_{i}$ at $N=1$ to describe how the angular momentum transfer increases with $Re_{i}$ and how $Nu$ varies differently for saturated and chaotic states.