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.

Neural network models have been employed to predict the instantaneous flow close to the wall in a viscoelastic turbulent channel flow. Numerical simulation data at the wall are used to predict the instantaneous velocity fluctuations and polymeric-stress fluctuations at three different wall-normal positions in the buffer region. Such an ability of non-intrusive predictions has not been previously investigated in non-Newtonian turbulence. Our comparative analysis with reference simulation data shows that velocity fluctuations are predicted reasonably well from wall measurements in viscoelastic turbulence. The network models exhibit relatively improved accuracy in predicting quantities of interest during the hibernation intervals, facilitating a deeper understanding of the underlying physics during low-drag events. This method could be used in flow control or when only wall information is available from experiments (for example, in opaque fluids). More importantly, only velocity and pressure information can be measured experimentally, while polymeric elongation and orientation cannot be directly measured despite their importance for turbulent dynamics. We therefore study the possibility to reconstruct the polymeric-stress fields from velocity or pressure measurements in viscoelastic turbulent flows. The neural network models demonstrate a reasonably good accuracy in predicting polymeric shear stress and the trace of the polymeric stress at a given wall-normal location. The results are promising, but also underline that a lack of small scales in the input velocity fields can alter the rate of energy transfer from flow to polymers, affecting the prediction of the polymeric-stress fluctuations.

Understanding the vertical coherence of the pressure structure and its interaction with velocity fields is critical for elucidating the mechanisms of acoustic generation and radiation in hypersonic turbulent boundary layers. This study employs linear coherence analysis to examine the self-similar coherent structures in the velocity and pressure fields within a Mach 6 hypersonic boundary layer, considering a range of wall-to-recovery temperature ratios. The influence of wall cooling on the geometric characteristics of these structures, such as inclination angles and three-dimensional aspect ratios, is evaluated. Specifically, the streamwise velocity exhibits self-similar coherent structures with the streamwise/wall-normal aspect ratio ranging from 16.5 to 38.7, showing a linear increases with decreasing wall temperatures. Similar linear dependence between the streamwise/wall-normal aspect ratio and the wall temperatures are observed for the Helmholtz-decomposed streamwise velocity and the pressure field. In terms of velocity–pressure coupling, the solenoidal component exhibits stronger interactions with the pressure fields in the near-wall region, while the dilatational component has stronger interactions with the pressure field at large scales with the increase of height. Such coupling generally follows the distance-from-the-wall scaling of the pressure field, except in cooled wall cases. Using the linear stochastic estimation, the pressure field across the boundary layer is predicted by inputting the near-wall pressure/velocity signal along with the transfer kernel. The result demonstrates that near-wall pressure signals provide the most accurate description of the pressure field in higher regions of the boundary layer. As wall-mounted sensors can measure near-wall pressure fluctuations, this study presents a potential approach to predict the off-wall pressure field correlated with the near-wall structures based on wall-pressure measurements.

We present direct numerical simulations of a supersonic, zero-pressure-gradient, adiabatic turbulent boundary layer at a free-stream Mach number of $M_\infty =2$, over cubical roughness elements. The simulations are complemented by a subsonic rough-wall boundary layer over the same geometry, alongside reference smooth-wall data, allowing us to elucidate compressibility effects. The simulations feature turbulent flow transitioning from a smooth to a rough surface with an extended computational domain to facilitate recovery. At the smooth-to-rough transition, we compare the development of an internal boundary layer between the subsonic and supersonic cases, introducing a novel definition of its height that is less sensitive to local compressibility effects. We demonstrate that, although the internal boundary-layer growth is similar to the subsonic case, a delayed equilibrium is expected for the supersonic case due to the sudden growth of the external boundary-layer thickness at the onset of roughness. Turbulence statistics are then evaluated far from the surface transition, where various compressibility transformations reveal outer-layer similarity for the mean velocity. We find that the classical van Driest II transformation can also be applied to rough walls, at least in the adiabatic case. Analysis of thermal statistics for the supersonic case confirms the significant influence that roughness has on both mean and fluctuating temperature fields, which, unlike velocity fields, do not display outer-layer similarity. Nonetheless, we find that the temperature–velocity relation established for smooth walls is also valid over rough surfaces, implying that the mean temperature field can be predicted solely based on the mean velocity.

The acoustic receptivity of Tollmien–Schlichting (TS) waves due to two-dimensional sharp-edged rectangular bumps and gaps in a compressible boundary layer was investigated by direct numerical simulations. The conclusions were based on a new procedure proposed for obtaining the receptivity amplitudes which appeared to be more robust and accurate than previous ones. The procedure is particularly important for the correct evaluation of the receptivity of gaps. The receptivity amplitudes for gaps were smaller than those for bumps, except for the nominally zero height/depth roughness element, where, consistent with a linear behaviour, they had the same absolute value. The procedure also revealed in detail the behaviour in the region downstream of the roughness element where the TS wave is formed (the formation region). This region extends for approximately $50\delta ^*_{b}$, regardless of bump height or gap depth. For bumps, the receptivity scaled superlinearly with bump height while for the gaps it scaled sublinear with depth. This behaviour is associated with the different velocity profiles caused by bumps and gaps in the formation region. We also discussed issues regarding comparison with experiments. Investigation of the effect of compressibility confirmed that, in the subsonic regime, the receptivity reduces with Mach number. Finally, we addressed the receptivity scaling with the acoustic wave amplitude. It was found that the receptivity scales linearly with the acoustic wave amplitude in a range for which experiments available in the literature indicated a superlinearly scaling. Reasons for these conflicting results are discussed.

It is known that the complex eigenfrequencies of one-dimensional systems of large but finite extent are concentrated near the asymptotic curve determined by the dispersion relation of an infinite system. The global instability caused by uppermost pieces of this curve was studied in various problems, including hydrodynamic stability and fluid–structure interaction problems. In this study, we generalise the equation for the asymptotic curve to arbitrary frequencies. We analyse stable local topology of the curve and prove that it can be a regular point, branching point or dead-end point of the curve. We give a classification of unstable local tolopogies, and show how they break up due to small changes of the problem parameters. The results are demonstrated on three examples: supersonic panel flutter, flutter of soft fluid-conveying pipe, and the instability of rotating flow in a pipe. We show how the elongation of the system yields the attraction of the eigenfrequencies to the asymptotic curve, and how each locally stable curve topology is reflected on the interaction of eigenfrequencies.

The motion and deformation of a neutrally buoyant drop in a rectangular channel experiencing a pressure-driven flow at a low Reynolds number has been investigated both experimentally and numerically. A moving-frame boundary-integral algorithm was used to simulate the drop dynamics, with a focus on steady-state drop velocity and deformation. Results are presented for drops of varying undeformed diameters relative to channel height ($D/H$), drop-to-bulk viscosity ratio ($\lambda$), capillary number ($Ca$, ratio of deforming viscous forces to shape-preserving interfacial tension) and initial position in the channel in a parameter space larger than considered previously. The general trend shows that the drop steady-state velocity decreases with increasing drop diameter and viscosity ratio but increases with increasing $Ca$. An opposite trend is seen for drops with small viscosity ratio, however, where the steady-state velocity increases with increasing $D/H$ and can exceed the maximum background flow velocity. Experimental results verify theoretical predictions. A deformable drop with a size comparable to the channel height when placed off centre migrates towards the centreline and attains a steady state there. In general, a drop with a low viscosity ratio and high capillary number experiences faster cross-stream migration. With increasing aspect ratio, there is a competition between the effect of reduced wall interactions and lower maximum channel centreline velocity at fixed average velocity, with the former helping drops attain higher steady-state velocities at low aspect ratios, but the latter takes over at aspect ratios above approximately 1.5.

Experimental and numerical observations in turbulent shear flows point to the persistence of the anisotropy imprinted by the large-scale velocity gradient down to the smallest scales of turbulence. This is reminiscent of the strong anisotropy induced by a mean passive scalar gradient, which manifests itself by the ‘ramp–cliff’ structures. In the shear flow problem, the anisotropy can be characterised by the odd-order moments of $\partial _y u$, where $u$ is the fluctuating streamwise velocity component, and $y$ is the direction of mean shear. Here, we extend the approach proposed by Buaria et al. (Phys. Rev. Lett., 126, 034504, 2021) for the passive scalar fields, and postulate that fronts of width $\delta \sim \eta Re_\lambda ^{1/4}$, where $\eta$ is the Kolmogorov length scale, and $Re_\lambda$ is the Taylor-based Reynolds number, explain the observed small-scale anisotropy for shear flows. This model is supported by the collapse of the positive tails of the probability density functions (PDFs) of $(\partial _y u)/(u^{\prime }/\delta )$ in turbulent homogeneous shear flows (THSF) when the PDFs are normalised by $\delta /L$, where $u^{\prime }$ is the root-mean-square of $u$ and $L$ is the integral length scale. The predictions of this model for the odd-order moments of $\partial _y u$ in THSF agree well with direct numerical simulation (DNS) and experimental results. Moreover, the extension of our analysis to the log-layer of turbulent channel flows (TCF) leads to the prediction that the odd-order moments of order $p (p \gt 1)$ of $\partial _y u$ have power-law dependencies on the wall distance $y^{+}$: $\langle (\partial _y u)^p \rangle /\langle (\partial _y u)^2 \rangle ^{p/2} \sim (y^{+})^{(p-5)/8}$, which is consistent with DNS results.

We define ‘surface layer’ (SL) as an inertia-dominated turbulence region outside a viscous or roughness surface-adjacent sub-layer (SAS) that is characterised by linear scaling of specific coherence length scales on wall-normal distance, $z$. We generalise the mechanisms that underlie the formation of the classical inertial SL in the shear-dominated turbulent boundary layer (TBL) to wall-bounded turbulent flows with zero mean shear. Using particle image velocimetry data from two wind tunnel facilities, we contrast the classical TBL SL with a non-classical shear-free SL generated within grid turbulence advected over an impermeable plate using two grids with different turbulence length scales. Integral-scale variations with $z$ and other statistics are quantified. In both shear-dominated and shear-free SLs we observe well-defined linear increases in $z$ of the streamwise integral scale of vertical velocity fluctuations. In grid turbulence the shear-free SL initiates just above the SAS that confines friction-generated motions. By contrast, the TBL SL forms with non-zero mean shear rate that extends streamwise coherence lengths of streamwise fluctuations. In both flow classes only the integral scales of vertical fluctuating velocity increase linearly with $z$, indicating that the SL is generated by the blockage of vertical fluctuations in the vertical. Whereas the SAS in the TBL is much thinner than in the grid-turbulence flows, the generation of a shear-free SL by the interaction of turbulence eddies and a surface depends on the relative thinness of the SAS. We conclude that the common generalisable SL mechanism is direct blockage of vertical fluctuations by the impermeable surface.

Significant progress has been made in understanding planetary core dynamics using numerical models of rotating convection (RC) in spherical shell geometry. However, the behaviour of forces in these models within various dynamic regimes of RC remains largely unknown. Directional anisotropy, scale dependence and the role of dynamically irrelevant gradient contributions in incompressible flows complicate the representation of dynamical balances in spherical shell RC. In this study, we systematically compare integrated and scale-dependent representations of mean and fluctuation forces and curled forces (which contain no gradient contributions) separately for the three components ($\hat {r},\hat {\theta },\hat {\phi }$). The analysis is performed with simulations in a range of convective supercriticality $Ra_T/Ra_T^{c}=1.2{-}297$ where $Ra_T$ and $Ra^{c}_T$ are the Rayleigh and critical Rayleigh numbers, respectively and Ekman number $E=10^{-3}{-}10^{-6}$, with fixed Prandtl number $Pr=1$, along with no-slip and fixed flux boundaries. We have excluded regions from each boundary of the spherical shell, with a thickness equivalent to ten velocity boundary layers, which provides a consistent representation of the bulk dynamics between the volume-averaged force and curled force balance in the parameter space studied. Radial, azimuthal and co-latitudinal components exhibit distinct force and curled force balances. The total magnitudes of the mean forces and mean curled forces exhibit a primary thermal wind balance; the corresponding fluctuating forces are in a quasi-geostrophic primary balance, while the fluctuating curled forces transition from a Viscous–Archimedean–Coriolis balance to an Inertia–Viscous–Archimedean–Coriolis balance with increasing $Ra_T/Ra_T^{c}$. The curled force balances are more weakly scale-dependent compared to the forces, and do not show clear cross-over length scales. The fluctuating force and curled force balances are broadly consistent with three regimes of RC (weakly nonlinear, rapidly rotating and weakly rotating), but do not exhibit sharp changes with $Ra_{T}/Ra_{T}^{c}$, which inhibits the identification of precise regime boundaries from these balances.