Geophysical and astrophysical fluid flows are typically driven by buoyancy and strongly constrained at large scales by planetary rotation. Rapidly rotating Rayleigh–Bénard convection (RRRBC) provides a paradigm for experiments and direct numerical simulations (DNS) of such flows, but the accessible parameter space remains restricted to moderately fast rotation rates (Ekman numbers ${ {Ek}} \gtrsim 10^{-8}$), while realistic ${Ek}$ for geo- and astrophysical applications are orders of magnitude smaller. On the other hand, previously derived reduced equations of motion describing the leading-order behaviour in the limit of very rapid rotation ($ {Ek}\to 0$) cannot capture finite rotation effects, and the physically most relevant part of parameter space with small but finite ${Ek}$ has remained elusive. Here, we employ the rescaled rapidly rotating incompressible Navier–Stokes equations (RRRiNSE) – a reformulation of the Navier–Stokes–Boussinesq equations informed by the scalings valid for ${Ek}\to 0$, recently introduced by Julien et al. (2024) – to provide full DNS of RRRBC at unprecedented rotation strengths down to $ {Ek}=10^{-15}$ and below, revealing the disappearance of cyclone–anticyclone asymmetry at previously unattainable Ekman numbers (${Ek}\approx 10^{-9}$). We also identify an overshoot in the heat transport as ${Ek}$ is varied at fixed $\widetilde { {Ra}} \equiv {Ra}{Ek}^{4/3}$, where $Ra$ is the Rayleigh number, associated with dissipation due to ageostrophic motions in the boundary layers. The simulations validate theoretical predictions based on thermal boundary layer theory for RRRBC and show that the solutions of RRRiNSE agree with the reduced equations at very small ${Ek}$. These results represent a first foray into the vast, largely unexplored parameter space of very rapidly rotating convection rendered accessible by RRRiNSE.

Previous studies on the scaling of pressure fluctuations in wall-bounded turbulent flows have typically employed the same frameworks as those used for mean flow, with inner scaling based on frictional velocity and viscous length scales, and outer scaling relying on boundary layer thickness or displacement thickness. These traditional scales primarily reflect the characteristics of the mean streamwise velocity profile and momentum balance. In this work, we propose novel scaling frameworks for pressure fluctuations in turbulent channel and pipe flows, derived from the Poisson equation for pressure fluctuations. Applying the scaling patch approach, we analyse the rapid and slow terms in the Poisson equation, and introduce new scaling for pressure fluctuation variance in both the inner and outer regions. These new scales are designed to better capture the influence of Reynolds stresses by incorporating their peak values. Additionally, we establish a strong correlation between the root mean square (r.m.s.) of pressure fluctuations and the Reynolds shear stress, resulting in an empirical equation that accurately predicts their ratio. This equation provides a practical method for estimating the r.m.s. of pressure fluctuations in the flow, which remains challenging to measure in experimental investigations.

In this paper, we discuss the transport of sediment and the formation of bedforms in turbulent river flows, under flow conditions typical of flooding events. Through the implementation of an immersed boundary method, a wall model and a morphological model, we were able to simulate complex and mobile geometries under high Reynolds numbers at an affordable computational cost. In particular, we examined the evolution of bedforms on a loose sediment bed under turbulent flow conditions, using input parameters obtained from laboratory measurements. Over time, the bedforms become more three-dimensional and irregular in shape, leading to changes in the shear layer, crest angle and separation patterns. The bedforms continue to evolve until a quasi-steady equilibrium is reached. Our simulations highlight the crucial role played by the small-scale bedforms, which significantly affect the flow dynamics: an increase in the total drag is observed, related to the form drag generated by the local recirculation and the increased size of the large-scale recirculation bubble. Furthermore, a stronger turbulent activity ensues from the shear layers forming on the crests of the small-scale bedforms. Finally, a wider shedding angle of the shear layer is caused by the irregular crest line.

Motivated by microfluidic applications, we investigate drag reduction in laminar pressure-driven flows in channels with streamwise-periodic superhydrophobic surfaces (SHSs) contaminated with soluble surfactant. We develop a model in the long-wave and weak-diffusion limit, where the streamwise SHS period is large compared with the channel height and the Péclet number is large. Using asymptotic and numerical techniques, we determine the influence of surfactant on drag reduction in terms of the relative strength of advection, diffusion, Marangoni effects and bulk–surface exchange. In scenarios with strong exchange, the drag reduction exhibits a complex dependence on the thickness of the bulk-concentration boundary layer and surfactant strength. Strong Marangoni effects immobilise the interface through a linear surfactant distribution, whereas weak Marangoni effects yield a quasi-stagnant cap. The quasi-stagnant cap has an intricate structure with an upstream slip region, followed by intermediate inner regions and a quasi-stagnant region that is mediated by weak bulk diffusion. The quasi-stagnant region differs from the immobile region of a classical stagnant cap, observed for instance in surfactant-laden air bubbles in water, by displaying weak slip. As exchange weakens, the bulk and interface decouple: the surfactant distribution is linear when the surfactant is strong, whilst it forms a classical stagnant cap when the surfactant is weak. The asymptotic solutions offer closed-form predictions of drag reduction across much of the parameter space, providing practical utility and enhancing understanding of surfactant dynamics in flows over SHSs.

Carbon storage in saline aquifers is a prominent geological method for reducing CO2 emissions. However, salt precipitation within these aquifers can significantly impede CO2 injection efficiency. This study examines the mechanisms of salt precipitation during CO2 injection into fractured matrices using pore-scale numerical simulations informed by microfluidic experiments. The analysis of varying initial salt concentrations and injection rates revealed three distinct precipitation patterns, namely displacement, breakthrough and sealing, which were systematically mapped onto regime diagrams. These patterns arise from the interplay between dewetting and precipitation rates. An increase in reservoir porosity caused a shift in the precipitation pattern from sealing to displacement. By incorporating pore structure geometry parameters, the regime diagrams were adapted to account for varying reservoir porosities. In hydrophobic reservoirs, the precipitation pattern tended to favour displacement, as salt accumulation occurred more in larger pores than in pore throats, thereby reducing the risk of clogging. The numerical results demonstrated that increasing the gas injection rate or reducing the initial salt concentration significantly enhanced CO2 injection performance. Furthermore, identifying reservoirs with high hydrophobicity or large porosity is essential for optimising CO2 injection processes.

Periodic gravity-capillary waves on a fluid of finite depth with constant vorticity are studied theoretically and numerically. The classical Stokes expansion method is applied to obtain the wave profile and the interior flow up to the fourth order of approximation, which thereby extends the works of Barakat & Houston (1968) J. Geophys. Res. 73 (20), 6545–6554 and Hsu et al. (2016) Proc. R. Soc. Lond. A 472, 20160363. The classical perturbation scheme possesses singularities for certain wavenumbers, whose variations with depth are shown to be affected by the vorticity. This analysis also reveals that for any given value of the physical depth, there exists a threshold value of the vorticity above which there are no singularities in the theoretical solution. The validity of the third- and fourth-order solutions is examined by comparison with exact numerical results, which are obtained with a method based on conformal mapping and Fourier series expansions of the wave surface. The outcomes of this comparison are surprising as they report important differences in the internal flow structure, when compared with the third-order predictions, even though both approximations predict almost perfectly the phase velocity and the surface profiles. Usually, this occurs when the wavenumber is far enough from a critical value and the steepness is not too large. In these non-resonant cases, it is found that the fourth-order theory is more consistent with the exact numerical results. With negative vorticity the improvement is noticeable both beneath the crest and the trough, whereas with positive vorticity the fourth-order theory does a better job either beneath the crest or beneath the trough, depending of the type of the wave.

Two-dimensional simulations incorporating detailed chemistry are conducted for detonation initiation induced by dual hot spots in a hydrogen/oxygen/argon mixture. The objective is to examine the transient behaviour of detonation initiation as facilitated by dual hot spots, and to elucidate the underlying mechanisms. Effects of hot spot pressure and distance on the detonation initiation process are assessed; and five typical initiation modes are identified. It is found that increasing the hot spot pressure promotes detonation initiation, but the impact of the distance between dual hot spots on detonation initiation is non-monotonic. During the initiation process, the initial hot spot autoignites, and forms the cylindrical shock waves. Then, the triple-shock structure, which is caused by wave collisions and consists of the longitudinal detonation wave, transverse detonation wave and cylindrical shock wave, dominates the detonation initiation behaviour. A simplified theoretical model is proposed to predict the triple-point path, whose curvature quantitatively indicates the diffraction intensity of transient detonation waves. The longitudinal detonation wave significantly diffracts when the curvature of the triple-point path is large, resulting in the failed detonation initiation. Conversely, when the curvature is small, slight diffraction effects fail to prevent the transient detonation wave from developing. The propagation of the transverse detonation wave is affected not only by the diffraction effects but also by the mixture reactivity. When the curvature of the triple-point trajectory is large, a strong cylindrical shock wave is required to compress the mixture, enhancing its reactivity to ensure the transverse detonation wave can propagate without decoupling.

The Edgerton crown is an iconic manifestation of drop impact splashing, with its prominent cylindrical edge decorated with detaching droplets. Herein, we identify the formation of an intriguing double-crown, when a high-viscosity drop impacts on a shallow pool of a lower-viscosity immiscible liquid. High-speed imaging shows that after the initial fine horizontal ejecta sheet, the first inner crown emerges vertically from the film liquid. This is followed by the second crown which forms near the outer base of the first crown, as the tip of the horizontally spreading viscous drop approaches the outer free surface. Axisymmetric numerical simulations, using the volume-of-fluid method with adaptive grid refinement, show that the flow squeezed out between the viscous drop and the solid surface, generates two counter-rotating vortex rings, which travel radially outwards together and drive out the second crown through the free surface. The bottom vortex emerges from the separated boundary layer at the solid wall, while the top one detaches from the underside of the viscous drop. We map out the narrow parameter regime, where this ephemeral structure emerges, in terms of viscosity ratio, impact velocity and film thickness.

We investigate the drag reduction effects by two representative blowing/suction-based control methods having different drag reduction mechanisms, i.e. the opposition control and uniform blowing (UB), in a bump-installed turbulent channel flow through direct numerical simulations. We consider two different bulk Reynolds numbers ${\textit {Re}}_b = 5600$ and $12\,600$, and bump heights $h^+ \approx 20$ and $40$. In the opposition-controlled case, the friction drag reduction effect in the case with a bump is similar to that in the case without a bump, while the control effect on the pressure drag is hardly observed. The total drag reduction rate decreases for the higher bump height because the ratio of the pressure drag to the total drag increases as the bump height. In the UB case, UB at $0.1\,\%$ or $0.5\,\%$ of the bulk-mean velocity is imposed on the lower wall with a bump, while the same amount of uniform suction (US) is applied on the upper flat wall to keep the mass flow rate. Although the total friction drag increases due to a detrimental effect of US on the upper wall, the wall-normal motions due to the existence of a bump on the lower wall are suppressed by the UB, so that the pressure drag is decreased, unlike the opposition-controlled case. Due to the difference in the inherent drag reduction mechanisms, the flow separation in the region behind the bump is enhanced by the opposition control, while suppressed by UB.

The critical points of vorticity in a two-dimensional viscous flow are essential for identifying coherent structures in the vorticity field. Their bifurcations as time progresses can be associated with the creation, destruction or merging of vortices, and we analyse these processes using the equation of motion for these points. The equation decomposes the velocity of a critical point into advection with the fluid and a drift proportional to viscosity. Conditions for the drift to be small or vanish are derived, and the analysis is extended to cover bifurcations. We analyse the dynamics of vorticity extrema in numerical simulations of merging of two identical vortices at Reynolds numbers ranging from 5 to 1500 in the light of the theory. We show that different phases of the merging process can be identified on the basis of the balance between advection and drift of the critical points, and identify two types of merging, one for low and one for high values of the Reynolds number. In addition to local maxima of positive vorticity and minima of negative vorticity, which can be considered centres of vortices, minima of positive vorticity and maxima of negative vorticity can also exist. We find that such anti-vortices occur in the merging process at high Reynolds numbers, and discuss their dynamics.