Shock interactions on a V-shaped blunt leading edge (VBLE) that are commonly encountered at the cowl lip of an inward-turning inlet are investigated at freestream Mach numbers ($ M_\infty$) 3–6. The swept blunt leading edges of the VBLE generate a pair of detached shocks with varying shapes due to the changes in $ M_\infty$ and $L/r$ (i.e. the ratio of the leading-edge length $L$ to the leading-edge blunt radius $r$), which causes intriguing shock interactions at the crotch of the VBLE. Three subtypes of regular reflection (RR) and a Mach reflection (MR) are produced successively with increasing $ M_\infty$ for a given $L/r$, which appear in the opposite order to those with increasing $L/r$ for a given $ M_\infty$. These shock interactions identified in numerical simulations are verified in supersonic and hypersonic wind tunnel experiments. It is demonstrated that the relative position of the shocks is crucial in determining the transitions of shock interactions by varying either $L/r$ or $ M_\infty$. Transition criteria between subtypes of RR and from RR to MR are theoretically established in the parameter space $(M_\infty,L/r)$ by analysing the shock structures, showing good agreement with the numerical and experimental results. Interactions between either immature or fully developed detached shocks are embedded in these criteria. Specifically, the transition criteria asymptotically approach the corresponding critical $ M_\infty$ when $L/r$ is sufficiently large. These transition criteria provide guidelines for improving the design of the cowl lip of an inward-turning inlet in supersonic and hypersonic regimes.

Experiments were performed that (i) document the effect of the steady spanwise buffer layer blowing on the mean characteristics of the turbulent boundary layer for a range of momentum thickness Reynolds numbers from 4760 to 10 386, and (ii) document the effect of the buffer layer blowing on the unsteady characteristics and coherent vorticity in a boundary layer designed to provide sufficiently high spatial resolution. The spanwise buffer layer blowing of the order of $u_{\tau }$ is produced by a surface array of pulsating direct current (pulsed-DC) plasma actuators. This was found to substantially reduce the wall shear stress that was directly measured with a floating element coupled with a force sensor. The direct wall shear measurements agreed with values derived using the Clauser method to within $\pm 0.85$ %. The degree to which the buffer layer blowing affected $\tau _w$ was found to primarily depend on the inner variable spanwise spacing between the pulsed-DC actuator electrodes, i.e. ‘blowing sites’. Utilizing pairs of $[u,v]$ and $[u,w]$ hot-wire sensors, the latter experiments correlated significant reductions in the $\omega _y$ and $\omega _x$ vorticity components that resulted from the buffer layer blowing and translated into lower Reynolds stresses and turbulence production. The time scale to which these observed changes in the boundary layer characteristics would return to the baseline condition was subsequently documented. This revealed a recovery length of $x^+ \approx 86\,000$ that translated to a streamwise fetch of $x \approx 66\delta$. Finally, a comparison with the recent work by Cheng et al. (2021, J. Fluid Mech. vol. 918, A24) and Wei & Zhou (2024 in TSFP13, June 25–28, 2024) that followed our experimental approach to achieve comparable wall shear stress (drag) reductions has led to a new scaling based on the baseline boundary layer $\textit{Re}_{\tau }$ and buffer layer blowing velocity.

The Taylor–Melcher leaky dielectric (LD) model is often used to study the physics of electrosprays operating in the cone-jet mode. Despite its success, there are electrospraying conditions in which the ion concentration fields must be retained, which requires an electrokinetic model. This article reproduces cone-jets with two electrokinetic formulations: the standard Poisson–Nernst–Planck (PNP) equations, and a modified electrokinetic (MEK) model that accounts for overscreening and overcrowding of electrolytes, which is important in fluids with high electrical conductivities such as ionic liquids (Kilic et al. 2007 Phys. Rev. E vol. 75, no. 2, 021502, 021503; Bazant et al. 2011 Phys. Rev. Lett. vol. 106, no. 4, 46102). In the case of liquids with low electrical conductivities, it is observed that the LD and PNP models agree under certain limiting conditions, but they are less restrictive than previously proposed (Baygents & Saville 1990 AIP Conf. Proc. vol. 197, 7–17; Schnitzer & Yariv 2015 Fluid Mech. vol. 773, 1–33); the effects of dissimilar ion diffusivities are also investigated. In the case of liquids with high electrical conductivities, in particular ionic liquids, overscreening and overcrowding effects are important, resulting in significant differences between the solutions of the PNP, MEK and LD models. In particular, the electrokinetic models yield increased dissipation and self-heating, leading to higher temperature variations and currents, in agreement with measurements. Furthermore, the MEK formulation describes the ion concentration fields with higher fidelity than the PNP equations.

In this study, we demonstrate, for the first time, the existence of a short-wave instability in a Lamb–Oseen vortex subjected to a triangular strain field generated by three satellite vortices, which we term the triangular instability. We identify this instability by numerically integrating the linearised Navier–Stokes equations around a quasi-steady base flow to capture the most unstable mode and validate it by comparing results with theoretical predictions. We evaluate this instability by calculating the growth rates associated with the parametric resonant coupling of two Kelvin waves with the triangular strain field in the limit of small strain rate and large Reynolds number. Our analysis reveals that resonance occurs only for combinations of the azimuthal wavenumbers $m = 1$ and $m = - 2$ (or their symmetric counterparts with opposite signs). We observe several unstable modes with positive growth rates for a moderate viscous Reynolds number $10^4$ and straining parameter value $\epsilon = 0.008$, defined as the cube of the ratio of the core size to the distance from the satellite vortices. The most unstable mode, dominant at typically high Reynolds numbers, has $k \approx 5.18/a$ and $\omega \approx - 0.312\Omega$ (where $a$ and $\Omega$ denote the core size and central angular velocity). It exhibits negligible critical layer damping and remains the most unstable mode over a wide range of ${Re}$ and $\epsilon$. At lower Reynolds numbers, another mode with $k \approx 1.76/a$ and $\omega \approx - 0.407\Omega$, despite significant critical layer damping, becomes the most unstable.

We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of dilute polymer solutions. In this framework the training of the neural network is guided by an evolution equation for the conformation tensor, which is GENERIC-compliant. We compare two training methodologies for the data-driven PINN constitutive models: one trained on data from the analytical solution of the Oldroyd-B (OB) model under steady-state rheometric flows (PINN-rheometric), and another trained on in silico data generated from computational fluid dynamics (CFD) simulations of complex flow around a cylinder that use the OB model (PINN-complex). The capacity of the PINN models to provide good predictions is evaluated by comparison with CFD simulations using the underlying OB model as a reference. Both models are capable of predicting flow behaviour in transient and complex conditions; however, the PINN-complex model, trained on a broader range of mixed-flow data, outperforms the PINN-rheometric model in complex flow scenarios. The geometry agnostic character of our methodology allows us to apply the learned PINN models to flows with topologies different from those used for training.

Viscous fingering is a hydrodynamic instability typically occurring when a less viscous fluid displaces a more viscous one and which deforms the interface between the two fluids into finger-shaped intrusions. For miscible fluids, the fingering pattern is usually followed visually by adding a passive dye into one of the two fluids. The reverse displacement of a less viscous fluid by a more viscous one is classically stable, featuring a planar interface. Here, we show experimentally that in some cases, the dye can actively modify the viscosity of a polymer solution and trigger fingering in the reverse displacement. This dye-induced destabilisation is shown to be due to double-diffusive effects triggering a non-monotonic viscosity profile with a maximum because the dye diffuses faster than the polymer.

Direct numerical simulation (DNS) studies of power-law (PL) fluids are performed for purely viscous-shear-thinning ($n\in [0.5,0.75]$), Newtonian ($n=1$) and purely viscous-shear-thickening ($n=2.0$) fluids, considering two Reynolds numbers ($Re_{\tau }\in [395,590]$), and both smooth and rough surfaces. We carefully designed a numerical experiment to isolate key effects and simplify the complex problem of turbulent flow of non-Newtonian fluids over rough surfaces, enabling the development of a theoretical model to explain the observed phenomena and provide predictions. The DNS results of the present work were validated against literature data for smooth and rough Newtonian turbulent flows, as well as smooth shear-thinning cases. A new analytical expression for the mean velocity profile – extending the classical Blasius $1/7$ profile to power-law fluids – was proposed and validated. In contrast to common belief, the decrease in $n$ leads to smaller Kolmogorov length scales and the formation of larger structures, requiring finer grids and longer computational domains for accurate simulations. Our results confirm that purely viscous shear-thinning fluids exhibit drag reduction, while shear-thickening fluids display an opposite trend. Interestingly, we found that viscous-thinning turbulence shares similarities with Newtonian transitional flows, resembling the behaviour of shear-thinning, extensional-thickening viscoelastic fluids. This observation suggests that the extensional and elastic effects in turbulent flows within constant cross-section geometries may not be significant. However, the shear-thickening case exhibits characteristics similar to high-Reynolds-number Newtonian turbulence, suggesting that phenomena observed in such flows could be studied at significantly lower Reynolds numbers, reducing computational costs. In the analysis of rough channels, we found that the recirculation bubble between two roughness elements is mildly influenced by the thinning nature of the fluid. Moreover, we observed that shear-thinning alters the flow in the fully rough regime, where the friction factor typically reaches a plateau. Our results indicate the possibility that, at sufficiently high Reynolds numbers, this plateau may not exist for shear-thinning fluids. Finally, we provide detailed turbulence statistics for different rheologies, allowing, for the first time, an in-depth study of the effects of rheology on turbulent flow over rough surfaces.