Two-dimensional simulations are conducted to investigate the direct initiation of cylindrical detonation in hydrogen/air mixtures with detailed chemistry. The effects of hotspot condition and mixture composition gradient on detonation initiation are studied. Different hotspot pressures and compositions are first considered in the uniform mixture. It is found that detonation initiation fails for low hotspot pressures and the critical regime dominates with high hotspot pressures. Detonation is directly initiated from the reactive hotspot, whilst it is ignited somewhere beyond the non-reactive hotspots. Two cell diverging patterns (i.e. abrupt and gradual) are identified and the detailed mechanisms are analysed. Moreover, cell coalescence occurs if many irregular cells are generated initially, which promotes the local cell growth. We also consider non-uniform detonable mixtures. The results show that the initiated detonation experiences self-sustaining propagation, highly unstable propagation and extinction in mixtures with a linearly decreasing equivalence ratio along the radial direction, i.e. 1 → 0.9, 1 → 0.5 and 1 → 0. Moreover, the hydrodynamic structure analysis shows that, for the self-sustaining detonations, the hydrodynamic thickness increases at the overdriven stage, decreases as the cells are generated and eventually becomes almost constant at the cell diverging stage, within which the sonic plane shows a ‘sawtooth’ pattern. However, in the detonation extinction cases, the hydrodynamic thickness continuously increases, and no ‘sawtooth’ sonic plane can be observed.

Helicity, an invariant under ideal-fluid (Euler) evolution, has a topological interpretation in terms of writhe and twist for a closed vortex tube, but accurately quantifying twist is challenging in viscous flows. With a novel helicity decomposition, we present a framework to construct the differential twist that establishes the theoretical relation between the total twisting number and the local twist rate of each vortex surface. This framework can characterize coiling vortex lines and internal structures within a vortex – important in laminar–turbulence transition, and in vortex instability, reconnection and breakdown. As a typical example, we explore the dynamics of vortex rings with differential twist via direct numerical simulation (DNS) of the Navier–Stokes equations. Two twist waves with opposite chiralities propagate towards each other along the ring and then collide whence the local twist rate rapidly surges. Local vortex surfaces are squeezed into a disk-like dipole structure containing coiled vortex lines, leading to vortex bursting. We derive a Burgers-equation-like model to quantify this process, which predicts a bursting time that agrees well with DNS.

Wind tunnel experiments are performed in both neutral and stable boundary layers to study the effect of thermal stability on the wake of a single turbine and on the wakes of two axially aligned turbines, thereby also showing the influence of the second turbine on the impinging wake. In the undisturbed stable boundary layers, the turbulence length scales are significantly smaller in the vertical and longitudinal directions (up to 50 % and $\approx$40 %, respectively), compared with the neutral flow, while the lateral length scale is unaffected. The reductions are larger with the imposed inversion of a second stable case, except in the near-wall region. In the neutral case, the length scales in the wake flow of the single turbine are reduced both vertically and laterally (up to 50 % and nearly 40 %, respectively). While there is significant upstream influence of a second turbine (on mean and turbulence quantities), there is virtually no upstream effect on vertical length scales. However, curiously, the presence of the second turbine aids length-scale recovery in both directions. Longitudinally, each turbine contributes to successive reduction in coherence. The effect of stability on the turbulence length scales in the wake flows is non-trivial: at the top of the boundary layer, the reduction in the wall-normal length scale is dominated by the thermal effect, while closer to the wall, the wake processes strongly modulate this reduction. Laterally, the turbines’ rotation promotes asymmetry, while stability opposes this tendency. The longitudinal coherence, significantly reduced by the wake flows, is less affected by the boundary layer's thermal stability.

In this article, we study the behaviour of the Abels–Garcke–Grün Navier–Stokes–Cahn– Hilliard diffuse-interface model for binary-fluid flows, as the diffuse-interface thickness passes to zero. For the diffuse-interface model to approach a classical sharp-interface model in the limit $\varepsilon \to +0$, the so-called mobility parameter $m$ in the diffuse-interface model must scale appropriately with the interface-thickness parameter $\varepsilon$. In the literature various scaling relations in the range $o(1)$ to $O(\varepsilon ^3)$ have been proposed, but the optimal order to pass to the limit has not been explored previously. Our primary objective is to elucidate this optimal order of the $m$–$\varepsilon$ scaling relation in terms of the rate of convergence of the diffuse-interface solution to the sharp-interface solution. Additionally, we examine how the convergence rate is affected by a sub-optimal parameter scaling. We centre our investigation around the case of an oscillating droplet. To provide reference limit solutions, we derive new analytical expressions for small-amplitude oscillations of a viscous droplet in a viscous ambient fluid in two dimensions. For two distinct modes of oscillation, we probe the sharp-interface limit of the Navier–Stokes–Cahn–Hilliard equations by means of an adaptive finite-element method. The adaptive-refinement procedure enables us to consider diffuse-interface thicknesses that are significantly smaller than other relevant length scales in the droplet-oscillation problem, allowing an exploration of the asymptotic regime.

This paper investigates the effect of anisotropic turbulence on generating leading-edge aerofoil–turbulence interaction noise. Thin aerofoil theory is used to model an aerofoil as a semi-infinite plate, and the scattering of incoming turbulence is solved via the Wiener–Hopf technique. This theoretical solution encapsulates the diffraction problem for gust–aerofoil interaction and is integrated over a wavenumber–frequency spectrum to account for general incoming anisotropic turbulence. We develop a novel axisymmetric wavenumber–frequency model that captures the wall-normal variation in turbulence characteristics, differing from previous approaches. Then, the method of Gaussian decomposition, in which the generalised spectra are approximated through the weighted sum of individual Gaussian eddy models, is applied to fit the turbulence model to experimental data. Comparisons with experimental data show good agreement for a range of anisotropic ratios.