The hypersonic flow over 30$^{\circ }$–50$^{\circ }$ double-cone configurations with three nose bluntness levels was experimentally investigated at Mach 6. High-speed schlieren photography, pressure sensors and pressure-sensitive paint were used to examine both global flow patterns and unsteady dynamics at a transitional Reynolds number. The experimental results indicate that the size of the separation region at the cone junction increases with increasing nose bluntness. Type V shock–shock interactions were observed in all three configurations, while the shock wave structures in the region below the triple point exhibited two patterns: Mach shock wave reflection in the sharp and small-blunt-nose cases, and regular shock wave reflection in the large-blunt-nose case. Spectral analysis of high-speed schlieren sequences revealed two types of unsteadiness across all cases: low-frequency shock oscillations and high-frequency unsteady structures along the boundary of supersonic jet on the second cone. For the low-frequency unsteadiness, shock oscillations displayed a broadband nature in the sharp and small-blunt-nose configurations, while a dominant frequency of approximately 2 kHz was observed in the large-blunt-nose case, characterised by shock motion and bubble breathing – an observation not experimentally reported before. Additionally, spectral analysis of wall pressure contours indicated that the low-frequency unsteadiness was primarily characterised by axisymmetric modes for all configurations. Global stability analysis and resolvent analysis further demonstrated noise-amplifier behaviour in all configurations, and the dominant low-frequency unsteadiness in the large-blunt-nose case is attributed to modal resonance induced by environmental noise.

The explosive dispersal of granular media, exemplified by the rapid radial expansion of a dense particle ring driven by internal pressurised gases, serves as a paradigmatic system for investigating multiphase blast dynamics. Despite the ubiquity of jetting and clustering phenomena in explosive dispersal scenarios, their governing mechanisms remain poorly resolved. In this work, we combine compressible computational fluid dynamics–discrete parcel method simulations, and theoretical modelling to elucidate the multiscale physics underlying explosion-induced particle jetting. We reveal a hierarchy of jetting structures, comprising non-jetting, suppressed jetting and prominent jetting, which are governed by the interplay between microscale particle force-chain evolution, mesoscale gas–particle coupling and macroscale ring dynamics. Jetting initiation emerges from the transient competition between shock-induced particle compaction and gas filtration during the early expansion phase, whereas sustained jet development requires subsequent ring implosion driven by adverse pressure gradients. By unifying this multiscale dynamics, we reduce the system’s complexity into two dimensionless parameters: one characterising mesoscale gas–particle interactions and another quantifying macroscale implosion intensity. A phase diagram for jetting morphology under weak-shock conditions is established in this dimensionless parameter space, delineating two necessary criteria for jet formation. Systems failing either criterion exhibit no jetting, resolving long-standing ambiguities in the prediction of explosive dispersal structures.

The motion of a body through a superfluid can generate phenomena distinct from a normal viscous fluid. This includes the absence of drag below a critical body speed with the shedding of quantised vortices and non-zero drag above this speed. These phenomena are often modelled using the Gross–Pitaevskii (GP) equation, which describes the wavefunction of a weakly interacting Bose–Einstein condensate and its superfluid dynamics. We study the drag experienced by a penetrable circular disk of radius, $a$, in the form of a two-dimensional potential barrier of height, $V_0$, that is moving in a superfluid of bulk density, $n_\infty$, by solving the GP equation. The drag is found to exhibit a unimodal dependence on the disk speed for a fixed value of its barrier height. This behaviour is quantified analytically and confirmed using direct numerical solution. The maximum drag per unit length of $F_{\textit{drag}}^{\textit{max}} \approx 5 a n_\infty V_0$ occurs when the barrier height coincides with the relative kinetic energy of the fluid particles. Flow excitations are diminished at a high particle kinetic energy with a commensurate reduction in the drag. This generates a saddle-node bifurcation in the dynamics of a moving disk under an applied force. These results advance understanding of the motion of bodies with finite penetrability, which is relevant to laser experiments probing the superfluidity of Bose–Einstein condensates.

We investigate experimentally the flow structure in a fluid layer of thermal conductivity $k$, heated from below with a uniform heat flux $F$, and exposed to a horizontal temperature gradient, $\lambda$, on the top plate. This is a model system for the dynamics in subglacial lakes where such a competition between Rayleigh–Bénard convection (RBC) and horizontal convection (HC) is thought to happen. We evidence a hysteretic transition from a RBC flow structure to a HC flow structure when the non-dimensional control parameter, $\varLambda = k\lambda /F$, is $4\times 10^{-4}$ when $\varLambda$ is decreasing, and $7\times 10^{-4}$ when $\varLambda$ is increasing. These values are lower than the threshold value found in recent two-dimensional direct numerical simulations (Couston et al. 2022 J. Fluid Mech., vol. 947, p. A13), of order $10^{-2}$, highlighting the importance of exploring three-dimensional dynamics at higher realistic Prandtl numbers, and suggesting that HC may be more common in subglacial lakes than previously predicted. For large values of $\varLambda$, we observe that the warmest part of the top plate has approximately the same temperature as the bottom plate, such that a stable temperature gradient settles below the warm side of the top plate. Thermal plumes are no longer visible in this region, and seem to be replaced by internal gravity waves.

Turbulence-induced friction is a significant contributor to energy consumption in the fluid-transport and piping industries. Here, we describe a passive approach to suppress turbulence and reduce friction: we show that a local increase in streamwise flow curvature, combined with changing a circular cross-section to an oval, relaminarises turbulent flow in curved pipes. We exemplify this effect in a $180^{\circ }$ bend at ${\textit{Re}}_D=10\,000$ and $20\,000$ (based on bulk velocity $U_B$ and pipe diameter $D$), well above the limit for sustained turbulence in straight pipes and the linear stability limit in $180^{\circ }$ bends. Curvature inhibits streamwise Reynolds stresses, and cross-sectional modifications weaken the unstable secondary flow, together disrupting the near-wall regeneration cycle and collapsing turbulence. Simulations and experiments confirm that these geometric modifications suppress turbulence and reduce pressure loss by 53 % and 36 % compared with the baseline $180^{\circ }$ bend and a fully developed straight pipe of equal length, respectively. The results establish a passive, mechanism-based route to relaminarisation in curved pipes with implications for energy-efficient control in other wall-bounded flows with curvature.

We examine elastic travelling-wave (‘arrowhead’) solutions in a viscoelastic, unidirectionally body-forced flow, focusing on their existence and morphological changes as the Weissenberg number ${\textit{Wi}}$ and streamwise duct length $L$ are varied. We find that, First, branch topology varies from an isola at low $L$ through a two-sided reconnection at intermediate $L$ to a branch that exists at asymptotically large ${\textit{Wi}}$ for larger $L$. At intermediate $L$, more than two arrowhead solutions can coexist at a given $({\textit{Wi}},L)$ choice due to extra saddle–node bifurcations. Second, the canonical arrowhead consists of two legs joined by an arched head that blocks throughflow and traps a counter-rotating vortex pair, while a polymer strand can emerge as a by-product of a strong extensional region attached to/detached from the arrowhead arch. Third, a minimal domain length $L_{min }$ required to sustain an arrowhead is found to vary non-monotonically with ${\textit{Wi}}$; for ${{\textit{Wi}}}\geqslant 20$, detached-strand states control $L_{min }$ with a relation $L_{min }\approx 0.125\,{{\textit{Wi}}}+1.5$. And fourth, in sufficiently long domains, the upper branch becomes a localised single arrowhead whose streamwise extent depends on ${\textit{Wi}}$, whereas the lower branch can proliferate into a train of arrowheads at high ${\textit{Wi}}$, a phenomenon not previously reported.

The chemical step is an elementary pattern in chemically heterogeneous substrates, featuring two regions of different wettability separated by a sharp border. Within the framework of lubrication theory, we investigate droplet motion and the contact-line dynamics driven by a chemical step, with the contact-line singularity addressed by the Navier slip condition. For both two-dimensional (2-D) and three-dimensional (3-D) droplets, two successive stages are identified: the migration stage, when the droplet traverses both regions, and the asymmetric spreading stage, when the droplet spreads on the hydrophilic region while being constrained by the border. For 2-D droplets, we present a matched asymptotic analysis that agrees with numerical solutions. In the migration stage, a 2-D droplet can exhibit translational motion with a constant speed. In the asymmetric spreading stage, the contact line at the droplet rear is pinned at the border. We show that a boundary layer still exists near the pinned contact line, across which the slope is approximately constant, whereas the curvature would diverge in the absence of slip. For 3-D droplets, our numerical simulations show that the evolution is qualitatively analogous to the 2-D case, while being significantly affected by the lateral flow. The droplet length and width exhibit non-monotonic variations due to the lateral flow. Eventually, the droplet detaches from the border and approaches equilibrium at the hydrophilic substrate. Additionally, we demonstrate that the variation of the apparent contact angle at the instant of border contact only affects the early stage of droplet migration.

We numerically study weakly decaying two-dimensional turbulence over topography of varying roughness by comparing long-term flow states from simulations to the minimum enstrophy state (MES) proposed by Bretherton & Haidvogel (J. Fluid Mech., vol. 78, 1976, issue 1, pp. 129–154). The presence of isolated vortices in the numerical simulations leads to significant differences from the theory. These vortices are either roaming or topographically locked, with this distinction depending on the topographic roughness, the initial length scale and the initial non-dimensional energy ($E/E_{\#}$), where $E_{\#}$ denotes the critical energy proposed by Siegelman & Young (Proc. Natl. Acad. Sci. USA, vol. 120, 2023, issue 44, p. e2308018120). For low-energy and weakly rough topography, scatter plots show that the numerical results deviate from the MES due to the presence of vortices. As topographic roughness increases, the number, size and mobility of vortices decrease, leading to closer agreement between the numerical results and the MES. High energy and weakly rough topography lead to roaming vortices on a field of homogenised background potential vorticity. However, we observe topographically trapped eddies on highly rough topographies, even when initial length scales are much smaller than the domain size. The degree to which numerical results deviate from MES scaling is due to the presence of vortices, which, in turn, depend on topographic roughness and initial conditions in complex ways, suggesting a rich range of ways in which turbulence organises the long-term flow.