The interaction between cylindrically converging shock waves (SWs) in a water–gelatine solution and a coaxial cylindrical air bubble is studied experimentally and numerically. Two configurations are considered: (i) an azimuthally symmetric, cylindrically converging SW of Mach 1.35 impinging on a coaxial cylindrical bubble, and (ii) a semicylindrical converging SW of Mach 1.45 (corresponding to half of the cylindrical front), interacting with the same target. Shock waves are generated by exploding wire arrays driven by a high-voltage pulsed power system at beamline ID19 of the European Synchrotron Radiation Facility, delivering currents up to $130\,\text{kA}$ with rise times of $0.35$ and $0.55\,\unicode{x03BC} \text{s}$ to the cylindrical and semicylindrical wire loads, respectively. X-ray radiography is conducted at a pulse repetition rate of 5.68 MHz using two synchronised high-speed cameras. Numerical hydrodynamic simulations are performed using a compressible multiphase Navier–Stokes solver. A Gilmore-type model for compressible cylindrical bubble pulsation provides an independent analytical estimate of the interface evolution. In the cylindrical SW configuration, the bubble collapse in experiments exhibits Richtmyer–Meshkov instability spikes. The cylindrically converging shock is analysed with Guderley’s solution and Whitham’s approximation using a real-gas equation of state, predicting Mach 14.1 near the focus. In the semicylindrical configuration, momentum focuses into a single supersonic jet with a speed of 885 $\pm$ 30 m s−1, producing localised high-pressure regions, coherent vortices and complex internal Mach reflections. Experiments, simulations and theory are consistent in collapse time, interface motion and overall flow dynamics.

We investigate turbulent flows over canopies of rigid elements with different geometries, spacings and Reynolds numbers to identify and characterise different canopy density regimes. In the sparse regime, the overlying turbulence penetrates relatively unhindered within the canopy, whereas in the dense regime, this penetration is limited. The frontal density, $\lambda _f$, a common a measure of canopy density, is effective for e.g. conventional vegetation with no preferential orientation, but we observe that it does not fully characterise the density regime for some less conventional topologies, suggesting it may not always capture the underlying physics. To address this, we propose to quantify turbulence penetration directly, from the position and extent of individual turbulent eddies, particularly those associated with intense Reynolds shear stress. We analyse a series of direct simulations for isotropic- and anisotropic-layout canopies with frontal densities $\lambda _f\approx 0.01$–$2.04$, heights $h^+\approx 44$–$266$, element width-to-pitch ratios $w/s\approx 0.06$–$0.7$ and Reynolds numbers ${\textit{Re}}_{\tau} \approx 180$–$2000$. For the same $\lambda _f$, canopies with elements closely packed in the streamwise direction but large spanwise gaps result in deeper turbulence penetration, appearing sparser than isotropic or spanwise-packed ones. For the same spanwise gap, turbulence penetration remains similar across canopies independently of their streamwise pitch and gap. As the spanwise gap increases, eddies penetrate deeper and more vigorously into the canopy. Turbulence penetration is also Reynolds-number-dependent: the same canopy can behave as dense at low ${\textit{Re}}_{\tau}$, but increasingly sparse as ${\textit{Re}}_{\tau}$ increases. Our results suggest that turbulence penetration depends essentially on the ability of turbulent eddies to fit within the canopy as they travel downstream, and that this can be characterised by an effective spanwise gap, and its ratio to the typical eddy size; turbulence penetration is substantial when this gap is larger than the eddy size, and negligible in the opposite case. A penetration length $d_p$ can then be defined from the effective gap or the eddy size, whichever is smaller. For small $d_p/h$, the canopy behaves as dense; for moderate $d_p/h$, as intermediate; and for $d_p/h\approx 1$, turbulent eddies can penetrate all the way to the canopy bed and the canopy behaves as sparse.

We consider the axisymmetric, radial extrusion of Newtonian and shear-thinning, power-law fluids from a cylindrical source, which displace an ambient inviscid fluid of equal density. In unconfined geometries, the upper and lower fluid interfaces are stress free, and the flow is dominated by extensional stresses everywhere. In a layer of extruded shear-thinning fluid, a radially growing viscosity field, associated with a radially decaying velocity field, causes the current to bulge near the cylindrical source, with the thickness of the layer growing without bound over time. In contrast, with a Newtonian fluid, the thickness of the fluid layer never exceeds the height of the cylindrical source. We compute numerical solutions to this system, and find similarity solutions describing its late-time behaviour for values of the rheological power-law exponent $1\leqslant n\leqslant 3/2$. We also consider extrusion between parallel plates, in which the shear-thinning fluid displaces the inviscid fluid and fills the cell completely up to a grounding line, beyond which it separates from the boundaries to extend freely. In this case, we find similarity solutions for values of the power-law exponent $n \geqslant 1$.

Spanwise wall oscillation (SWO) of turbulent boundary layers (TBLs) is investigated via direct numerical simulations (DNS) over an extended actuation region (momentum Reynolds number $344\lt Re_\theta \lt 2340$) with oscillation periods up to $T_{\textit{sc}}^+=600$, scaled by the uncontrolled friction velocity $u_{\tau 0}$ at the onset of SWO (i.e. $ \textit{Re}_\theta =344$). For low periods ($T_{\textit{sc}}^+\lt 200$), drag reduction ($ \textit{DR} $) decreases with increasing $ \textit{Re}_\theta$, consistent with conventional inner-scaled control strategies targeting near-wall turbulence. In sharp contrast, for large periods ($T_{\textit{sc}}^+\gt 200$), $ \textit{DR} $ increases with $ \textit{Re}_\theta$. For example, at $T_{\textit{sc}}^+=600$, $ \textit{DR} $ rises from 1.3 % at $ \textit{Re}_\theta =713$ to 7.0 % at $ \textit{Re}_\theta =2340$. This unexpected growth is partly explained by the streamwise evolution of the effective oscillation parameter: as a TBL develops, $u_{\tau 0}$ decreases downstream, reducing the local-scaled period $T^+$ and thereby enhancing suppression of near-wall turbulence. Interestingly, if the results are compared at approximately fixed $T^+$, then $ \textit{DR} $ for $T^+\gt 350$ still exhibits a weak positive dependence on $ \textit{Re}_\theta$, consistent with recent experiments by Marusic et al. (2021, Nat. Commun., vol. 12, 5805). We further develop a new analytical relationship that links $ \textit{DR} $ to the upward shift of mean velocity in the wake region. Unlike previous formulations, the relationship avoids logarithmic-region fitting and does not rely on an invariant Kármán constant under SWO, while maintaining good agreement with DNS data. Flow diagnostics – including Reynolds stresses, skin-friction decomposition, and energy spectra – demonstrate that the observed variation of $ \textit{DR} $ with Reynolds number ($ \textit{Re}$) arises from period-dependent modulation of near-wall turbulence. Overall, these findings challenge the conventional view that $ \textit{DR} $ inevitably deteriorates with $ \textit{Re}$, and demonstrate that out-scaled actuation can instead enhance $ \textit{DR} $ performance – offering new physical insights for high-$ \textit{Re}$ control strategies.

The goal of this work is to investigate particle motions beneath unidirectional, deep-water waves up to the third-order in nonlinearity. A particular focus is on the approximation known as Stokes drift and how it relates to the particle kinematics as computed directly from the particle trajectory mapping. The reduced Hamiltonian formulation of Zakharov and Krasitskii serves as a convenient tool to separate the effects of weak nonlinearity, in particular, the appearance of bound harmonics and the mutual corrections to the wave frequencies. By numerical integration of the particle trajectory mappings, we are able to compute motions and resulting drift for sea-states with one, two and several harmonics. We find that the classical Stokes drift formulation provides a slight underestimate of the drift at the surface and a slight overestimate at depth. Incorporating difference harmonic terms into the formulation yields an improved agreement with the drift obtained from nonlinear wave theories, particularly at greater depth. The consequences of this are explored for regular and irregular waves, as well as parametric wave spectra.

We present a resolvent-based framework for estimating turbulent velocity fluctuations in the wake of a spanwise-periodic NACA0012 airfoil at Mach 0.3, Reynolds number 23 000, and an angle of attack of $6^{\circ }$. Building on the methodology of Jung et al. (2025, J. Fluid Mech. 1016, A41), we extend the approach to the more complex regime of a turbulent wake, which involves three primary challenges: (i) globally unstable modes in the linearised Navier–Stokes operator, (ii) multi-scale turbulent structures and (iii) high-dimensional datasets. To address these challenges, we employ a data-driven approach that constructs causal resolvent-based estimation kernels from cross-spectral densities obtained via large-eddy simulations. These kernels are derived using the Wiener–Hopf method, which optimally enforces causality, thereby enhancing real-time estimation accuracy. The framework captures the spectral signatures of coherent structures and, through the empirically determined cross-spectral densities, implicitly accounts for the coloured statistics of the nonlinear forcing acting on the linear system. To handle the computational demands of the high-dimensional estimation problem, we utilise parallel algorithms developed within the same framework. We further investigate sensor placement by analysing single-sensor estimation error and coherence with target flow quantities. Results demonstrate accurate causal estimation of streamwise velocity for the spanwise-averaged, spanwise-Fourier-transformed and mid-span flow using limited shear-stress measurements on the surface of the airfoil. This study underscores the potential of the resolvent-based framework for efficient estimation in compressible, turbulent environments.

An experimental study was conducted to investigate the characteristics of unsteady oblique shock trains in a constant-area rectangular duct under an asymmetric incoming boundary layer. High-speed schlieren techniques and high-frequency pressure measurements were utilised in this study. The results indicate that the oblique shock train mainstream leans significantly towards the thin-boundary-layer side. Under downstream periodic excitation, the shock train moves periodically, and its shape changes during the movement. This phenomenon occurs to match the downstream pressure by altering the relative Mach number in front of the shock train, with the average pressure rise slope along the thick-boundary-layer side changing periodically. Additionally, unlike a normal shock train, the pressure rise distribution along the thick-boundary-layer side is nearly linear, and the correlation coefficients between the transducers on this side and the most downstream transducer are higher than those on the thin-boundary-layer side. Due to differences in flow structure and pressure rise distribution, the existing amplitude prediction model proposed by Xiong et al. (J. Fluid Mech. vol. 846, 2018, pp. 240–262) for the unsteady normal shock train is no longer applicable to the unsteady oblique shock train. Therefore, a new prediction model is derived and verified by experiments. Moreover, it is found that using only the downstream pressure transducer information on the thick-boundary-layer side can effectively predict the amplitude of the shock-train motion. Combined with the prediction model, a novel method is proposed to estimate the amplitude of the shock-train motion conveniently.