We show that both temporal and spatial symmetry breaking in canonical K-type boundary layer transition arise as organised structures with quantifiable energetic pathways rather than unstructured noise. Before the skin-friction maximum, the flow is described by a periodic, spanwise-symmetric fundamental harmonic response (FHR) to the Tollmien–Schlichting wave. The FHR is spatially compact, produces hairpin packets and remains fully harmonic despite a turbulence-like appearance, thereby delimiting the deterministic regime. Past this point, a distinct regime change occurs: a hierarchy of quasi-periodic and aperiodic structures emerges, followed shortly by anti-symmetric structures that develop similarly despite no anti-symmetric inputs. We identify these structures as symmetry-decomposed spectral and space–time proper orthogonal modes that resolve the progression from deterministic harmonics to broadband dynamics. We introduce inter-modal and inter-symmetry energy budgets derived from symmetry-decomposed Navier–Stokes equations. They reveal a directed energy transfer from the FHR into the leading temporal and spatial symmetry breaking modes and, subsequently, into broadband residual fluctuations, showing that broadband dynamics grow only once inter-modal transfer is active, while inter-symmetry transfer also strongly amplifies broadband anti-symmetric fluctuations once asymmetry is present. These key insights support a view of laminar–turbulent transition as a sequence of symmetry breaking events, energetically driven by dominant space–time modes that route energy from harmonic flow to broadband turbulence.

We perform numerical simulations of forced homogeneous isotropic turbulence over a range of bulk viscosities, Reynolds numbers and Mach numbers to investigate the scaling of key flow statistics. Using the Helmholtz decomposition, we analyse the scalings of Favre-averaged turbulent kinetic energy (TKE), root-mean-square (r.m.s.) pressure, pressure dilatation, dilatational dissipation and higher-order velocity-gradient moments. Additionally, new models are proposed for the pressure-dilatation term and the bulk-viscosity dependence of dilatational dissipation. Although the solenoidal and dilatational components of the Favre-averaged TKE are not strictly orthogonal, our numerical results demonstrate that their ratio is well approximated by the squared ratio of the corresponding r.m.s. velocities. The r.m.s. pressure approaches the pseudo-sound scaling as bulk viscosity increases. Within the Donzis r.m.s. pressure model (Donzis & John 2020 Phys. Rev. Fluids 5(8), 084609), we find that the solenoidal contribution becomes dominant for large bulk viscosity. Pressure dilatation is found to depart systematically from pseudo-sound predictions: without bulk viscosity it favours transfer from kinetic to internal energy, while finite bulk viscosity can reverse this transfer at high Mach numbers. The scaling exponent of dilatational dissipation is shown to vary with bulk viscosity, enabling a corrected model for its exponent and prefactor. Velocity-gradient skewness and flatness reveal that the onset of shocklet-induced divergence is delayed with increasing bulk viscosity and may be suppressed entirely. The results extend recent velocity-ratio-based scaling frameworks and provide modelling insights into compressible turbulence.

Although Canada possesses abundant freshwater resources, uneven water distribution, rapid climate change, deteriorating source water quality, and insufficient water infrastructure put small, rural, and remote (SRR) communities at a risk of water advisories and waterborne disease that is 26 times higher than in cities. Approximately three-quarters of SRR communities are Indigenous, indicating that they are more likely to experience water insecurity than non-Indigenous communities. This review examines key factors exacerbating water insecurity in SRR communities, including: (i) the types and ranges of commonly detected contaminants in source water, (ii) contaminant pathways and associated health risks, and (iii) the performance and challenges of small water systems (SWSs) in Canadian SRR communities. Total coliforms and E. coli in the microbiological category, and arsenic, lead, and manganese in the heavy metals and trace minerals category, had the highest number of occurrences among contaminants reported in dedicated studies. In contrast, fewer studies have investigated contaminants of emerging concern (CECs) and the capacity of SWSs to remove them. Common SWSs such as, multistage sand filtration, roughing filtration, granular activated carbon, chlorination, and ozonation offer relatively simple and affordable decentralized options; however, their long-term performance, operation, maintenance, governance, and social acceptability remain challenging.

The variance and spectra of wall-normal velocities are investigated for direct numerical simulations of turbulent flow in a channel, pipe and zero-pressure-gradient boundary layer across a decade of friction Reynolds numbers. Spectra along the spanwise wavenumber have a pronounced peak well described by the turbulent dissipation rate and the local shear stress throughout the bottom half of the boundary layer. Deviations in the local stress from the surface shear velocity $U_\tau$ account for almost all of the differences in wall-normal velocity variance observed across different canonical flows, including for plane Couette flow. The dependence on the local stress is attributed to the fact that wall-normal motions are predominately ‘active’ per Townsend’s attached eddy hypothesis and directly contribute to the local shear stress, noting this hypothesis assumes simplified ideal conditions with constant turbulent shear stress. A semi-empirical fit applied to the Reynolds-number dependence of the variance matches the simulations across the lower half of the boundary layer and aligns with observed values in the literature. The fit extrapolates to a value between 1.45 and 1.65 times the local shear stress in the high-Reynolds-number limit, consistent with previous predictions relative to $U_\tau$ including for the vertical velocity in the near-neutral atmospheric boundary layer. However, universality in the exact proportional constant is precluded by small discrepancies in the variances corresponding to dissimilarity in the low-wavenumber contributions across different flow configurations and wall-normal positions. We speculate the dissimilarity is due to relatively weak ‘inactive’ wall-normal motions that are excluded from Townsend’s original hypothesis.

It is of great importance for fields such as implosion dynamics and fusion research to understand the dynamics of ejecta transport in converging gases. In this paper, the evolution of particulate flow within a cylindrically imploding system is investigated experimentally and numerically. The ejecta particles are emitted from the inner surface of a roughened Sn liner into vacuum, He and Ar gases. Dynamic images of liner implosion and ejecta transport are obtained with X-ray radiographs and multi-frame optical schlieren images. The transport of ejecta particles is simulated with a four-way coupled multiphase flow model, including modelling of gas–particle coupling and inter-particle collisions. Results reveal that the ejecta transport in shock-induced converging gases differs significantly from that in planar systems, primarily due to features such as interaction with the rebounding gas shock wave and continuous compression by the imploding liner. After being generated from the inner surface, the ejecta width undergoes an ‘expansion–compression’ variation. According to mechanisms governing ejecta–gas coupling, three distinct stages of ejecta evolution are identified: (i) post-shock transport dominated by drag and particle breakup; (ii) shock-particle interaction leading to quick reduction in particle size and rapid deceleration of the ejecta front; and (iii) dense ejecta compression governed by inter-particle collisions. Leveraging particle motion and size predictions at the ejecta front, combined with the self-similar converging shock solution, a theoretical model is established to estimate the three-stage evolution of ejecta width in a cylindrically converging system.

Dissipation mechanisms of low-mode internal tides, which travel far from their topographic generation sites, are an important consideration for the large-scale circulation and energy budget in the ocean. Modelling studies often decouple scattering and generation, i.e. study scattering in the absence of a local barotropic tide, or study generation in the absence of an incident internal tide. In this two-dimensional study using a semi-analytical Green function approach, we model the combined effects of internal wave generation by a barotropic forcing and scattering of an incident mode-1 internal wave, at an isolated Gaussian bottom topography in uniform stratification. Four different parameters govern the energetics – the non-dimensional topographic height (height ratio $h^*$) and slope (criticality $\epsilon$), and the normalised amplitude ($U_0$) and phase ($\varTheta$) of the barotropic forcing with respect to the incident mode-1 internal wave. The theory is first quantitatively validated by comparisons with numerical simulations for three different combinations of $(h^*,\epsilon )$, followed by a detailed parametric sweep. For a given topography and $U_0$, on an average across $\varTheta$, the total internal wave energy flux is the sum of the energy fluxes associated with generation in the presence of the barotropic forcing alone and the incident mode-1. For a given $ \varTheta$, however, the total energy flux can deviate significantly from its mean value due to constructive/destructive interferences of the individual modes; this occurs over a surprisingly wide range of $U_0$, $h^*$ and $\epsilon$. Depending on $U_0$, these deviations can be interpreted as either the extent to which a background barotropic forcing affects internal wave scattering, or the extent to which an incident mode-1 internal wave influences internal wave generation by barotropic forcing. The presence of barotropic forcing can significantly modify the scattering characteristics, including the possibility of losing a non-negligible fraction of the incident internal wave energy to another form. Similarly, internal wave generation characteristics can be sensitively dependent on the presence of an incident internal wave. These energy flux loss or gain effects are typically found for short subcritical ($h^*\lesssim 0.4$, $\epsilon \lt 1$) and sufficiently steep, tall ($h^*\gtrsim 0.4$) topographies.

Efforts on loss and damage assessments primarily focus on the macro-level assessments that often overlook micro-level heterogeneity. This paper adopts a bottom-up approach by measuring household-level L&Ds from cyclones. Estimates are derived for a representative household in Odisha, India, using two case studies: a super cyclone and a very severe cyclone., Data were collected through focus group discussions and household surveys, and were valued using the then prevailing market prices. The findings suggest that the annual L&Ds for a coastal household in Odisha amount to USD 193 from a super cyclone and USD 396 from severe cyclones, measured in 2014 prices and exchange rate (1 USD = INR 60.95). While the super cyclone caused extensive losses, a substantial portion of the damage was compensated through government support and international aid. In contrast, very severe cyclones are more frequent but receive limited external assistance, leaving households to cope largely on their own. L&D assessment across different occupational groups reveals significant disparities in aid distribution and insurance coverage. Given that the area is a core zone of cyclogenesis, localised resource mobilisation and expanded insurance coverage should be prioritised, along with a fairer aid distribution mechanism, to strengthen disaster management.

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.