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.

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.

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.

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.