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.

The purpose of this study is to further investigate the relationship between sweetener exposure and the risk of endometrial cancer (EC). Up until December 2022, a literature search in an electronic database was carried out utilizing PubMed, Web of Science, Ovid, and Scopus. The odds ratio (OR) and 95 % confidence interval (CI) were used to evaluate the results. Sweeteners were divided into nutritional sweeteners (generally refers to sugar, such as sucrose and glucose) and non-nutritional sweeteners (generally refers to artificial sweeteners, such saccharin and aspartame). Ten cohort studies and two case-control studies were eventually included. The study found that in 12 studies, compared with the non-exposed group, the incidence rate of EC in the sweetener exposed group was higher (OR = 1·15, 95 % CI = [1·07, 1·24]). Subgroup analysis showed that in 11 studies, the incidence rate of EC in the nutritional sweetener exposed group was higher than that in the non-exposed group (OR = 1·25, 95 % CI = [1·14, 1·38]). In 4 studies, there was no difference in the incidence rate of EC between individuals exposed to non-nutritional sweeteners and those who were not exposed to non-nutritional sweeteners (OR = 0·90, 95 % CI = [0·81, 1·01]). This study reported that the consumption of nutritional sweeteners may increase the risk of EC, whereas there was no significant relationship between the exposure of non-nutritional sweeteners and the incidence of EC. Based on the results of this study, it is recommended to reduce the intake of nutritional sweeteners, but it is uncertain whether use of on-nutritional sweeteners instead of nutritional sweetener.

Compressible turbulent plane Couette flows are studied via direct numerical simulation for wall Reynolds numbers up to $Re_w=10\ 000$ and wall Mach numbers up to $M_w=5$. Various turbulence statistics are compared with their incompressible counterparts at comparable semilocal Reynolds numbers $Re^*_{\tau,c}$. The skin friction coefficient $C_f$, which decreases with $Re_w$, only weakly depends on $M_w$. On the other hand, the thermodynamic properties (mean temperature, density and others) strongly vary with $M_w$. Under proper scaling transformations, the mean velocity profiles for the compressible and incompressible cases collapse well and show a logarithmic region with the Kárman constant $\kappa =0.41$. Compared with wall units, the semilocal units yield a better collapse for the profiles of the Reynolds stresses. While the wall-normal and spanwise Reynolds stress components slightly decrease in the near-wall region, the inner peak of the streamwise component notably increases with increasing $M_w$ – indicating that flow becomes more anisotropic when compressible. In addition, the near-wall turbulence production decreases as $M_w$ increases – due to rapid wall-normal changes of viscosity caused by viscous heating. The streamwise and spanwise energy spectra show that the length scale of near-wall coherent structures does not vary with $M_w$ in semilocal units. Consistent with those in incompressible flows, the superstructures (the large-scale streamwise rollers) with a typical spanwise scale of $\lambda _z/h\approx 1.5{\rm \pi}$ become stronger with increasing $Re_w$. For the highest $Re_w$ studied, they contribute about $40\,\%$ of the Reynolds shear stress at the channel centre. Interestingly, flow visualization and correlation analysis show that the streamwise coherence of these structures degrades with increasing $M_w$. In addition, at comparable $Re^*_{\tau,c}$, the amplitude modulation of these structures on the near-wall small scales is quite similar between incompressible and compressible cases – but much stronger than that in plane Poiseuille flows.

Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius $R$ and axial length $10{\rm \pi} R$ at friction Reynolds numbers up to $Re_\tau =5200$ using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor $\lambda$ overshoots by $2\,\%$ and undershoots by $0.6\,\%$ the Prandtl friction law at low and high $Re$ ranges, respectively. In addition, $\lambda$ in our results is slightly higher than in Pirozzoli et al. (J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichi et al. (Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to $y^+=250$, has not yet developed a plateau farther away from the wall in the pipes even for the $Re_\tau =5200$ cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with $Re_\tau$ – are lower in the pipe than in the channel, but the difference decreases with increasing $Re_\tau$. While the wall value is slightly lower in the channel than in the pipe at the same $Re_\tau$, the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a $k^{-1}$ dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.

Well-resolved direct numerical simulations of turbulent open channel flows (OCFs) are performed for friction Reynolds numbers up to $Re_\tau =2000$. Various turbulent statistics are documented and compared with the closed channel flows (CCFs). As expected, the mean velocity profiles of the OCFs match well with the CCFs in the near-wall region but diverge notably in the outer region. Interestingly, a logarithmic layer with Kárman constant $\kappa =0.363$ occurs for OCF at $Re_\tau =2000$, distinctly different from CCF. Except for a very thin layer near the free surface, most of the velocity and vorticity variances match between OCFs and CCFs. The one-dimensional energy spectra reveal that the very-large-scale motions (VLSMs) with streamwise wavelength $\lambda _x>3 h$ or spanwise wavelength $\lambda _z>0.5 h$ contribute the most to turbulence intensity and Reynolds shear stress in the overlap and outer layers (where h is the water depth). Furthermore, the VLSMs in OCFs are stronger than those in CCFs, resulting in a slightly higher streamwise velocity variance in the former. Due to the footprint effect, these structures also have significant contributions to the mean wall shear stress, and the difference between OCF and CCF enlarges with increasing $Re_\tau$. In summary, the free surface in OCFs plays an essential role in various flow phenomena, including the formation of stronger VLSMs and turbulent kinetic energy redistribution.

The dynamics of two slender Hopf-linked vortex rings at vortex Reynolds numbers ($Re \equiv \varGamma /\nu, \mathrm {circulation/viscosity}$) $2000$, $3000$ and $4000$ is studied using direct numerical simulations of the incompressible Navier–Stokes equations. Under self-induction, the initially perpendicularly placed vortex rings approach each other and reconnect to form two separate vortex rings. The leading ring is closely cuddled and further undergoes secondary reconnection to form two even smaller rings. At high $Re$, the leading ring and the subsequent smaller rings are unstable and break up into turbulent clouds consisting of numerous even smaller-scale structures. Although the global helicity $H$ remains constant before reconnection, it increases and then rapidly decays during reconnection – both the growth and decay rates increase with $Re$. In the two higher $Re$ (i.e. 3000 and 4000) cases, $H$ further rises after the first reconnection and reaches a quasi-plateau with the asymptotic value continuously increasing with $Re$ – suggesting that $H$ for viscous flows is not conserved at very high $Re$. Further flow analysis demonstrates that significant numbers of positive and negative helical structures are simultaneously generated before and during reconnection, and their different decay rates is the main reason for the complex evolution of $H$. By examining the topological aspects of the helicity dynamics, we find that, different from $H$, the sum of link and writhe ($L_k+W_r$) continuously drop during reconnection. Our results also clearly demonstrate that the twist, which increases with $Re$, plays a significant role in the helicity dynamics, particularly at high $Re$.

Topological transition and helicity conversion of vortex torus knots and links are studied using direct numerical simulations of the incompressible Navier–Stokes equations. We find three topological transitional routes (viz. merging, reconnection and transition to turbulence) in the evolution of vortex knots and links over a range of torus aspect ratios and winding numbers. The topological transition depends not only on the initial topology but also on the initial geometry of knots/links. For small torus aspect ratios, the initially knotted or linked vortex tube rapidly merges into a vortex ring with a complete helicity conversion from the writhe and link components to the twist. For large torus aspect ratios, the vortex knot or link is untied into upper and lower coiled loops via the first vortex reconnection, with a helicity fluctuation including loss of writhe and link, and generation of twist. Then, the relatively unstable lower loop can undergo a secondary reconnection to split into multiple small vortices with a similar helicity fluctuation. Surprisingly, for moderate torus aspect ratios, the incomplete reconnection of tangled vortex loops together with strong vortex interactions triggers transition to turbulence, in which the topological helicity decomposition fails due to the breakdown of vortex core lines.

A slender trefoil knotted vortex is studied using direct numerical simulation of the Navier–Stokes equations for vortex Reynolds numbers ($Re \equiv \varGamma /\nu$, circulation/viscosity) up to 12 000. For initially zero twist ($T_{w,0}=0$), neither the writhe $W_r$ nor the global helicity $H$ is conserved. Initially $W_r$ slowly decreases, then suddenly drops during reconnection and becomes almost constant thence; its evolution is almost $Re$ independent. Before reconnection, $H$ also gradually decreases but sharply increases during reconnection. The evolution of $H$ after reconnection strongly depends on $Re$. While steadily decreasing at low $Re$, $H$ significantly increases before eventually decaying at high $Re$. Flow visualization, helicity decomposition and helical wave decomposition reveal that significant amounts of positive and negative twist helicities are simultaneously generated before and during reconnection. Also, the small leading and large trailing rings resulting from asymmetric reconnection have respectively negative and positive twists, which then decay differently due to different initial values, geometries and mutual induction. In particular, at high $Re$, the twist in the small ring, under stretching by the large trailing ring, decays much faster and even switches sign to become positive by the writhe-to-twist conversion – the main reason for the ‘transient growth’ of $H$. Simulations with non-zero initial twists ($T_{w,0}=7.48$ and $22.48$) reveal that the overall dynamics is similar to the $T_{w,0}=0$ case. Hence, the evolution of the trefoil knotted vortex is mainly governed by $W_r$, not $T_w$, although the latter is found to play an essential role in enstrophy growth as well as energy cascade.

Polarized vortical structures (i.e. with axial flow, thus coiled vortex lines) are generic to turbulent flows – hence the importance of their dynamics, interactions and cascade. Direct numerical simulations of two anti-parallel polarized vortex tubes are performed for vortex Reynolds numbers $Re$ ($\equiv \varGamma /\nu$) up to $9000$ and initial polarization strength $q$ (ratio of peak axial to azimuthal velocities) between $0$ and $4/3$. For both counter- and co-polarized cases, although the reconnection is delayed as $q$ increases – mainly due to weakened self-induction – it is more rapid and more complete for small $q$. Enstrophy growth and energy cascade are suppressed for weak polarization ($q < 1/2$) due to depleted nonlinearity, but are enhanced for strong polarization ($q > 1/2$) due to instability and/or transient growth. When counter-polarized, numerous structures with both positive and negative helicity densities (i.e. $\pm h$) are generated. For large $q$, strong axial flows opposite to the initial flows occur – causing polarization reversals. For the co-polarized cases, although $+h$ predominates, $-h$ structures also form and interact with positive ones – leading to helicity cascade to small scales. As $Re$ increases, small scales are more numerous: for counter-polarized cases, the threads undergo successive reconnections in a cascade – akin to the unpolarized case; for co-polarized cases, the newly formed vortex ring breaks up with numerous hairpin vortices wrapping around it. Increasing $q$ alters the energy spectrum in the inertial range with a scaling varying from $k^{-5/3}$ for the unpolarized case to $k^{-7/3}$ for the strongly polarized case, which seems to be associated with the enhanced vortex spiralling. In addition, for the strongly co-polarized cases, a $k^{-4/3}$ helicity spectrum develops. Furthermore, most of the energy and helicity in the inertial range with scale $L$ transfer to scales between $0.3L$ and $0.4L$. Therefore, polarization can significantly alter the dynamics of vortex reconnection as well as turbulence cascade.

A multicenter study of sharps injuries (SIs) and other blood or body fluid (OBBF) exposures was conducted among 33,156 healthcare workers (HCWs) from 175 hospitals in Anhui, China. In total, 12,178 HCWs (36.7%) had experienced at least 1 SI in the previous 12 months and 8,116 HCWs (24.5%) had experienced at least 1 OBBF exposure during the previous 12 months.

To improve the stability of Cs2SnCl6 under aqueous/moisture environments, we applied a concept of artificial passivation by depositing a protective TiO2 coating of 10 nm on the surface of Cs2SnCl6. Static leaching experiments results indicate that the initial release rates of Cs+ and Cl− are decreased by 20–30 times with TiO2 coating, suggesting its possibility to improve the short-term water/environmental stability of Cs2SnCl6. An amorphous-to-crystalline phase transition in TiO2 film was observed, possibly resulting in degradation of Cs2SnCl6. However, the crystalline TiO2 film still remains after 21 days water exposure and can still act as an effective passivation layer to reduce the release rates of Cs+ and Cl- by as much as about 17 and 7 times, respectively, relative to static leaching without artificial coatings. Therefore, the water/environmental stability of metal halide perovskite Cs2SnCl6, which is a highly soluble molecular salt, can be enhanced by the nanoscale TiO2 coating as an artificial passivation film.

Reconnection plays a significant role in the dynamics of plasmas, polymers and macromolecules, as well as in numerous laminar and turbulent flow phenomena in both classical and quantum fluids. Extensive studies in quantum vortex reconnection show that the minimum separation distance $\delta$ between interacting vortices follows a $\delta(t) \sim t^{1/2}$ scaling. Due to the complex nature of the dynamics (e.g. the formation of bridges and threads as well as successive reconnections and avalanche), such scaling has never been reported for (classical) viscous vortex reconnection. Using direct numerical simulation of the Navier–Stokes equations, we study viscous reconnection of slender vortices, whose core size is much smaller than the radius of the vortex curvature. For separations that are large compared to the vortex core size, we discover that $\delta (t)$ between the two interacting viscous vortices surprisingly also follows the 1/2-power scaling for both pre- and post-reconnection events. The prefactors in this 1/2-power law are found to depend not only on the initial configuration but also on the vortex Reynolds number (or viscosity). Our finding in viscous reconnection, complementing numerous works on quantum vortex reconnection, suggests that there is indeed a universal route for reconnection – an essential result for understanding the various facets of the vortex reconnection phenomena and their potential modelling, as well as possibly explaining turbulence cascade physics.

Hubei province in China has had the most confirmed coronavirus disease 2019 (COVID-19) cases and has reported sustained transmission of the disease. Although Lu'an city is adjacent to Hubei province, its community transmission was blocked at the early stage, and the impact of the epidemic was limited. Therefore, we summarised the overall characteristics of the entire epidemic course in Lu'an to help cities with a few imported cases better contain the epidemic. A total of 69 confirmed COVID-19 cases and 11 asymptomatic carriers were identified in Lu'an during the epidemic from 12 January to 21 February 2020. Fifty-two (65.0%) cases were male, and the median age was 40 years. On admission, 56.5% of cases had a fever as the initial symptom, and pneumonia was present in 89.9% of cases. The mean serial interval and the mean duration of hospitalisation were 6.5 days (95% CI: 4.8–8.2) and 18.2 days (95% CI: 16.8–19.5), respectively. A total of 16 clusters involving 60 cases (17 first-generation cases and 43 secondary cases) were reported during the epidemic. We observed that only 18.9% (7/37) index cases resulted in community transmission during the epidemic in Lu'an, indicating that the scale of the epidemic was limited to a low level in Lu'an city. An asymptomatic carrier caused the largest cluster, involving 13 cases. Spread of COVID-19 by asymptomatic carriers represents an enormous challenge for countries responding to the pandemic.

This paper presents a computational study on the free forward flight and sideslip manoeuvre of an insect-like flapping-wing flyer modelled after the hummingbird hawkmoth (Macroglossum stellatarum), with Reynolds number ${\sim}3000$. The numerical model integrated a Navier–Stokes fluid solver with the Newtonian free-body dynamics of the flyer. A generic proportional–integral–derivative (PID)-based wing kinematics controller was used to achieve stable controlled flight. State-equation analyses of flight dynamics were helpful in identifying the roles of kinematic wing actions and for establishing control coefficients for stable flight. Forward flights up to a speed of $4.3~\text{m}~\text{s}^{-1}$ were simulated, which show that the wingbeat frequency decreased below the hovering frequency for cruising flight in the low- and medium-speed range, and higher frequency was only needed for high-speed flight. Similarly, the aerodynamic power consumption was also lower than that for hovering flight over the simulated speed range, due to the contribution of wing drag to overall lift. In addition, flight with higher speed tends to be more efficient in terms of energy consumption for the same distance travelled. In a complete sideslip manoeuvre, the model hawkmoth took approximately 20 wing cycles to translate laterally 4.5 wing lengths to its right and another 30 wing cycles to stabilize hovering at the new location. Slightly higher wingbeat frequency and power were required during the sideslipping phase to adjust for drop in lift due to body roll. The evolution of the vortical wakes reflects quite well the major mechanisms of force generation that were at play at key stages in these flights.

Recognizing the fact that the finite-time singularity of the Navier–Stokes equations is widely accepted as a key issue in fundamental fluid mechanics, and motivated by the recent model of Moffatt & Kimura (J. Fluid Mech., vol. 861, 2019a, pp. 930–967; J. Fluid Mech., vol. 870, 2019b, R1) on this issue, we have performed direct numerical simulation (DNS) for two colliding slender vortex rings of radius $R$. The separation between the two tipping points $2s_{0}$ and the scale of the core cross-section $\unicode[STIX]{x1D6FF}_{0}$ are chosen as $\unicode[STIX]{x1D6FF}_{0}=0.1s_{0}=0.01R$; the vortex Reynolds number ($Re=\text{circulation/viscosity}$) ranges from 1000 to 4000. In contrast to the claim that the core remains compact and circular, there is notable core flattening and stripping, which further increases with $Re$ – akin to our previous finding in the standard anti-parallel vortex reconnection. Furthermore, the induced motion of bridges arrests the curvature growth and vortex stretching at the tipping points; consequently, the maximum vorticity grows with $Re$ substantially slower than the exponential scaling predicted by the model – implying that, for this configuration, even physical singularity is unlikely. Our simulations not only shed light on the longstanding question of finite-time singularities, but also further delineate the detailed mechanisms of reconnection. In particular, we show for the first time that the separation distance $s(\unicode[STIX]{x1D70F})$ before reconnection follows 1/2 scaling exactly – a significant DNS result.