Hand, foot, and mouth disease (HFMD) shows spatiotemporal heterogeneity in China. A spatiotemporal filtering model was constructed and applied to HFMD data to explore the underlying spatiotemporal structure of the disease and determine the impact of different spatiotemporal weight matrices on the results. HFMD cases and covariate data in East China were collected between 2009 and 2015. The different spatiotemporal weight matrices formed by Rook, K-nearest neighbour (KNN; K = 1), distance, and second-order spatial weight matrices (SO-SWM) with first-order temporal weight matrices in contemporaneous and lagged forms were decomposed, and spatiotemporal filtering model was constructed by selecting eigenvectors according to MC and the AIC. We used MI, standard deviation of the regression coefficients, and five indices (AIC, BIC, DIC, R2, and MSE) to compare the spatiotemporal filtering model with a Bayesian spatiotemporal model. The eigenvectors effectively removed spatial correlation in the model residuals (Moran’s I < 0.2, p > 0.05). The Bayesian spatiotemporal model’s Rook weight matrix outperformed others. The spatiotemporal filtering model with SO-SWM was superior, as shown by lower AIC (92,029.60), BIC (92,681.20), and MSE (418,022.7) values, and higher R2 (0.56) value. All spatiotemporal contemporaneous structures outperformed the lagged structures. Additionally, eigenvector maps from the Rook and SO-SWM closely resembled incidence patterns of HFMD.

Direct numerical simulations in a low-curvature viscoelastic turbulent Taylor vortex flow, with Reynolds numbers ranging from 1500 to 8000 and maximum chain extensibility ($L$) from 50 to 200, reveal a maximum drag reduction (MDR) asymptote. Compared with the classical MDR observed in planar wall-bounded shear flows, that is, drag reduction (DR) is $\sim -80\, \%$, this MDR state achieves only moderate levels of DR ($\sim -60\,\%$). This is due to the existence of large-scale structures (LSSs). A careful examination of the flow structures reveals that the polymer–turbulence interaction suppresses small-scale vortices and stabilizes the LSSs. These structural changes in turn lead to a reduction of Reynolds stress, and consequently to a DR flow state. Although Reynolds stress does not vanish as observed in classical MDR states, the small-scale vortices that heavily populate the near-wall region are also almost completely eliminated in this flow state. Concurrently, significant polymer stresses develop as a consequence of the interaction between polymer chains and LSSs that partially offset the magnitude of DR, leading to MDR asymptotes with moderate levels of DR. Moreover, we demonstrate that polymer deformation, i.e. deviation from the equilibrium state, is directly correlated with the LSSs dynamics, while the polymer deformation fluctuation displays a universal property in the MDR state. Hence, it is not surprising that the extent of DR exhibits a non-monotonic dependence on the maximum chain extensibility. Specifically, the variation in $L$ alters the incoherent and coherent angular momentum transport by small- and large-scale flow structures, respectively. To that end, the most DR flow state occurs at a moderate value $L=100$. Overall, this study further supports the universal property of polymer-induced asymptotic states in wall-bounded turbulence and paves the way for mechanistic understanding of drag modification that arises from the interaction of polymers with small- and large-scale flow structures.

Little is known about the association between iodine nutrition status and bone health. The present study aimed to explore the connection between iodine nutrition status, bone metabolism parameters, and bone disease (osteopenia and osteoporosis). A cross-sectional survey was conducted involving 391, 395, and 421 adults from iodine fortification areas (IFA), iodine adequate areas (IAA), and iodine excess areas (IEA) of China. Iodine nutrition status, bone metabolism parameters and BMD were measured. Our results showed that, in IEA, the urine iodine concentrations (UIC) and serum iodine concentrations (SIC) were significantly higher than in IAA. BMD and Ca2+ levels were significantly different under different iodine nutrition levels and the BMD were negatively correlated with UIC and SIC. Univariate linear regression showed that gender, age, BMI, menopausal status, smoking status, alcohol consumption, UIC, SIC, free thyroxine, TSH, and alkaline phosphatase were associated with BMD. The prevalence of osteopenia was significantly increased in IEA, UIC ≥ 300µg/L and SIC > 90µg/L groups. UIC ≥ 300µg/L and SIC > 90µg/L were risk factors for BMD T value < -1.0 SD. In conclusion, excess iodine can not only lead to changes in bone metabolism parameters and BMD, but is also a risk factor for osteopenia and osteoporosis.

Energy inefficiency and environmental damages caused by this inefficiency are increasingly common in developing countries. As the largest developing country, China is experiencing a rapid growth in outward foreign direct investment (OFDI). Do OFDI firms have higher energy efficiency in the same sector? After OFDI, how does the energy efficiency of the firms change? In this study, we employ the data from Chinese industrial firms to empirically investigate these questions. Our results show that OFDI firms have higher energy efficiency and total factor energy efficiency (TFEE) relative to non-OFDI firms in the same sector. After OFDI, firms improve energy efficiency and TFEE through expanding output scale. In addition, these effects are found to be heterogeneous in terms of energy types as well as OFDI motivations and destinations. In general, this study provides some initial evidence for the relationship between OFDI and energy performance at the firm level.

Turbulent flow induced by elastorotational instability in viscoelastic Taylor–Couette flow (TCF) with Keplerian rotation is analogous to a turbulent accretion disk destabilized by magnetorotational instability. We examine this novel viscoelastic Keplerian turbulence via direct numerical simulations (DNS) for the shear Reynolds number ($Re$) ranging from $10^2$ to $10^4$. The observed characteristic flow structure consists of penetrating streamwise vortices with axial length scales much smaller than the gap width, distinct from the classic centrifugally induced Taylor vortices, which have axial lengths of the gap width. These intriguing vortices persist for the wide $Re$ range considered and give rise to intriguing scaling behaviour in key flow quantities. Specifically, the characteristic axial length of the penetrating vortices is shown to scale as $Re^{-0.22}$; the angular momentum transport scales as $Re^{0.42}$; the kinetic and elastic boundary-layer thicknesses based on angular velocity and hoop stress near the inner cylinder wall scale as $Re^{-0.48}$ and $Re^{-0.49}$, respectively. This implies that the viscoelastic Keplerian turbulence belongs to the classical turbulent regime of TCF with the Prandtl–Blasius-type boundary layer. Furthermore, we present an analytical relation between the viscous and elastic dissipation rates of kinetic energy and the angular momentum transport and in turn demonstrate its validity using our DNS data. This study has paved the way for future research to explore astrophysics-related Keplerian turbulence and angular momentum transport via the scaling relations of the analogous TCF of dilute polymeric solutions.

Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$, due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.

A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a unified and concise mathematical form, with clear physical meanings and extensibility. The bubble oscillation equation can be simplified to the Keller–Miksis equation by neglecting the effects of phase transition and bubble migration. The present theoretical model effectively captures the experimental results for bubbles generated in free fields, near free surfaces, adjacent to rigid walls, and in the vicinity of other bubbles. Based on the present theory, we explore the effect of the bubble content by changing the vapour proportion inside the cavitation bubble for an initial high-pressure bubble. It is found that the energy loss of the bubble shows a consistent increase with increasing Mach number and initial vapour proportion. However, the radiated pressure peak by the bubble at the collapse stage increases with decreasing Mach number and increasing vapour proportion. The energy analyses of the bubble reveal that the presence of vapour inside the bubble not only directly contributes to the energy loss of the bubble through phase transition but also intensifies the bubble collapse, which leads to greater radiation of energy into the surrounding flow field due to the fluid compressibility.

This study aimed to explore the combined association between the dietary antioxidant quality score (DAQS) and leisure-time physical activity on sleep patterns in cancer survivors. Data of cancer survivors were extracted from the National Health and Nutrition Examination Surveys database in 2007–2014 in this cross-sectional study. Weighted multivariable logistic regression models were used to estimate OR and 95 % CI for the association of DAQS and leisure-time physical activity on sleep patterns. The combined association was also assessed in subgroups of participants based on age and use of painkillers and antidepressants. Among the eligible participants, 1133 had unhealthy sleep patterns. After adjusting for covariates, compared with low DAQS level combined with leisure-time physical activity level < 600 MET·min/week, high DAQS level combined with leisure-time physical activity ≥ 600 MET·min/week was associated with lower odds of unhealthy sleep patterns (OR = 0·41, 95 % CI: 0·23, 0·72). Additionally, the association of high DAQS level combined with high leisure-time physical activity with low odds of unhealthy sleep patterns was also significant in < 65 years old (OR = 0·30, 95 % CI: 0·13, 0·70), non-painkiller (OR = 0·39, 95 % CI: 0·22, 0·71), non-antidepressant (OR = 0·49, 95 % CI: 0·26, 0·91) and antidepressant (OR = 0·11, 95 % CI: 0·02, 0·50) subgroups. DAQS and leisure-time physical activity had a combined association on sleep patterns in cancer survivors. However, the causal associations of dietary nutrient intake and physical activity with sleep patterns in cancer survivors need further clarification.

The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

The evolution of the water-entry cavity affects the impact load and the motion of the body. This paper adopts the Eulerian finite element method for multiphase flow for simulations of the high-speed water-entry process. The accuracy and convergence of the numerical method are verified by comparing it with the experimental data and the results of the transient cavity dynamics theory. Based on the results, the representative characteristics of the cavity are discussed from the perspective of the cavity cross-section. It is found that the asymmetry of the cavity expansion and contraction durations is related to the motion of the free surface and the closure of the cavity. The uplift of the free surface suppresses cavity expansion, while the jet generated from free surface closure accelerates cavity contraction. The duration of the contraction of the cavity near the free surface is shorter than the expansion duration due to the change in the velocity distribution caused by the free surface motion. The necking phenomenon during deep closure leads to an increase in the internal pressure of the cavity, prolonging cavity contraction near the deep closure area. This work provides new insights into the cavity dynamics in high-speed water entry.

The deceleration effect of the deployable aerodynamic decelerator is not as good as a parachute in the subsonic region. This paper proposes a novel concept of using a parachute-like configuration (PLC) to enhance the deceleration performance of the mechanically deployable aerodynamic decelerator (MDAD) through structural transformation. The MDAD turned into the PLC from the sphere cone configuration (SCC) at Ma 0.8. The aerodynamic characteristics of the two configurations are analysed deeply. Compared to the SCC, the results show that the drag coefficient increases effectively, and the maximum increases is about 10% in the PLC. The airflow is altered by the MDAD configuration, which can affect the surface pressure and temperature. During the transformation process, the axial and normal force coefficients tend to stabilise. However, the static stability of the PLC deteriorates sharply compared to the SCC when the angle-of-attack exceeds 45°.

The fall armyworm (FAW) Spodoptera frugiperda (J.E. Smith) is a highly damaging invasive omnivorous pest that has developed varying degrees of resistance to commonly used insecticides. To investigate the molecular mechanisms of tolerance to tetraniliprole, spinetoram, and emamectin benzoate, the enzyme activity, synergistic effect, and RNA interference were implemented in S. frugiperda. The functions of cytochrome P450 monooxygenase (P450) in the tolerance to tetraniliprole, spinetoram, and emamectin benzoate in S. frugiperda was determined by analysing changes in detoxification metabolic enzyme activity and the effects of enzyme inhibitors on susceptibility to the three insecticides. 102 P450 genes were screened via transcriptome and genome, of which 67 P450 genes were differentially expressed in response to tetraniliprole, spinetoram, and emamectin benzoate and validated by quantitative real-time PCR. The expression patterns of CYP9A75, CYP340AA4, CYP340AX8v2, CYP340L16, CYP341B15v2, and CYP341B17v2 were analysed in different tissues and at different developmental stages in S. frugiperda. Silencing CYP340L16 significantly increased the susceptibility of S. frugiperda to tetraniliprole, spinetoram, and emamectin benzoate. Furthermore, knockdown of CYP340AX8v2, CYP9A75, and CYP341B17v2 significantly increased the sensitivity of S. frugiperda to tetraniliprole. Knockdown of CYP340AX8v2 and CYP340AA4 significantly increased mortality of S. frugiperda to spinetoram. Knockdown of CYP9A75 and CYP341B15v2 significantly increased the susceptibility of S. frugiperda to emamectin benzoate. These results may help to elucidate the mechanisms of tolerance to tetraniliprole, spinetoram and emamectin benzoate in S. frugiperda.

Vegetables are known to be beneficial to human health, but the association between vegetable consumption and gastric cancer remains uncertain. To synthesise knowledge about the relationship between vegetable group consumption and gastric cancer risk, update present meta-analyses and estimate associations between vegetable consumption and gastric cancer risk based solely on prospective studies, we perform a PRISMA-compliant three-level meta-analysis. Systematic search identified thirteen prospective studies with fifty-two effect sizes that met all inclusion criteria and no exclusion criteria for our meta-analysis. Pooled risk ratios (RRs) showed a positive association between high vegetable consumption and low gastric cancer risk (pooled RR 0·93, 95% confidence interval 0·90–0·97, P = 0·06). In moderator analyses for indicators of gender, region and quantity of vegetable intake, there was no significant difference between subgroups. However, the effect became significant in populations with lower than the minimum risk exposure level (TMREL) of vegetable consumption (P < 0·05). Higher vegetable intake is associated with a decreased risk of gastric cancer. This effect may be limited to specific populations, such as ones with lower vegetable consumption. Evidence from our study has important public health implications for dietary recommendations.

This study presents a comprehensive analysis on the extreme positive and negative events of wall shear stress and heat flux fluctuations in compressible turbulent boundary layers (TBLs) solved by direct numerical simulations. To examine the compressibility effects, we focus on the extreme events in two representative cases, i.e. a supersonic TBL of Mach number $M=2$ and a hypersonic TBL of $M=8$, by scrutinizing the coherent structures and their correlated dynamics based on conditional analysis. As characterized by the spatial distribution of wall shear stress and heat flux, the extreme events are indicated to be closely related to the structural organization of wall streaks, in addition to the occurrence of the alternating positive and negative structures (APNSs) in the hypersonic TBL. These two types of coherent structures are strikingly different, namely the nature of wall streaks and APNSs are shown to be related to the solenoidal and dilatational fluid motions, respectively. Quantitative analysis using a volumetric conditional average is performed to identify and extract the coherent structures that directly account for the extreme events. It is found that in the supersonic TBL, the essential ingredients of the conditional field are hairpin-like vortices, whose combinations can induce wall streaks, whereas in the hypersonic TBL, the essential ingredients become hairpin-like vortices as well as near-wall APNSs. To quantify the momentum and energy transport mechanisms underlying the extreme events, we proposed a novel decomposition method for extreme skin friction and heat flux, based on the integral identities of conditionally averaged governing equations. Taking advantage of this decomposition method, the dominant transport mechanisms of the hairpin-like vortices and APNSs are revealed. Specifically, the momentum and energy transports undertaken by the hairpin-like vortices are attributed to multiple comparable mechanisms, whereas those by the APNSs are convection dominated. In that, the dominant transport mechanisms in extreme events between the supersonic and hypersonic TBLs are indicated to be totally different.

Instability evolutions of shock-accelerated thin cylindrical SF$_6$ layers surrounded by air with initial perturbations imposed only at the outer interface (i.e. the ‘Outer’ case) or at the inner interface (i.e. the ‘Inner’ case) are numerically and theoretically investigated. It is found that the instability evolution of a thin cylindrical heavy fluid layer not only involves the effects of Richtmyer–Meshkov instability, Rayleigh–Taylor stability/instability and compressibility coupled with the Bell–Plesset effect, which determine the instability evolution of the single cylindrical interface, but also strongly depends on the waves reverberated inside the layer, thin-shell correction and interface coupling effect. Specifically, the rarefaction wave inside the thin fluid layer accelerates the outer interface inward and induces the decompression effect for both the Outer and Inner cases, and the compression wave inside the fluid layer accelerates the inner interface inward and causes the decompression effect for the Outer case and compression effect for the Inner case. It is noted that the compressible Bell model excluding the compression/decompression effect of waves, thin-shell correction and interface coupling effect deviates significantly from the perturbation growth. To this end, an improved compressible Bell model is proposed, including three new terms to quantify the compression/decompression effect of waves, thin-shell correction and interface coupling effect, respectively. This improved model is verified by numerical results and successfully characterizes various effects that contribute to the perturbation growth of a shock-accelerated thin heavy fluid layer.

Six consecutive solitary waves with identical wave height and separation time are generated to study the flow structures during the uprush–downwash interactions in the swash zone. Using particle image velocimetry, the cross-shore velocity fields are captured. Two different wave conditions are examined with different wave-height-to-water-depth ratios, i.e. $H_o/h=0.11$ and 0.22. The uprush–downwash interaction reaches quasi-steady state from the third solitary wave for both cases. For the former case, a weak non-stationary hydraulic jump appears during the downwash flow for all the six consecutive waves. The weak hydraulic jump evolves into a momentarily ‘stationary’ broken bore when the next wave arrives. For the latter case, the larger wave height generates stronger wave breaking. No non-stationary hydraulic jump is observed as the duration of downwash flow is relatively short. The flow reverses to the onshore direction before the downwash Froude number reaches the hydraulic jump condition. The temporal and spatial evolution of turbulence structure at the quasi-steady state is quantified using the spatial spectral analysis, the integral length scale and turbulence eddy viscosity. The results suggest that the large-scale energy generated during the uprush–downwash interaction modified the slope of the turbulence energy spatial spectrum in the inertial subrange from $-$5/3 to $-$1 in the larger length scale region, indicating the energy cascade depends not only on the dissipation rate, but also on the turbulent kinetic energy from the large-scale turbulence structure because of the large-scale energy injection in the inertial subrange.

A novel data-driven modal analysis method, reduced-order variational mode decomposition (RVMD), is proposed, inspired by the Hilbert–Huang transform and variational mode decomposition (VMD), to resolve transient or statistically non-stationary flow dynamics. First, the form of RVMD modes (referred to as an ‘elementary low-order dynamic process’, ELD) is constructed by combining low-order representation and the idea of intrinsic mode function, which enables the computed modes to characterize the non-stationary properties of space–time fluid flows. Then, the RVMD algorithm is designed based on VMD to achieve a low-redundant adaptive extraction of ELDs in flow data, with the modes computed by solving an elaborate optimization problem. Further, a combination of RVMD and Hilbert spectral analysis leads to a modal-based time-frequency analysis framework in the Hilbert view, providing a potentially powerful tool to discover, quantify and analyse the transient and non-stationary dynamics in complex flow problems. To provide a comprehensive evaluation, the computational cost and parameter dependence of RVMD are discussed, as well as the relations between RVMD and some classic modal decomposition methods. Finally, the virtues and utility of RVMD and the modal-based time-frequency analysis framework are well demonstrated via two canonical problems: the transient cylinder wake and the planar supersonic screeching jet.

Iodine is an essential nutrient that may change the occurrence of autoimmune thyroiditis (AIT). Apoptosis and DNA methylation participate in the pathogenesis and destructive mechanism of AIT. We detected the methylation and the expression of mRNA of intrinsic apoptosis-associated genes (YWHAG, ING4, BRSK2 and GJA1) to identify the potential interactions between the levels of methylation in these genes and different levels of iodine. 176 adult patients with AIT in Shandong Province, China, were included. The MethylTargetTM assay was used to verify the levels of methylation. We used PCR to detect the mRNA levels of the candidate genes. Interactions between methylation levels of the candidate genes and iodine levels were evaluated with multiplicative and addictive interaction models and GMDR. In the AIT group, YWHAG_1 and six CpG sites and BRSK2_1 and eight CpG sites were hypermethylated, whereas ING4_1 and one CpG site were hypomethylated. A negative correlation was found between methylation levels of YWHAG and mRNA expression. The combination of iodine fortification, YWHAG_1 hypermethylation and BRSK2_1 hypermethylation was significantly associated with elevated AIT risk. A four-locus model (YWHAG_1 × ING4_1 × BRSK2_1 × iodine level) was found to be the best model of the gene–environment interactions. We identified abnormal changes in the methylation status of YWHAG, ING4 and BRSK2 in patients with AIT in different iodine levels. Iodine fortification not only affected the methylation levels of YWHAG and BRSK2 but also interacted with the methylation levels of these genes and may ultimately increase the risk of AIT.

Vertically neutral collapse of a pulsating bubble occurs when the boundaries above or below the bubble balance the buoyancy effect over a pulsation. In this study, the vertically neutral collapse of a bubble near a vertical rigid wall below the free surface is investigated. The boundary integral method (BIM) is employed to model the bubble dynamics with an open-domain free surface. Moreover, this method is validated against several buoyant bubble experiments. Bubble dynamics in such conditions are associated with three dimensionless parameters: the bubble-free surface distance $\gamma _{{f}}$, bubble–wall distance $\gamma _{{w}}$ and buoyancy parameter $\delta$. We derive the Kelvin impulse of a spherical bubble and the algebraic relationship for vertically neutral collapse, which proves to be accurate for predicting vertically neutral collapse when the bubble is relatively far from the boundaries. Four patterns of the vertically neutral collapse of the bubble for different $\gamma _{{w}}$ and $\gamma _{{f}}$ are identified: (i) formally downward jet; (ii) annular collapse; (iii) horizontal jet; and (iv) weak jet. Despite the downward jet shape, the ‘formally downward jet’ is in the vertically neutral collapse state in terms of the profile of toroidal bubbles and the orientation of local high-pressure zones around the bubble at jet impact. A bulge with a high curvature above the bubble in the ‘annular collapse’ pattern is formed during bubble collapse under two local high-pressure zones at the left and right extremities of the bubble. The ‘horizontal jet’ pattern has the greatest potential to attack the wall, and the power laws of the moment of the jet impact, jet velocity and bubble displacement with respect to the theoretical Kelvin impulse are discussed. In particular, we quantitatively illustrate the role of the free surface on bubble migration towards the wall through the variational power-law exponents of the bubble displacement with respect to $\gamma _{{w}}$.