Direct numerical simulations are performed to elucidate the influence of counter- and co-rotation on turbulent viscoelastic Taylor–Couette flow in the Rossby number range $ \textit{Ro}^{-1}=-0.6$ to $ \textit{Ro}^{-1}=1$. A novel polymer-induced transition pathway is discovered that is fundamentally different from Newtonian flows. In the counter-rotation regime, the neutral surface is elastically modified and separates the turbulent inner-wall region containing chaotic vortices from the relaminarised layer adjacent to the outer cylinder. Strikingly, co-rotation triggers an elasto-rotational instability, which leads to the breakdown of large-scale Taylor vortices into small-scale penetrating structures, thereby preventing the relaminarisation at high co-rotation rates. Examination of turbulence dynamics demonstrates that the structural changes with increasing $ \textit{Ro}^{-1}$ are accompanied by a transition from elasto-inertial to elastically dominated turbulence. Specifically, the polymer stress progressively exceeds the Reynolds stress and monotonically enhances angular momentum transport, which eliminates the optimal transport characteristic found in the Newtonian flow. The elastically dominated nature of the turbulent flow under co-rotation is further corroborated by the more significant elastic production of the turbulent kinetic energy, as well as the monotonic enhancement of the polymer elongation as $ \textit{Ro}^{-1}$ increases. Furthermore, it is indicated that the polymer orientation strongly depends on vortical structures, with enhanced radial alignment occurring in the boundary region between adjacent vortices. This vortex-mediated polymer orientation is crucial for generating substantial polymer shear stress, establishing a direct link between coherent structures and polymer dynamics.

Accurate prediction of the hydrodynamic coefficients of non-spherical particles in wall-confined flows is crucial for understanding particle–fluid interactions and reliable modelling of particle motion. Under strong wall confinement, the hydrodynamic coefficients exhibit a highly nonlinear dependence on the Reynolds number, wall distance and particle orientation – posing significant modelling challenges. In this study, we propose a multi-stage physics-informed machine-learning (MSPIML) framework for modelling the drag, lift and pitching torque coefficients of a wall-bounded prolate spheroid over the explored parameter space. In the first stage, a physics-informed mixture-of-experts (PIMoE) model predicts the drag coefficient by intelligently blending empirical correlations with a data-driven statistical expert. The resulting high-fidelity drag coefficient is then injected as an auxiliary input to a second-stage model, either a deep neural network (DNN) or an additional MoE, that predicts lift and pitching torque coefficients, thereby leveraging the strong physical coupling among the three coefficients. Trained on a comprehensive dataset of 720 direct numerical simulations covering wide ranges of Reynolds number, wall distance and particle orientation, the optimal PIMoE–DNN and PIMoE–MoE configurations achieve relative errors below 2.2 % for drag, 11.4 % for lift and 7.0 % for pitching torque while maintaining excellent generalisation across the entire parameter space. Moreover, the Shapley additive explanations analysis confirms that the MSPIML framework correctly captures the physical dependencies: dominant influence of Reynolds number and strong pitching torque dependence on the drag coefficient. The MSPIML framework provides an interpretable and efficient approach to the prediction of hydrodynamic coefficients and offers substantial potential for dynamic modelling of non-spherical particles in multiphase flows.

The study of rotating Rayleigh–Taylor (RT) turbulence is of fundamental significance for geophysical processes and certain engineering applications. This work systematically investigates the effects of rotation on RT turbulence using direct numerical simulation (DNS), focusing primarily on the generation of kinetic energy and enstrophy, as well as the scale-to-scale transfer of kinetic energy. Based on the DNS results, it is demonstrated that there is a notable delay and inhibition of the mixing layer growth with enhancing rotation (quantified as a decreasing Rossby number, $Ro$). That is, energy conversion efficiency drops substantially, from approximately $50\,\%$ in the non-rotating case $Ro = \infty$ to only $10\,\%$ in the strong rotating case $Ro=0.1$. This is because rotation amplifies the viscous dissipation associated with the shear stress components in the vertical direction within the mixing layer. Regarding enstrophy generation, baroclinic effects dominate during the early stage of flow evolution, while vortex stretching and tilting become the primary contributors in the later stage. Notably, the vortex stretching and tilting term is significantly suppressed by the rotation, resulting in three-dimensional RT turbulence exhibiting an enstrophy generation mechanism more akin to two-dimensional flow. Furthermore, analysis of scale-to-scale transfer of kinetic energy reveals an increased likelihood of local inverse energy transfer events under enhanced rotation. Specifically, strong rotation (e.g. $Ro=0.1$) results in strongly helical turbulence, which contains more high-helicity regions favourable for local inverse energy transfer. Moreover, the presence of rotation leads to more coherent and elongated flow structures and an enhanced efficiency of fluid mixing within the mixing layer.

Compressible wall-bounded turbulent flows exhibit complex mean profiles because of the pronounced compressibility effects and heat transfer. We propose a hybrid transformation framework to collapse compressible mean velocity and temperature profiles onto incompressible forms through scaling each layer by its effective transformation, with the underlying mapping functions discovered via a physics-informed symbolic regression (PISR) method. The hybrid velocity transformation incorporates an intrinsic compressibility correction for the buffer layer and a PISR-derived mapping function for the logarithmic layer. For temperature, we introduce a hybrid transformation that integrates the Mach-invariant-type transformation in the viscous sublayer and a novel PISR-derived scaling in the logarithmic layer. The performance of these transformations is evaluated across compressible turbulent boundary layers with free-stream Mach numbers ranging from 0.5 to 8 and wall-to-recovery-temperature ratios ranging from 0.25 to 1. The hybrid velocity transformation outperforms Griffin–Fu–Moin transformation for the transformed mean velocity profiles, with the mean integrated percent error across the dataset decreasing from 1.67 % to 0.96 %. The hybrid temperature transformation performs better than the Mach-invariant-type and Trettel–Larsson-type transformations for mean temperature profiles. Moreover, the inverse hybrid velocity and temperature transformations can effectively predict the compressible mean velocity and temperature profiles with only wall conditions.

Despite its significant role in relation to wellbeing among older adults with disabilities, the quality of care from family care-givers is largely understudied. This study aims to (a) investigate the mediating roles of care-giving appraisals in the association between care-giving stressors and quality of care; and (b) examine the moderating role of shared care-giving in the above associations. This study adopted a cross-sectional survey design. Data were collected in Changchun, China using stratified sampling. A total of 416 family care-givers of older adults with disabilities were enrolled. Structural equation modelling, including mediation analysis and multiple-group analysis, was performed to examine the proposed hypotheses. Results showed that low levels of care-giving burden and high levels of positive aspects of care-giving were related to higher quality of care. Older adults’ cognitive impairment had direct negative association with quality of care, while impairment in activities of daily living and instrumental activities of daily living had indirect negative associations with quality of care through care-giving burden. Shared care-giving significantly moderated the association between care-giving burden and quality of care, with the negative association being significant only among sole care-givers. In sum, this study suggested that care-giving stressors and appraisals were important factors associated with quality of care, and shared care-giving could attenuate the negative association between care-giving burden and quality of care. Social services and interventions on both primary care-givers and the family care-giving system should be provided to enhance quality of care for older adults with disabilities.

Asymptotic flow states with limiting drag modification are explored via direct numerical simulations in a moderate-curvature viscoelastic Taylor–Couette flow of the FENE-P fluid. We show that asymptotic drag modification (ADM) states are achieved at different solvent-to-total viscosity ratios ($\beta$) by gradually increasing the Weissenberg number from 10 to 150. As $\beta$ decreases from 0.99 to 0.90, for the first time, a continuous transition pathway is realised from the maximum drag reduction to the maximum drag enhancement, revealing a complete phase diagram of the ADM states. This transition originates from the competition between Reynolds stress reduction and polymer stress development, namely, a mechanistic change in angular momentum transport. Reduced $\beta$ has been found to effectively enhance elastic instability, suppressing large-scale Taylor vortices while promoting the formation of small-scale elastic Görtler vortices. The enhancement and in turn dominance of small-scale structures result in stronger incoherent transport, facilitating efficient mixing and substantial polymer stress development that ultimately drives the AMD state transition. Further analysis of the scale-decomposed transport equation of turbulent kinetic energy reveals an inverse energy cascade in the gap centre, which is attributed to the polymer-induced energy redistribution: polymers extract more energy from large scales than they can dissipate, with the excess energy redirected to smaller scales. However, the energy accumulating at smaller scales cannot be dissipated immediately and is consequently transferred back to larger scales via nonlinear interactions, thereby unravelling a novel polymer-mediated cycle for the reverse energy cascade. Overall, this study unravels the challenging puzzle of the existence of distinct dynamically connected ADM states and paves the way for coordinated experimental, simulation and theoretical studies of transition pathways to desired ADM states.

Wall pressure fluctuations (WPFs) over aerodynamic surfaces contribute to the physical origin of noise generation and vibrational loading. Understanding the generation mechanism of WPFs, especially those exhibiting extremely high amplitudes, is important for advancing design and control in practical applications. In this work, we systematically investigate extreme events of WPFs in turbulent boundary layers and the compressibility effects thereon. The compressibility effects, encompassing extrinsic and intrinsic ones, ranging from weak to strong, are achieved by varying Mach numbers and wall temperatures. A series of datasets at moderate Reynolds numbers obtained from direct numerical simulation are analysed. It is found that the intermittency of WPFs depends weakly on extrinsic compressibility effects, whereas intrinsic compressibility effects significantly enhance intermittency at small scales. Coherent structures related to extreme events are identified using volumetric conditional average. Under extrinsic compressibility effects, extreme events are associated with the weak dilatation structures induced by interactions of high- and low-speed motions. When intrinsic compressibility effects dominate, these events are associated with the strong alternating positive and negative dilatation structures embedded in low-speed streaks. Furthermore, Poisson-equation-based pressure decomposition is performed to partition pressure fluctuations into components governed by distinct physical mechanisms. By analysing the proportion of each pressure component in extreme events, it is found that the contributions of the slow pressure and viscous pressure exhibit weak dependence on the compressibility effects, especially the extrinsic ones, and the varying trend of contributions of the rapid pressure with compressibility effects is opposite to that of the compressible pressure component.

The featured article introduces a much-needed theoretical framework for developing a dual-process model of life history calibration. This model accounts for the counterbalancing effects of individual energetic stresses and extrinsic mortality threats of the environment. This framework also reinstates resource availability – a key determinant of energetic conditions – into life history research, resolving its previous exclusion due to similar countervailing influences relative to extrinsic mortality threats.

Large-scale circulation (LSC) dynamics have been studied in thermal convection driven by heat-releasing particles via the four-way coupled Euler–Lagrange approach. We consider a wide range of Rayleigh–Robert number (${\textit{Rr}}=4.97\times 10^{5} - 4.97 \times 10^{8}$) and density ratio ($\hat {\rho }_r=1- 1000$) that characterize the thermal buoyancy and the particle inertia, respectively. An intriguing flow transition has been found as $\hat {\rho }_r$ continuously increases, involving in sequence three typical LSC regimes, i.e. the bulk-flow-up regime, the marginal regime and the bulk-flow-down (BFD) regime. The comprehensive influence of the LSC regime transition is demonstrated by examining the key flow statistics. As integral flow responses, the heat transfer efficiency and flow intensity change substantially when the LSC regime transition happens, and the thermal boundary layer thicknesses at the top and bottom walls exhibit similar alterations. Significant local accumulation of particles occurs as $\hat {\rho }_r$ increases to a sufficiently high value, resulting in a great modification in the flow dynamics. Specifically, particles aggregate near the sidewalls and heat the local surrounding fluid to generate rising warmer plumes that drive the LSC regime transition. Of interest, well-patterned cellular structures of particles take place near the top wall and obtain notable deviation from the thermal convection cells for the BFD regimes. A mechanical interpretation is proposed and substantiated based on a conceptual vortex–particle model, namely, the centrifugal motion of heat-releasing particles that is confirmed to play a driving role for the LSC regime transition.

The evolution of the mixing layer in rotation-driven Rayleigh–Taylor (RT) turbulence is investigated theoretically and numerically. It is found that the evolution of the turbulent mixing layer in rotation-driven RT turbulence is self-similar, but the width of the mixing layer does not follow the classical quadratic growth observed in planar RT turbulence induced by constant external acceleration. Based on the approach used in cylindrical RT turbulence without rotation (Zhao et al. 2021, Phys. Rev. E, vol. 104, 055104), a theoretical model is established to predict the growth of mixing widths in rotation-driven RT turbulence, and the model’s excellent agreement with direct numerical simulations (DNS) serves to validate its reliability. The model proposes a rescaled time that allows for the unification of the evolutions of the mixing layers in rotation-driven RT turbulence with various Atwood numbers and rotation numbers. It is further identified that the growth law described by the model of rotation-driven RT turbulence can be recovered to quadratic growth when the effects of geometrical curvature, radial inhomogeneity of the centrifugal force, and Coriolis force become negligible. Moreover, based on the DNS results, we find that turbulent mixing layers in rotation-driven RT turbulence cover a wide range of length scales. The strong rotation at the same Atwood number enhances the generation of fine-scale structures but is not conducive to overall fluid mixing within the mixing layer.

The effect of Stokes number on turbulence modulation in particle-laden channel flow is investigated through four-way coupled point-particle direct numerical simulations, with the mass loading fixed at 0.6 and the friction Stokes number $St^+$ varying from 3 to 300. A full transition pathway is observed, from a drag-enhanced to a drag-reduced regime, eventually approaching the single-phase state as $St^+$ increases towards 300. A set of transport equations for the particle phase is derived analytically to characterise the interphase coupling, within the framework of the point-based statistical description of particle-laden turbulence. By virtue of this, two dominant mechanisms are identified and quantitatively characterised: a positive, particle-induced extra transport that decreases monotonically with increasing $St^+$, and a negative, particle-induced extra dissipation that varies non-monotonically with $St^+$. The coupling of these two mechanisms leads to a direct contribution of the particle phase to the shear stress balance, the turbulent kinetic energy budgets and the Reynolds stress budgets. Consequently, as $St^+$ increases, the self-sustaining cycle of near-wall turbulence transitions from being augmented to being suppressed and, eventually, returns to the single-phase state. This gives rise to an indirect effect, manifested as a non-monotonic modulation of Reynolds shear stress and turbulence production rate. Taken together, complex interplays between particle-modified turbulent transport, particle-induced extra transport and extra dissipation are analysed and summarised, providing a holistic physical picture composed of consistent interpretations of turbulence modulation induced by small heavy particles.

Public health crises like Covid-19 profoundly influence informal care-givers of older adults with functional health limitations. This study deepens existing understanding of care-giving processes during the pandemic to uncover insights useful for developing effective care-giving interventions for the post-pandemic era and future public health crises. Specifically, it examined (1) how care-giving activities during the pandemic impacted care-giver psychological wellbeing by affecting caregiving burden and the positive aspects of caregiving and (2) the moderating effect of pandemic-specific factors (i.e., care recipients’ unmet health-care needs due to the pandemic). Multiple-group analyses were conducted on data on 906 informal care-givers of older adults with functional health limitations, obtained from the Covid-19 Supplement and Round 10 Survey of the National Health and Aging Trends Study conducted in the United States. The mean age of participants was approximately 60 years, and most were white women. Positive aspects of care-giving significantly mediated the relationships between providing assistance in activities of daily living (ADL), instrumental ADL, and emotional support and positive affect. Care-giving burden significantly mediated the relationship between assistance in ADL and positive and negative affect. Care recipients’ unmet health-care needs moderated the relationships between assistance in ADL and burden, assistance in ADL and negative affect, and emotional support and positive affect. In sum, this study underscores the positive aspects of care-giving as well as care-giving burden and demonstrates that greater attention should be paid to care-givers caring for individuals with unmet health-care needs during public health crises. The results suggest that more-effective responses to public health crises must be developed, especially within health-care systems.

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.

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.

Scholars have not yet explored the relationship between community social capital and self-rated health (SRH) among older adults in China in depth, including potential moderators in this relationship. In response to this gap, this study aimed to investigate the association between community social capital and SRH among urban Chinese older adults and the moderating roles of instrumental activities of daily living (IADLs) and smoking. We used a quota sampling method to recruit 800 respondents aged 60 years and older from 20 communities in Shijiazhuang and Tianjin, China. SRH was used as the dependent variable. Binary logistic regression models with interaction terms were used to analyse the data. The results showed that trust (a cognitive social capital indicator), volunteering (a structural social capital indicator) and family social capital were significantly associated with SRH when controlling for other social capital indicators and covariates. Difficulties with IADL and smoking significantly moderated the association between community social capital and SRH. Cognitive social capital was only positively associated with SRH health among respondents who did not experience difficulty with IADLs. The positive association between citizenship activities and SRH was only significant among those who experienced difficulty with IADLs. The number of organisational memberships was negatively associated with SRH among respondents with a history of smoking. Volunteering was positively associated with SRH in respondents with a history of smoking. These findings highlight the important role of social capital in promoting SRH among older adults in urban areas of China and notably identify within-population heterogeneity in the associations between social capital and SRH. This study offers insights useful for developing social capital policies and interventions to meet the specific social needs of older adults with varied levels of difficulty with IADLs and health behaviours.

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.

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.

The highly nonlinear evolution of the single-mode stratified compressible Rayleigh–Taylor instability (RTI) is investigated via direct numerical simulation over a range of Atwood numbers ($A_T=0.1$–$0.9$) and Mach numbers ($Ma=0.1$–$0.7$) for characterising the isothermal background stratification. After the potential stage, it is found that the bubble is accelerated to a velocity which is well above the saturation value predicted in the potential flow model. Unlike the bubble re-acceleration behaviour in quasi-incompressible RTI with uniform background density, the characteristics in the stratified compressible RTI are driven by not only vorticity accumulation inside the bubble but also flow compressibility resulting from the stratification. Specifically, in the case of strong stratification and high $A_T$, the flow compressibility dominates the bubble re-acceleration characters. To model the effect of flow compressibility, we propose a novel model to reliably describe the bubble re-acceleration behaviours in the stratified compressible RTI, via introducing the dilatation into the classical model that takes into account only vorticity accumulation.