Vorticity Transport Research Articles

Solar Vortex Tubes. III. Vorticity and Energy Transport

This study investigated the mechanisms of vorticity generation and the role of vortex tubes in plasma heating and energy transport. Vortex tubes were identified using the instantaneous vorticity deviation technique in the MURaM data set of a simulated solar plage region of the solar photosphere. Within 3D kinetic vortex tubes, the misalignment of the magnetic pressure and the inverse of the density gradient, rather than baroclinic effects, primarily drive vorticity within the tubes. During their lifetime, vortices become less dense as the Lorentz force pushes plasma outwards against pressure gradients. In the simulated upper photosphere, the Lorentz force contributes to adiabatic cooling and heating by expanding or compressing the plasma around the vortex tubes. In turn, vortex motion affects the magnetic field, enhancing current generation and intensifying the Lorentz force, which may further increase adiabatic cooling and heating. Moreover, our results confirm that vortices can significantly boost viscous and ohmic heating on intergranular scales in the photosphere. They generate more magnetic than kinetic energy, with energy transport by Poynting flux notably nonuniform and dominant at the vortex boundaries. This creates energy circulation in which the net upwards Poynting flux can enhance chromospheric plasma heating and support chromospheric temperatures.

Influence of the channel inclination on the exchange flow and vorticity transport characteristics in a regenerative flow pump

To enhance the overall performance of regenerative flow pump (RFP) to achieve efficient and stable operation over a broad range, this paper employs numerical simulation to study the internal flow conditions of RFP models with three different inclination coefficients (Ic = −0.25, Ic = 0, Ic = 0.25). The analysis focuses on the pressure distribution, energy exchange, velocity variation, and vorticity distribution characteristics within the impeller and channel. The comparison indicates that at Ic = −0.25 with an outward channel, the flow within the pump is stabilized, and the rate of pressure growth and exchange intensity are increased. When Ic = 0 with a semi-circular channel and Ic = 0.25 with an inward channel, there are narrower flow space at the channel's outer diameter, impeding effective fluid motion along the channel and inducing chaotic flow. This condition escalates flow losses and adversely affects the hydraulic performance of the RFP. Additionally, the analysis based on the vorticity transport equation reveals that the Coriolis force term significantly contributes to the generation and transport of vortex in the impeller, while the vortex stretching term dominates the transport of vortex in the channel.

Numerical studies of hydrodynamic relativistic astrophysical jet: The modification of vorticity transport equation

In this Letter, we have carried out the two-dimensional numerical simulation of axisymmetric relativistic jet in cylindrical coordinates by employing higher order finite volume method in PLUTO [Mignone et al., “PLUTO: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. 170, 228 (2007)] solver. The modified vorticity transport equation has been proposed for relativistic flow by taking the curl of the momentum equation, which shows significant change in the baroclinic vorticity production term due to relativistic effect. Both mathematical analysis and numerical results show that the vorticity production term due to baroclinic torque is heavily influenced due to the presence of specific enthalpy gradient and square of Lorentz factor gradient in a relativistic fluid flow.

An improved detached eddy simulation method for cavitation multiphase flow

The evolution of cavitation flow involves intense transient characteristics and complex multi-scale motions, significantly increasing the difficulty and computational cost of solving in separation zones. This study proposes an Improved Detached Eddy Simulation (IDES) method, based on a single-equation eddy-viscosity model, aimed at enhancing the resolution of small-scale cavitation flows. By incorporating the broad-spectrum von Karman scale concept, the method effectively improves the resolution capability for small-scale flows in separated zones. The performance of the IDES model was validated through three computational cases, and the main conclusions are as follows: The results of the triangular cylinder flows show that the IDES model demonstrates a resolution capability for large-scale turbulence comparable to the Large Eddy Simulation (LES) model. The orifice flow results indicate that activating the LES method with insufficient grid resolution is highly discouraged, whereas the IDES model performs more robustly under such conditions. For hydrofoil flows, the IDES model more accurately captures the temporal evolution of cavitation, avoiding the premature cavity shedding predicted by LES under coarse grid conditions. The decomposition results of the vorticity transport equation show that both the dilatation term and viscous term are significant contributors in the vorticity transport process, with their average contributions to vorticity reaching 49.25% and 39.99%, respectively. Vortices can be considered the primary controllers of cavitation dynamics, while the dilatation term and viscous term can be regarded as the main controllers of vorticity. Overall, the energy compensation mechanism of the IDES model, based on local flow information, gives it unique advantages in handling small-scale turbulence and cavitation phenomena, providing both high computational efficiency and accuracy.

Trough‐Scale Slope Countercurrent Over the East China Sea Continental Slope Driven by Upwelling Divergence

AbstractObservations have revealed the existence of persistent slope countercurrents (SCCs) that flow southwestward beneath the Kuroshio Current at several locations over the East China Sea (ECS) continental slope. It was not clear whether these flows are localized circulation features or segments of a trough‐scale circulation system in the Okinawa Trough (OT). We demonstrate that there indeed exists a potentially continuous trough‐scale SCC along the ECS slope that is associated with an OT‐wide cyclonic circulation using high‐resolution model simulations and physical interpretations. The detailed features of the deep OT circulation are illustrated by the trajectories of the Lagrangian drifters and the time‐varying distributions of passive tracers. The SCC in the ECS is characterized by its weak yet persistent nature, typically located in narrow sloping regions at the isopycnal layer of 26.6–27.3 kg m−3. It exhibits a characteristic speed of approximately O‐(1) cm s−1. Analyses and experiments suggest that the divergence of upwelling in the SCC layer (26.6–27.3 σθ surface) gives rise to lateral potential vorticity transport, ultimately driving the deep cyclonic circulation. Furthermore, the SCC also displays a substantial connection with the onshore intrusion of the Kuroshio Current, particularly to the northeast of Taiwan Island. The SCC may potentially play a crucial role in the transport of heat and nutrients, as well as in regulating sediment distributions within the deep OT. This mechanism offers fresh insights into explaining the presence of undercurrents in semi‐enclosed marginal seas.

Cavitation analysis of plunging hydrofoils using large eddy simulations

This study employs numerical analysis to investigate the behavior of the National Advisory Committee for Aeronautics (NACA)66 modified (mod) hydrofoil under plunging motion, considering various cavitation numbers. The Large Eddy Simulation (LES) method is utilized to model turbulence. The hydrofoil's plunging motion leads to an increase in lift force and a decrease in drag force. Our research indicates that increasing the speed of the hydrofoil's heaving motion delays the onset of cavitation and enhances the formation of cavity clouds. Furthermore, during the peak oscillatory motion of the hydrofoil in the plunging phase, the detachment length of cavitation bubbles decreases. Additional investigations reveal that cavitation on the hydrofoil's surface accelerates the transition from a laminar to a turbulent boundary layer, strengthening the turbulent boundary layer and postponing the onset of flow separation. This research involves an in-depth investigation of the terms in the vorticity transport equation in cavitation inception, finding a correlation between vapor volume fraction and vorticity dilatation near the hydrofoil surface. This correlation proves crucial to the initial stages of the cavitation inception process.

Research on the starting-up process of a prototype reversible pump turbine with misaligned guide vanes: An energy loss analysis

With fossil fuel depletion and rising demand for renewable energy, reversible pump turbines (RPTs) are crucial for balancing energy supply. Understanding the dynamics of RPTs during starting-up is essential for optimal performance and stability in renewable energy systems. The unique “S" curve of RPTs can lead to instability under transient conditions. This study aimed to investigate the impacts of misaligned guide vanes (MGV) devices on prototype RPT stability, pressure pulsation, and performance improvement during the starting-up process. Using CFD simulation, flow characteristics and energy loss during start-up were analyzed and validated against experimental data. The results show that MGV enhances stability but induces significant energy loss. The analysis of entropy production, vorticity transport, and pressure fluctuation revealed high energy loss regions and the evolution of vortices during the starting-up process. This study provides new insights into hydrodynamic challenges and energy loss with MGV in prototype RPT start-up, with implications for optimizing pumped storage hydropower operations. Overall, this study has valuable engineering significance for the development and application of RPT in renewable energy systems.

Investigations on cavitation flow and vorticity transport in a jet pump cavitation reactor with variable area ratios

Hydrodynamic cavitation (HC) has emerged as a promising technology for water disinfection. Interestingly, when subjected to specific cavitation pressures, jet pump cavitation reactors (JPCRs) exhibit effective water treatment capabilities. This study investigated the cavitation flow and vorticty transport in a JPCR with various area ratios by utilizing computational fluid dynamics. The results reveal that cavitation is more likely to occur within the JPCR as the area ratio becomes smaller. While as the area ratio decreases, the limit flow ratio also decreases, leading to a reduced operational range for the JPCR. During the cavitation inception stage, only a few bubbles with limited travel distances are generated at the throat inlet. A stable cavitation layer developed between the throat and downstream wall during the limited cavitation stage. In this phase, the primary flow carried the bubbles towards the outlet. In addition, it was found that the vortex stretching, compression expansion, and baroclinic torque terms primarily influence the vorticity transport equation in this context. This work may provide a reference value to the design of JPCRs for water treatment.

Dynamic characteristics of the tip leakage vortex in an oil–gas multiphase pump based on vorticity decomposition theory

AbstractThe paper combines experimental and numerical simulation methods to investigate the tip leakage vortex (TLV) in an oil–gas multiphase pump. The study aims to understand the evolution and dynamic characteristics of the TLV. The vorticity decomposition theory is used to analyze the spatial–temporal evolution, transient behavior, and rigid vorticity of the TLV. The findings reveal that the TLV is formed near the pressure surface when the tip clearance jet passes through the shear layer. In one impeller rotation period, transient fluctuations of the TLV are attributed to pressure differences and velocity changes across the tip clearance, and the TLV undergoes two split–dissipation–recurrence processes within one impeller rotation cycle. The presence of the gas phase enhances the scale and strength of the TLV while prolonging its existence in the flow channel. Analysis based on the rigid vorticity transport equation shows that the growth of the TLV and collapse are primarily governed by the rigid vortex generation term. The Coriolis force term contributes to stabilizing the TLV, while the rigid vorticity stretching term affects its shape. Furthermore, the gas phase significantly increases the value of the Rigid vorticity Curl of pseudo‐Lamb vector Term (RCT), which plays a crucial role in the prolonged existence of the TLV under gas–liquid two‐phase conditions. From an inlet gas void fraction of 0%–20%, the RCT value increases by 4.8 × 106/s2, the entropy production value increases by 75.55%, and the hydraulic efficiency decreases by 16.29%.

Numerical investigation of the vorticity transportation and energy dissipation in a variable speed pump-turbine

Variable speed technology is utilized in pump turbines to enhance their operational efficiency and stability. The unsteady internal flows of a variable speed pump turbine operating at different rotation speeds are numerically investigated with SST k-ω turbulence model. Firstly, the ideal rotating speed is selected for each output. Amongst three researched output levels, the lowest entropy production consistently occurs at minimum rotation speed,1350 rpm. Under similar outputs, higher rotation speeds result in higher entropy production. Difference between various rotation speed is up to 40 %. Secondly, Liutex method is used to structure the vortex while vorticity transport equation is applied to analyze its evolution. Results show that variable speed operation can effectively reduce pressure fluctuation amplitude with approximately 20 %–40 % amplitude drop. Subsequently, the relationship between vortex rope and entropy production in the draft tube is deeply explored as it reveals that entropy production in the draft tube correlates with vortex rope evolution. Moreover, direct dissipation's entropy production and turbulence dissipation's entropy production are two primary components leading to irreversible energy loss. It is clearly revealed that the entropy production reduces with rotation speed. The relationship between entropy production and vortex rope in the draft tube is confirmed.

Multiscale interaction analysis of Landfall Typhoon Lekima (2019) based on vorticity equation diagnosis

To investigate the multiscale interaction characteristics of Landfall Typhoon Lekima (2019), this study analyzed the characteristics of the different scale vortex structure and interactions among different scales based on vorticity equation diagnosis. The analysis is based on the simulation results of the WRF model which has been thoroughly verified. The main results are as follows: the original vorticity dominated by the meso-α scale vorticity increases with height and then decreases, with maximum vorticity distributed at 900 hPa. The meso-β scale vorticity varies significantly with altitude, while the meso-γ scale vorticity field exhibits obvious positive vorticity below 850 hPa. The meso-α scale vorticity tendency primarily maintains negative, contributing significantly to the overall reduction in the original vorticity field over time. The increase in mid-to-upper-level (above 550 hPa) original vorticity is mainly related to the variations in the meso-β and meso-γ scale vorticity fields. The original vorticity dominated by the meso-α scale vorticity increases with height and then decreases, and the whole layer vorticity decreases over time. The meso-β scale vorticity varies significantly with altitude and time, while the meso-γ scale vorticity field consistently exhibits significant positive vorticity below 850 hPa. The vorticity equation diagnosis revealed that the primary source terms of the vorticity tendencies are the twisting and stretching terms, and the main sink terms being horizontal and vertical vorticity transport terms below 900 hPa. The source terms and sink terms exchange above 850 hPa. Scale separation results show that the primary contributions of all impact factors originate from the meso-α and meso-γ scale fields (accounting for over 80% of the total), with the contribution of the meso-α scale being less than that of the meso-γ scale and a notable contribution over 35.5% of the interactions between different scales.

The maintenance of coherent vortex topology by Lagrangian chaos in drift-Rossby wave turbulence

This work introduces the “potential vorticity bucket brigade,” a mechanism for explaining the resilience of vortex structures in magnetically confined fusion plasmas and geophysical flows. Drawing parallels with zonal jet formation, we show how inhomogeneous patterns of mixing can reinforce, rather than destroy non-zonal flow structure. We accomplish this through an exact stochastic Lagrangian representation of vorticity transport, together with a near-integrability property, which relates coherent flow topology to fluid relabeling symmetries. We demonstrate these ideas in the context of gradient-driven magnetized plasma turbulence, though the tools we develop here are model-agnostic and applicable beyond the system studied here.

Numerical Investigation on the Spatiotemporal Correlation between Hydraulic Loss and Vortex at Turbine Mode of a Pump-turbine

Abstract Hydraulic loss and vortex analysis are two most widely-used methods investigating flow characteristics from macroscopic view and microscopic view respectively although the correlation between these two methods are still not fully clarified. Based on kinetic energy equation and Boussinesq hypothesis, hydraulic loss is resulted from the joint work of the dissipation loss and the transportation loss in flow domain while vorticity can be further divided into local rigid rotational part and deformational part with the help of the newly proposed concept Liutex. Thereafter, enstrophy as well as vorticity transport intensity is selected as the count part of hydraulic loss through dimensional analysis. Finally, the spatial correlation between hydraulic loss and vortex evolution in small guide vane opening at turbine mode is analyzed with the help of SST k–ω model and the temporal correlation at runaway point is analyzed through DES model. For spatial correlation, the dissipation loss and transportation loss are mainly caused by the deformational enstrophy Ω S and the rigid vorticity transport intensity T R , respectively. For temporal correlation, the correlation order nearly remains unchanged while the degree of correlation decreases to some extent. Based on our work, the hydraulic loss caused by different structure of vortex can be quantified and compared.

Effects of Reynolds Number on the Wake Characteristics of a Notchback Ahmed Body

Abstract This paper investigates the effects of Reynolds number on the wake characteristics of a notchback Ahmed body with effective backlight angle, βe=17.8 deg. The Reynolds number based on the body height was varied from 5×103 to 5×104. Prior to the Reynolds number investigation, a Reynolds-averaged Navier–Stokes (RANS) model assessment was performed using nine turbulence models consisting of one- and two-equation eddy-viscosity models and second moment closure models. The standard Spalart–Allmaras model was the only model that accurately predicted the asymmetric time-averaged wake topology, as reported in previous studies, for the βe=17.8 deg notchback Ahmed body at Re=5×104. The drag coefficient decreased with increasing Reynolds number, while the lift coefficient remained constant for Re≥1×104. The wake structure exhibited three regimes: symmetric (Re≤1×104), transitionally asymmetric (1×104<Re≤3.5×104), and fully asymmetric (Re>3.5×104) states. The wake asymmetry was attributed to an imbalance in entrainment from the sides and asymmetric separation from the roof and the C-pillars of the body. The tilting and stretching terms in the vorticity transport equation were used to provide insight into the source of asymmetry in the vorticity field around the body.

On the role of aortic valve architecture for physiological hemodynamics and valve replacement, Part I: Flow configuration and vortex dynamics

Aortic valve replacement has become an increasing concern due to the rising prevalence of aortic stenosis in an ageing population. Existing replacement options have limitations, necessitating the development of improved prosthetic aortic valves. In this study, flow characteristics during systole in a stenotic aortic valve case are compared with those downstream of two newly designed surgical bioprosthetic aortic valves (BioAVs). To do so, advanced three-dimensional fluid–structure interaction simulations are conducted and dedicated analysis methods to investigate jet flow configuration and vortex dynamics are developed. Our findings reveal that the stenotic case maintains a high jet flow eccentricity due to a fixed orifice geometry, resulting in flow separation and increased vortex stretching and tilting in the commissural low-flow regions. One BioAV design introduces non-axisymmetric leaflet motion, which reduces the maximum jet velocity and forms more vortical structures. The other BioAV design produces a fixed symmetric triangular jet shape due to non-moving leaflets and exhibits favourable vorticity attenuation, revealed by negative temporally and spatially averaged projected vortex stretching values, and significantly reduced drag. Therefore, this study highlights the benefits of custom-designed aortic valves in the context of their replacement through comprehensive and novel flow analyses. The results emphasise the importance of analysing jet flow, vortical structures, momentum balance and vorticity transport for thoroughly evaluating aortic valve performance.

Numerical investigation on cavitation and induced noise reduction mechanisms of a three-dimensional hydrofoil with leading-edge protuberances

In this work, a National Advisory Committee for Aeronautics 66 hydrofoil with leading-edge protuberances is designed. The large eddy simulation combined with the Schnerr–Sauer cavitation model is used to obtain a satisfactory result as compared with the experimental measurement, integrating the permeable Ffowcs Williams–Hawkings equation for cavitation-induced noise analysis. It is found that the special leading-edge geometric structure deflects the incoming flow, creating two counter-rotating streamwise vortices at the peak shoulders. These lead to upwash and downwash effects and alter the pressure distribution on the suction side. The low pressure localized in the trough facilitates the advancement of the leading-edge cavitation while severely limiting the spanwise development of the cloud cavity, shortening the cavitation evolution by about 20% and reducing the maximum cavitation volume by about 35%. Analysis using the vorticity transport equation indicates that different vorticity transport equation splitting terms play dominant roles at different stages of cavitation evolution. Although the cavitation induces disturbances in the primary vortex, the effect is limited. Acoustic simulation shows that the bionic structure can reduce the total sound pressure level by 7.8–8.3 dB. The spherical noise reduction is not as effective as expected due to the similar cavitation volume acceleration processes of the two hydrofoils. However, the pressure fluctuation caused by the collapse of the cloud cavity is reduced by cavitation suppression, which reduces the linear noise. In addition, the protuberances suppress the generation of large-scale vortex systems and transform them into smaller ones, resulting in reduced spanwise correlation and coherence of the shedding vortices. This is a critical factor in noise reduction. Finally, we hypothesize that the unstable noise reduction is related to the streamwise vortices in the trough regions. These vortices increase the momentum exchange within the boundary layer, affecting its stability and weakening the acoustic feedback loop.

Joint Observations of Energy Transport and Dissipation during Plasma Flow Vortex in the Terrestrial Magnetotail

Plasma flow vorticity is ubiquitous in space and plays a key role in material mixing and energy transfer. The five THEMIS satellites orbiting in different regions of the terrestrial magnetotail provide an unprecedented opportunity to study the temporal–spatial evolution characteristics of a plasma flow vortex on large spatial scales. We present an analysis of the flow vorticity that occurred between 05:50 and 06:30 UT on 2009 March 23 during a quiet time of the terrestrial magnetotail. The uneven distributions of the density and temperature of the vortex observed by the three near-Earth satellites (THA, THD, and THE) indicate that the plasma in the solar wind gradually mixed into the near-Earth magnetotail through a series of nonequilibrium processes. Both the flow vortices and dipolarization observed by the three near-Earth satellites were about 10 minutes earlier than those observed by the two satellites (THB and THC) in the mid-magnetotail. Further analysis of the relationship between vorticity, field-aligned current, and energy transport reveals that the flow vortex interacted with the surrounding plasma during its tailward propagation. The field-aligned current related to the vorticity could only generate a pseudo-breakup of the aurora in the ionosphere. Thus, we speculate that this flow vortex mainly transports mass and energy from the solar wind to the near-magnetotail, propagates tailward to the mid-magnetotail, and heats the encountered plasma by dissipating its bulk flow and dominant thermal energy. These results shed light on the mass mixing, energy transport, and dissipation of the plasma flow vortex during quiet levels of geomagnetic activity on large spatial scales.

Numerical and experimental analysis of the cavitation and flow characteristics in liquid nitrogen submersible pump

In this paper, the cavitation and flow characteristics of the unsteady liquid nitrogen (LN2) cavitating flow in a submersible pump are investigated through both experimental and numerical approaches. The performance curve of the LN2 submersible pump is obtained via experimental measurement. Numerical simulations are performed using a modified shear stress transport k–ω turbulence model, incorporating corrections for rotation and thermal effects as per the Schnerr–Sauer cavitation model. The numerical framework is verified by comparing the cavitation morphology features with previously reported visual data of the LN2 inducer and aligning pump performance data with those obtained from experimental tests of the LN2 submersible pump. The results indicate that cavitation at the designed flow rate predominantly manifests as tip clearance vortex cavitation in the inducer. Increased flow rates exacerbate cavitation, potentially obstructing the flow passage of the impeller. The vortex identification method and the vorticity transport equation are employed to identify the vortex structures and analyze the interaction between cavitation and vortices in the unsteady LN2 cavitating flow. The vortex structures primarily concentrate at the outlet of the impeller flow passage, largely attributed to the vortex dilation term and baroclinic torque. The influence of thermal effects on the cavitation flow of submersible pumps is analyzed. An entropy production analysis model, comprehensively involving various contributing factors, is proposed and utilized to accurately predict the entropy production rate within the pump. This study not only offers an effective numerical approach but also provides valuable insight into the cavitation flow characteristics of the LN2 submersible pump.

Numerical simulation of cavitation-vortex interaction mechanism in an advanced rotational hydrodynamic cavitation reactor

Hydrodynamic cavitation (HC), a promising technology for enhancing processes, has shown distinct effectiveness and versatility in various chemical and environmental applications. The recently developed advanced rotational hydrodynamic cavitation reactors (ARHCRs), employing cavitation generation units (CGUs) to induce cavitation, have demonstrated greater suitability for industrial-scale applications than conventional devices. However, the intricate interplay between vortex and cavitation, along with its spatial-temporal evolution in the complex flow field of ARHCRs, remains inadequately elucidated. This study investigated the interaction mechanism between cavitation and vortex in a representative interaction-type ARHCR for the first time using the “simplified flow field strategy” and the Q-criterion. The findings reveal that the flow instability caused by CGUs leads to intricate helical and vortex flows, subsequently giving rise to both sheet and vortex cavitation. Subsequently, utilizing the Q-criterion, the vortex structures are identified to be concentrated inside and at CGU edges with evolution process of mergence and separation. These vortex structures directly influence the shape and dimensions of cavities, establishing a complex interaction with cavitation. Lastly, the vorticity transport equation analysis uncovered that the stretching and dilatation terms dominate the vorticity transport process. Simultaneously, the baroclinic term focuses on the vapor-liquid interface, characterized by significant alterations in density and pressure gradients. These findings contribute to a better comprehension of the cavitation-vortex interaction in ARHCRs.

Formation mechanisms of persistent extreme precipitation events over the eastern periphery of the Tibetan Plateau: Synoptic conditions, moisture transport and the effect of steep terrain

The eastern periphery of the Tibetan Plateau (EPTP) is prone to frequent and severe Persistent Extreme precipitation (PEP) events in summer. Given the complexity of weather systems and the intricate nature of terrain over this region, the generation and development mechanisms of the PEP in the EPTP remain to be determined. In this study, the formation and persistence mechanisms are further explored from the perspective of the general features of large-scale circulations, moisture source diagnosis and the influence of steep topography by using a thermal-dynamical diagnosis method, a mesoscale numerical simulation and a Lagrangian identification of the main moisture sources. The results show that during PEP events, the corresponding atmospheric circulation systems are characterized by an anomalous Rossby wave train at middle levels, an intensified westerly jet, an eastward extension of the South Asian high and a westward extension of the western Pacific subtropical high, all of which are possible to facilitate the development of potential instability and anticyclonic convergence of water vapor transport. The evaporative moisture sources from the Southeastern Asia (SEA), Bay of Bengal (BOB), and Southern China Sea (SCS) are remarkably enhanced during PEP events, with a contribution of 56.44%, which is 28.5% higher than the climatic mean. The further sensitive experiment indicates that the steep terrain could enhance the continuous transport of positive potential vorticity and the downward propagation of upper-level isentropic potential vorticity disturbances, thereby playing an essential role in the triggering and development of PEP events.