Vertical Vorticity Research Articles

Numerical Simulation Research Considering the Influence of Bridge Deck Cross Slope on Wind Performance of π-Type Composite Beam Cable-Stayed Bridge with a Symmetric Elevation Arrangement

Based on a symmetrical cable-stayed bridge, the wind resistance performance of a proposed π-type composite beam is analyzed, and the influence of changing the bridge deck cross slope ratio on the static and dynamic wind characteristics is emphatically studied. The purpose is to provide a design reference for the preliminary wind resistance study of the cable-stayed bridge. The CFD (Computational Fluid Dynamics) numerical calculation method is used to solve the vibration problem of wind-bridge coupling with the help of the software Fluent. It is found that variation of four deck cross slope rates 0%, 1.5%, 2%, and 2.5% has large effects on the static wind coefficient and flutter critical wind speed of a π-type combination beam. In the range of a −3–3° wind attack angle, the static wind drag coefficient will be decreased as the beam deck cross slope rate increases, and in which the drag coefficient at 0% slope rate is the largest. Within the discounted wind speed 13, changing the bridge deck cross slope has little effect on the aerodynamic derivatives of a π-type composite beam. However, the beam deck slope increases the critical wind speed of the bridge, and the critical wind speed at 2.5% is the largest of the four deck slope rates. In addition, it is found that the beam leeward surface keeps generating up and down vortices when the incoming flow wind speed is in the range of 2.5–4.0 m/s, which led the beam to be under vertical vortex vibration, and further research is needed on vibration suppression measures.

Flow‐Topography Interaction Along the Spanish Slope in the Alboran Sea: Vorticity Generation and Connection to Interior Fronts

AbstractFlow‐topography interaction is examined using a realistic simulation at submesoscale resolution. The study focuses on a strong, eastward fresh current flowing along the Spanish margin in the Alboran Sea. The current develops large cyclonic vertical vorticity over the irregular slope and separates downstream at a headland; vertical vorticity is advected offshore and an interior density front is sustained by the presence of denser waters to the east. Using a depth‐integrated vorticity balance formulation, we evince the major role of bottom stress as a vorticity generation mechanism, in the form of a bottom stress divergence torque. Our proposed formulation provides an alternative to the classic transport curl balance for quantifying vorticity budgets around the oceans, using high resolution models with well resolved bottom boundary layers. Also as a result of topographic interaction, we show that the fronts observed in the basin interior could be originated along the margins prior to current separation. This is manifested by large values of the Lagrangian frontogenetic tendency for buoyancy gradients, spanning the vertical extent of the boundary current and extending toward the interior.

Synoptic‐scale and mesoscale controls for tornadogenesis on cold fronts: A tornadic cold front in amplifying northwesterly flow

AbstractThe structure and evolution of a cold front that produced a tornadic narrow cold‐frontal rainband (NCFR) over the UK on 20 November 2013 is explored using reanalysis data, high‐resolution model simulations and observations. Physical links are found to exist across a range of spatiotemporal scales, through which the evolving large‐scale flow field exerts an influence on the timing and location of miso‐scale vortex genesis, and therefore the potential for tornado genesis. The synoptic‐scale flow pattern exhibited amplification, consisting of upstream ridge building and downstream trough extension. A prominent jet streak and associated positive potential vorticity (PV) anomaly and tropopause fold moved rapidly southeastward on the rear flank of the extending upper‐level trough, the leading edge of these features eventually overspreading the surface cold front over the UK. Increasing 850 hPa frontogenesis occurred underneath the left exit of the jet streak and associated, intensifying, PV anomaly. A filament of dry, high‐PV air was extruded from the overlying tropopause fold within an intensifying front‐transverse circulation in this region. This dry filament eventually penetrated to low levels immediately behind the front, where it undercut the upper, rearward parts of the wide cold‐frontal precipitation band. Model fields and observations suggest that diabatic cooling, associated with sublimation of solid hydrometeors falling into the dry filament, led to the development of local downdraft and near‐surface divergence maxima and a prominent cold pool immediately behind the surface cold front over central England. Increases in horizontal convergence, updraft speed, and horizontal temperature gradients along the frontal boundary immediately ahead of the cold pool resulted in development of a locally well‐defined cold front and associated NCFR, where the surface front was formerly (and elsewhere continued to be) relatively weak. Tornadoes occurred in association with miso‐scale vortices that developed rapidly along an intensifying vertical vortex sheet at the NCFR.

Improved Equations for the Profile of a Vertical Air-Core Vortex

The available formulas for the profile of a vertical non-air-entraining vortex are not practical because they involve unknown parameters and need measurements of the local viscous-core radii across the height of the air-core vortex. Also, these formulas can not be used for the air-entraining vortices. In the present study, the available formulas involving unknown parameters were further improved. Findings are as follows. 1) the magnitudes of the unknown parameters vary across the height of the profile of the air-core vortex and they are the function of the ratio of the height of the air-core vortex to the submergence of the intake; 2) simple charts and formulas were obtained for the variations of the unknown parameters for the air-core vortices with and without an intake; 3) in lieu of the local viscous-core radius, the radius at the half-depth of the profile of the air-core vortex was used; 4) no laborious work of measurements are needed to determine the local viscous-core radii along the profile of the vortex; and 5) the improved formulas are in good agreement with available test data for the profiles of both the non-air-entraining and the air-entraining vortices with or without a vertically flowing downward intake.

Energy balances for the collision of gravity currents of equal strengths

Collision of two counterflowing gravity currents of equal densities and heights was investigated by means of three-dimensional high-resolution simulations with the goal of understanding the flow structures and energetics in the collision region in more detail. The lifetime of collision is approximately $3 \tilde {H}/\tilde {u}_f$ , where $\tilde {H}$ is the depth of heavy and ambient fluids, and $\tilde {u}_f$ is the front velocity of the approaching gravity currents, and the lifetime of collision can be divided into three phases. During Phase I, $-0.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 0.5$ , where $\tilde {t}$ is the time, and $\tilde {t}_c$ is the time instance at which the two colliding gravity currents have fully osculated, geometric distortions of the gravity current fronts result in stretching of pre-existing vorticity in the wall-normal direction inside the fronts, and an array of vertical vortices extending throughout the updraught fluid column develop along the interface separating the two colliding gravity currents. The array of vertical vortices is responsible for the mixing between the heavy fluids of the two colliding gravity currents and for the production of turbulent kinetic energy in the collision region. The presence of the top boundary deflects the updraughts into the horizontal direction, and a number of horizontal streamwise vortices are generated close to the top boundary. During Phase II, $0.5 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 1.2$ , the horizontal streamwise vortices close to the top boundary induce turbulent buoyancy flux and break up into smaller structures. While the production of turbulent kinetic energy weakens, the rate of transfer of energy to turbulent flow due to turbulent buoyancy flux reaches its maximum and becomes the primary supply in the turbulent kinetic energy in Phase II. During Phase III, $1.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 2.8$ , the collided fluid slumps away from the collision region, while the production of turbulent kinetic energy, turbulent buoyancy flux and dissipation of energy attenuate. From the point of view of energetics, the production of turbulent kinetic energy and turbulent buoyancy flux transfers energy away from the mean flow to the turbulent flow during the collision. Our study complements previous experimental investigations on the collision of gravity currents in that the flow structures, spatial distribution and temporal evolution of the mean flow and turbulent flow characteristics in the collision region are presented clearly. It is our understanding that such complete information on the energy budgets in the collision region can be difficult to attain in laboratory experiments.

How Do Dust Devil-Like Vortices Depend on Model Resolution? A Grid Convergence Study Using Large-Eddy Simulation

Dust devils are organized convective vortices with pressure drops of hundreds of pascals that spirally lift surface material into the air. This material modifies the radiation budget by contributing to the atmospheric aerosol concentration. Quantification of this contribution requires good knowledge of the dust devil statistics and dynamics. The latter can also help to understand vortex genesis, evolution and decay, in general. Dust devil-like vortices are numerically investigated mainly by large-eddy simulation (LES). A critical parameter in these simulations is the grid spacing, which has a great influence on the dust devil statistics. So far, it is unknown which grid size is sufficient to capture dust devils accurately. We investigate the convergence of simulated convective vertical vortices that resemble dust devils by using the LES model PALM. We use the nesting capabilities of PALM to explore grid spacings from 10 to 0.625 m. Grid spacings of 1 m or less have never been used for the analysis of dust devil-like vortices that develop in a horizontal domain of more than 10 km^2. Our results demonstrate that a minimum resolution of 1.25 m is necessary to achieve a convergence for sample-averaged quantities like the core pressure drop. This grid spacing or smaller should be used for future quantifications of dust devil sediment fluxes. However, sample maxima of the investigated dust devil population and peak velocity values of the general flow show no convergence. If a qualitative description of the dust devil flow pattern is sufficient, we recommend a grid spacing of 2.5 m or smaller.

A lower frequency signal emitted from tornadoes based on a new mechanism

Tornadoes have been shown to radiate infrasound to great distances. After using Lighthill's acoustical analogy to study sound generated by a numerical tornado, we found that there is a significant low-frequency signal between 0.1 Hz and 0.5 Hz. We hypothesized that there is a Kirchhoff vortex-like source at the center of the numerical tornado. Based on vortex sound theory, characteristic frequencies only depend on the strength of the vertical vorticity which can change at different heights of the tornado. Compared to real data analysis, there is a possibility that when a tornado occurs, infrasonic sensors can detect a significant increase in low-frequency signals. This hypothesis is being tested against data collected in the field during the passage of tornado-producing storms.

A direct numerical simulation study on the structures and turbulence–flame interactions of a laboratory-scale lean premixed jet flame in cross-flow

In the present work, direct numerical simulation of a laboratory-scale lean premixed reacting jet in cross-flow was performed to explore the flow–flame structures and turbulence–flame interactions. A jet of lean premixed ethylene–air mixtures (equivalence ratio $\phi = 0.6$ ) was injected into a hot vitiated cross-flow. Both non-reacting and reacting cases were simulated. It was found that the reacting jet penetrates deeper in the cross-flow with a weaker shear layer compared with the non-reacting one. The wake of the non-reacting and reacting jet is characterized by vertical vortices and recirculation zones, respectively. As for the flame structure of the reacting case, the reaction intensity varies considerably in different flame zones. The heat release rate on the leeward side is higher than that on the windward side, but lower than that of the corresponding laminar flame. The analysis of the turbulence–flame interactions of the reacting case showed that the large local Damköhler number ( $Da$ ) related to reaction-induced dilatations results in an increased tendency of the scalar gradient to align with the most extensive strain rate, which is more evident in the regions with high heat release rate on the leeward side. Negative dilatation regions with positive tangential strain rate and negative normal strain rate are observed on the windward side. High positive dilatations appear on the flame front of the leeward side. The tangential strain rate is negatively correlated with the normal strain rate and curvature. Regions with a high local $Da$ on the windward side correspond with high positive curvature regions.

Impact of Parameterized Topographic Drag on a Simulated Northeast China Cold Vortex

AbstractNortheast China cold vortex (NECV) is the major influencing weather system in northern China. Yet the impacts of complex terrain on the evolution of NECV remains poorly understood. This work studies the influence of subgrid orographic drag (SOD) on a heavy‐rain‐producing NECV occurred in July 2011 using the Weather Research and Forecasting model. A series of numerical experiments are conducted with different parameterizations of SOD including turbulent orographic form drag (TOFD), flow blocking drag (FBD), and mountain wave drag (MWD). Results show that the NECV intensity is overestimated in the absence of SOD parameterization, accompanied with too‐low geopotential height (GPH) and too‐strong horizontal winds. The parameterization of TOFD can significantly decelerate the 10‐m winds, whereas the FBD and MWD play a minor role. However, the influence of TOFD is overwhelmed by FBD and MWD in the troposphere, especially the latter. This implies that the breaking of mountain waves play a more important role in weakening the NECV than the low‐level flow blocking. The lower‐tropospheric MWD directly weakens the convergence and ascent motion of the NECV, producing an anti‐cyclonic circulation that uplifts the GPH under the constraint of quasi‐geostrophic vertical vorticity. This MWD‐induced circulation indirectly weakens the NECV in the mid‐upper troposphere by producing a warm advection that counters the low‐level cold advection to the southwest of the NECV. The findings provide useful insights into the impacts of complex terrain on the NECV and highlight the importance of topographic drag parameterization in the simulation and short‐range forecast of NECV.

Hydrodynamic adjustment subject to a submerged canopy partially obstructing a flume: Implications for junction flow behaviour

AbstractThe scenario of a submerged canopy partially obstructing a channel is common in the natural aquatic flow environment. This study experimentally evaluated the flow adjustment performance and vertical flow structure adaptive to a submerged partially distributed canopy. The experimental results showed that the canopy interior velocity adjustment distance for submerged partially distributed canopies was comparable with that for emergent ones. However, it was smaller than that for submerged fully distributed canopies but comparable with that for emergent fully distributed ones. For the fully developed flow, the neighbouring open waters insignificantly impact the flow structure in the vegetation region (VR), where the mixing‐layer flow behaviour arising from the generation of the vertical coherent vortices was maintained. The vertical mixing‐layer flow behaviour characterised by pronounced vertical Reynolds shear stress transversely extended into the nonobstructed region, suggesting that the canopy‐side waters significantly impacted the neighbouring open flow. This effect decayed in the case of decreasing canopy density and as the location leaving the junction region (JR). Of importance was that near‐bed velocity deflection occurred in the JR and was facilitated by canopy density. Vertically nonuniform distribution of transverse momentum exchange from horizontal coherent vortices due to bed depression can account for the near‐bed velocity deflection. The gained knowledge allowed the development of a phenomenological model for understanding the vertical flow structure in partially vegetated channels.

Exact solutions to the Navier–Stokes equations for describing inhomogeneous isobaric vertical vortex fluid flows in regions with permeable boundaries

A family of exact solutions to the Navier–Stokes equations is constructed to describe nonuniform two-dimensional fluid motions. The superposition of the main unidirectional flow with the secondary flow is considered. The secondary flow is determined by suction or injection through permeable boundaries. This class of exact solutions is obtained by multiplicative and additive separation of variables. The flow of a viscous incompressible fluid is described by a polynomial of the horizontal (longitudinal) coordinate. The polynomial coefficients are functions of the vertical (transverse) coordinate and time. They are determined by a chain of homogeneous and inhomogeneous parabolic partial differential equations with a convective term. In the case of a steady flow, it is described by a system of ordinary differential equations with constant coefficients. An algorithm for integrating a system of ordinary differential equations for studying the steady motion of a viscous fluid is presented. In this case, all the functions defining the velocity are quasipolynomials since the system of ordinary differential equations has an Euler-form exact solution.

Research on the influence of the jet flow regime in the kerf on the cutting surface accuracy in WJGL

Water jet-guide laser processing technology (WJGL) has a good application prospect in the field of non-metallic materials with high brittleness and hardness for its high machining precision. However, the premise of smooth and efficient machining is to ensure that the jet can transmit light energy stably into the material. Especially in complex trajectory cutting, the jet in the channel is prone to instability, which affects the processing results. Therefore, the purpose of this paper is to construct a complex environment with sufficient turbulence of the jet in the cutting channel, and carries out a research plan with sharp corners. The forming mechanism of the machined surface was deduced by visual observation. Combined with the simulation results, the key factors of the disturbance of the jet flow pattern are obtained. It is considered that vertical angular vortices are formed at the corners due to the high-pressure gradient induced by the jet, which causes the laser energy to diverge from the water-fiber prematurely, and the processing accuracy declines. Finally, an optimization scheme is proposed to replace the straight corner with a low-curvature cross arc, which can avoid the problem of accuracy and efficiency decline caused by jet instability. After optimization, the surface quality of cutting surface is improved by 6 times.

Numerical Study of the Dynamics of a Cyclone Modeled by a Vertical Vorticity Vector Considering a Radial Velocity as a Function of Time

In this article, the work carried out is a numerical study of the dynamics of a cyclone modeled by a vertical vorticity vector by considering a radial velocity as a function of time t. We made a short general study on cyclones by modeling a vertical cyclone starting from the Navier-Stokes equations. A study of the vorticity as a function of the radius and as a function of the radial abscissa at different times has been made. We also studied the radial and ortho radial components of the velocity as a function of the radius and as a function of the radial abscissa by varying the Ekman number and the Rossby number by looking at their impacts when they are increased or they are reduced. In the same dynamics, the influence of the decrease in the suction speed over time on the radius of the vortex core has been studied. In short, we have studied the effects of the variation of the radial velocity as a function of time. We ended our study by showing that the Ekman number is the most important parameter in the dynamics of the cyclone, by showing the relationship that exists between the Ekman number and the growth of the rotational motion of a cyclone.

Meridional circulation dominates the record-breaking “Dragon Boat Water” rainfall over south China in 2022

During the “Dragon Boat Water” season in 2022, record-breaking anomalous rainfall occurred over South China (SC). In this study, the causes of anomalous rainfall are investigated by using the novel moisture budget equation of three-pattern circulations. The results show that the anomalous rainfall over SC caused by the horizontal, meridional, and zonal circulations was −10 mm, 168 mm, and 45.3 mm, which contribute −5%, 86%, and 23% of the actual rainfall anomaly (195.1 mm), respectively, suggesting that the meridional circulation contributes most to anomalous rainfall, followed by zonal circulation, and horizontal circulation contributes negatively. Further analysis based on the three-pattern decomposition of the global atmospheric circulation shows that the spatial configuration of the anomalous horizontal circulation and vertical vorticity provides the background for generating the anomalous divergence and convergence of meridional and zonal circulations and further anomalous vertical velocity of the meridional and zonal circulations, ultimately resulting in anomalous rainfall.

Numerical study of instability mechanism in the air-core vortex formation process

Air-core vortices are a ubiquitous phenomenon in the intakes of hydropower stations. Due to the transient and instability of two-phase vorticial flow, the prediction of air-core vortex formation is challenging, and understanding of the instability mechanism remains elusive. In this study, the large eddy simulation (LES) method and a coupled level-set and volume-of-fluid (CLSVOF) method are performed to study air-core vortex formation in a benchmark reservoir with a horizontal intake pipe. The process of air-core vortex formation can be classified into an inception stage, an instability stage, and a stability stage. In the instability stage, the surface vortex repeatedly goes through the process of inception, enhancement, attenuation, and extinction. The movement of the counterrotating secondary vortices and water surface level fluctuation plays a negative role in air-core vortex formation. The additional motion generated by the counterrotating pair drives the pair to the back wall. The main vortex undergoes attenuation due to the stretching/tilting effects induced by the secondary vortex. Water level fluctuations briefly increase the submergence depth, which in turn reduces the vertical velocity gradient and vertical vorticity, destabilizing the vortex. The perturbation of the air-core vortex by water level fluctuations is present only at the beginning of the instability stage.

Impact of the Streamwise Vorticity Current on Low‐Level Mesocyclone Development in a Simulated Supercell

AbstractResults from a large eddy simulation of a tornadic supercell developing in a horizontally homogeneous environment are presented which clearly illustrate a connection between low‐level mesoyclone development and the development of a streamwise vorticity current (SVC). Although the environment supports tornadic supercells, a strong low‐level mesocyclone (LLM) does not develop until a well‐defined SVC forms in the storm's forward flank. As the streamwise vorticity in the SVC flows southward and is tilted into the storm updraft creating updraft helicity, the LLM strengthens and lowers toward the surface. The SVC also focuses LLM development in a confined storm‐relative position favorable for converging/stretching preexisting vertical vorticity. Tornadogenesis occurs within ∼5 min of the establishment of a strong LLM. These results illustrate a possible mode of internal storm variability that may be an important factor in explaining why some supercells produce tornadoes while others do not in similar favorable environments.

ON THE NONLINEAR STABILITY FOR QUASI-GEOSTROPHIC FORCED ZONAL FLOWS

This paper continues a series of studies providing stability crite¬ria for quasigeostrophic forced zonal flows in in the presence of lateral diffusion and bottom dissipation of the vertical vorticity. We study the Lyapunov stability of a stationary and longitude independent ba¬sic flow, obtaining linear and nonlinear stability criteria expressed in terms of the maximum shear of the basic flow and/or its meridional derivative, extending some previous results.

An Inhomogeneous Steady-State Convection of a Vertical Vortex Fluid

An exact solution of the Oberbeck – Boussinesq equations for the description of the steady-state Bénard – Rayleigh convection in an infinitely extensive horizontal layer is presented. This exact solution describes the large-scale motion of a vertical vortex flow outside the field of the Coriolis force. The large-scale fluid flow is considered in the approximation of a thin layer with nondeformable (flat) boundaries. This assumption allows us to describe the large-scale fluid motion as shear motion. Two velocity vector components, called horizontal components, are taken into account. Consequently, the third component of the velocity vector (the vertical velocity) is zero. The shear flow of the vertical vortex flow is described by linear forms from the horizontal coordinates for velocity, temperature and pressure fields. The topology of the steady flow of a viscous incompressible fluid is defined by coefficients of linear forms which have a dependence on the vertical (transverse) coordinate. The functions unknown in advance are exactly defined from the system of ordinary differential equations of order fifteen. The coefficients of the forms are polynomials. The spectral properties of the polynomials in the domain of definition of the solution are investigated. The analysis of distribution of the zeroes of hydrodynamical fields has allowed a definition of the stratification of the physical fields. The paper presents a detailed study of the existence of steady reverse flows in the convective fluid flow of Bénard – Rayleigh – Couette type.

Cloud‐Radiation Feedback Prevents Tropical Cyclones From Reaching Higher Intensities

AbstractThe prediction of tropical cyclone (TC) intensity remains a major scientific challenge. Recent studies indicate that cloud‐radiation feedback (CRF) plays a positive role in the intensification of TCs during their genesis. However, little attention has been given to how CRF affects TC intensity after genesis. This study shows that CRF may prevents TCs from attaining higher maximum intensities. The ascending motion induced by the anomalous radiative heating of TC promotes more latent heating on the outer side of the upper eyewall, resulting in a more tilted eyewall. A more tilted eyewall leads to a larger inner‐core size and less inward flux of absolute vertical vorticity within the inner core, thus preventing the TC from reaching higher intensity. This work highlights that CRF may affect TC intensity by modulating the structure of the inner‐core convection, and further advances our understanding of the interaction between radiation effect and TC dynamics.

Mesoscale and submesoscale turbulence in the Northwest Pacific Ocean revealed by numerical simulations

As the intermit between geostrophic-balanced mesoscale eddies and three-dimensional dissipation, submesoscale turbulence (1–50 km) plays a key role in the ocean energy cascade. Based on the output of 1/48° MITgcm llc4320 simulation, mesoscale and submesoscale turbulence in the upper ocean and kinetic energy (KE) cascade between them are investigated in two different mesoscale dynamical regimes. When the timing of mesoscale seasonality varies with the mesoscale dynamical regimes, the timing of submesoscale seasonality is almost uniform. In this 1/48o simulation, the inverse KE cascade, through which mesoscale KE is transferred from small scales to larger scales in altimeter observation, expands farther into the submesoscale range, with a minimum of about 15 km. The inversely transferred submesoscale KE is 1–2 orders of magnitude larger than that transferred forward. Both the inverse and forward KE cascades vary seasonally. While the amplitude of the forward KE cascade changes synchronously with the mixed layer depth, the amplitude of the inverse KE cascade lags behind them by ∼1-month This is due to nonlinear interactions between submesoscale processes and more slowly evolving mesoscale eddies which takes a little longer than direct dissipation. The inverse KE cascade leads to the mesoscale seasonality in the Kuroshio Extension, which is invisible in conventional altimeter observation. In terms of depth dependency, both the eddy kinetic energy (EKE) and normalized vertical vorticity (ξ/f) decrease rapidly with depth in the upper ocean, while the EKE-containing scale increases with depth and the ξ-containing scale has a large core in the mixed layer. It indicates that the upper ocean is full of mesoscale eddies on a relatively small scale which are accompanied by active submesoscale turbulence. The submesoscale seasonality is still significant at 300–400 m, and shows vertically consistency in the whole upper ocean, so there may be downward development in the nonlinear evolution of submesoscale turbulence.