The interaction of binary vortices in a barotropic model

Summary The interaction of binary cyclonic vortices is investigated using the nondivergent barotropic model of Chan and Williams (1987) under two situations: a quiescent environment and a linearly-sheared background flow. It is found that the mutual interaction between the vortices results from a combination of two processes: the advection of symmetric vorticity by the asymmetric flow and the advection of asymmetric vorticity by the symmetric flow. The latter contribution is rather significant. Whether the vortices in a binary system attract or repel each other depends on the asymmetric vorticity distribution associated with the two vortices. Such a distribution is governed by the structure (size) of and the separation between the vortices. In the presence of a sheared flow, the contribution from the advection of asymmetric vorticity by the symmetric flow may also become appreciable depending on the structure and magnitude of the shear. Furthermore, the geographical locations of the vortices in relation to the sheared flow are also important in determining the relative movement of the vortices.In the presence of , the movements of the vortices are modified by the northwestward -drift However, the relative motion between the vortices is almost identical to that on an f-plane. In other words, the mutual interaction between the vortices is largely independent of . Alternatively, the two vortices can be considered to be one system which drifts towards the northwest under the influence of while they interact with each other within the system. Physically, this independence arises because the two relative vorticity advection terms have much larger magnitudes than the planetary vorticity advection term. However, the -effect is still important in that it modifies the asymmetric flow associated with each vortex and hence the asymmetric vorticity. Such modifications change the advection patterns compared with the =0 case and hence lead to different vortex movements. The presence of a linear shear causes the binary system to move as if it was a large (for a cyclonic shear) or smaller (for an anticyclonic shear) vortex under the influence of .With 22 Figures     

一次高原低涡与高原切变线演变过程与机理分析

对一次东移高原低涡减弱、高原切变线生成并在有利的环流背景下东南移,进而引发川渝强降水的高原切变线生成机制以及演变过程进行了初步分析。首先引入描写热带气旋的Okubo-Weiss（OW）参数（V_OW）来定量表达低涡、切变气流中旋转和变形的相对大小,确定高原切变线的潜在生成区域和发展状况。得出在高原切变线生成阶段,500 hPa等压面上V_OW值由正转负,V_OW负值带可以很好地指示高原切变线的潜在生成区域。V_OW负值强度与高原切变线强度有很好的相关性。高原切变线上以V_OW负值中心为主,但也会存在正值中心,说明在切变线上也会有气旋性涡度。此个例高原切变线以伸缩变形为主,高原切变线沿变形场的拉伸轴分布。然后通过涡度方程和总变形方程进一步分析了高原低涡减弱、高原切变线生成的动力机制。高原低涡的减弱、消失主要受散度项的影响,时间演变分析表明系统由强气旋性涡度的高原低涡演变为强辐合性的高原切变线。总变形方程中的扭转项对高原切变线的生成贡献最大,其次为水平气压梯度项,散度项最小;当高原切变线上以拉伸变形为主时,不利于其上高原低涡的发展,切变线可能是影响低涡发展的背景流场。     

非轴对称双涡相互作用的研究

在平流动力学的框架内,用准地转正压涡度方程模式实施了19组试验,研究双涡合并的条件及较大尺度涡旋自组织的问题。结果指出:(1)存在着两个影响双涡合并的因素,即初始双涡中心之间的距离和初始涡旋的非轴对称分布。初始两个对称涡旋合并具有明显的临界距离效应,但初始两个非轴对称涡旋能否合并还受到初始涡旋的非对称结构的复杂影响。(2)存在着两类不同的较大尺度涡旋的自组织过程,形成较大尺度涡旋。第一类,初始两个涡旋相同,均呈轴对称分布。双涡作用经历了缓变、快变,以及涡量羽翼的生成、拉伸和发展的过程,合并后呈对称性流型;终态涡内区涡量的堆积来源于两个初始涡,终态涡外区的螺旋带来源于两个初始涡外缘线涡量羽翼的拉伸。第二类,初始两个涡旋不同,一个为椭圆型,一个为偏心型,均呈非轴对称分布。双涡作用中,椭圆涡一边互旋,一边向计算区域中心靠近,同时涡量范围加大,形成了终态涡的内核区;偏心涡一边互旋,一边被不断拉伸,形成了终态涡的螺旋带区;表现出终态涡内区的涡量堆集来源于椭圆涡,终态涡外区螺旋带主要来源于偏心涡的反复拉伸及断裂的特性。     

2019年8月16日沈阳极端降水事件的低空γ中尺度涡旋观测特征和机理分析

2019年8月16日沈阳市区受伴有低空γ中尺度涡旋的强对流系统影响,发生了1951年有观测记录以来的最大小时降水（102 mm）。为了提高对此类涡旋所致强降水天气的认识和预报能力,综合利用多源观测和ERA5再分析资料,对此次过程中低空γ中尺度涡旋的观测特征、形成原因和对强降水的影响机制开展研究。此次过程期间,500 hPa沈阳位于东北冷涡东南侧,850 hPa以下低空位于“利奇马”台风残涡西侧的偏北气流水汽输送带内,16日午后沈阳市区具有低层大气气温廓线接近干绝热递减率、较低抬升凝结高度和逐渐加强的风垂直切变等环境条件特征;风廓线雷达资料显示降水前0—6 km风矢量差最大达17 m/s,有利于较浅薄中尺度涡旋对发生。16时前后,沈阳市区内γ中尺度辐合风场首先触发局地风暴,随后有对流风暴群移入沈阳,在局地风暴具有反气旋式旋转处合并。合并风暴在初期产生强降水后,回波顶降低、降水强度减小,低空出现了生命期约30 min的γ中尺度涡旋对,更是出现罕见的具有辐合特征的反气旋式涡旋加强的现象,伴有低空涡旋的风暴再次加强并导致后期更强的降水。相比中国中气旋统计特征,本次低空浅薄涡旋生命期较短、尺度小...     

高原低涡与西南涡结伴而行的不同活动形式个例的环境场和位涡分析

本文利用NCEP/NCAR-FNL再分析资料、历史天气图、青藏高原低涡切变线年鉴,通过分析1998~2015年持续高原涡影响西南涡结伴而行（简称两涡伴行）过程的活动形式,并对不同活动形式的个例进行了环境场与位涡分析,得出了不同活动形式两涡伴行的环境场特征,揭示了冷空气活动、200 hPa急流对不同活动形式的两涡伴行的影响原因。结果表明:（1）两涡伴行有三种活动形式,它们是高原涡诱发西南涡、高原涡与西南涡耦合以及同一天气系统下两涡,其中以高原涡诱发西南涡的活动形式占多数。（2）两涡伴行的500 hPa环境场主要是40°N以北东亚环流经向度不强,纬向气流主导,受500 hPa低槽、冷空气活动的影响;200 hPa环境场主要与200 hPa急流的强度、距急流核距离、在急流两侧的位置密切相关;不同活动形式的西南涡上空200 hPa、500 hPa环境场特征是有差别的。（3）受500 hPa低槽、冷空气影响的两涡伴行中的西南涡的生成是通过500 hPa高位涡空气伸入西南涡上空,造成西南涡上空斜压不稳定所至;在西南涡上空500 hPa斜压不稳定增强且具有较强的斜压不稳定时西南涡加强;200 hPa西南风急流影响高原涡诱发或耦合、加强西南涡是分别在高空高位涡下传影响到高原涡与西南涡上空、西南涡的情况下实现的,同一天气系统下,高空高位涡下传只影响高原涡,而未影响西南涡。     

A STUDY ON MESOSCALE VORTICITY PROPAGATION IN A TYPHOON-LIKE VORTEX*

By using an f-plane barotropic quasi geostrophic model in the rectangular coordinates with a grid spacing of 5 km,ten experiments whose integration time is 36 hours are performed in order to study the interaction between a typhoon vortex and a mesoscale vortex whose initial center position is located at 2 r_m northwest to the typhoon center,where r_m is the radius of maximum wind of the typhoon vortex. Results show that the interaction can create a pair of smaller scale vortices or lumps,which extend from the outside region of the typhoon to near its center,resulting in the inward propagation of mesoscale vorticity.In this process,the vorticity concentration of the mesoscale vortex may appear.The coexistence of the propagation and the concentration makes the increase of vorticity in the inside region i.e.a more intensive typhoon.Meanwhile,the intensity of the lump with positive vorticity oscillates with time,with the oscillation period being several hours,the distance from the typhoon center to the lump center also has a similar oscillation period,which reduces the oscillation of typhoon intensity.In the case of stronger circular basic flow,the interaction can make the intensification of typhoon more obviously. In addition,in some parametric conditions,the interaction may break down the continuous vorticity zone,exhibiting a cluster of smaller vorticity lumps.     

Study on the Interaction of Non-axisymmetric Binary Vortices

In the context of advection dynamics,19 experiments(Exps.)are performed using a quasi-geostrophic barotropic vorticity equation model to explore the condition for the mergence of binary vortices and the self-organization of the larger scale vortex.Results show that the initial distance between the centers of binary vortices and the non-axisymmetric distributions of their initial vorticity are two factors affecting the mergence of binary vortices.There is a critical distance for the mergence of initial symmetric binary vortices, however,the mergence of initial non-axisymmetric binary vortices is also affected by the asymmetric structure of initial vortices.The self-organization processes in 19 experiments can be classified into two types:one is the merging of identical,axisymmetric binary vortices in which the interaction of the two vortices undergoes slowly change,rapid change,and the formation,stretching,and development of the filaments of vorticity, and the two vortices merge into a symmetric vortex,with its vorticity piled up in the inner region coming from the two initial vortices,and the vorticity of the spiral band in the outer region from the stretching of the filaments of the two initial vortices.And the other type is the merging of the two non-axisymmetric initial vortices of an elliptic vortex and an eccentric vortex in which the elliptic vortex,on the one hand, mutually rotates,and on the other hand moves towards the center of the computational domain,at the same time expands its vorticity area,and at last forms the inner core of resultant state vortex;and the eccentric vortex mutually rotates,meanwhile continuously stretches,and finally forms the spiral band of resultant state vortex.The interaction process is characteristic of the vorticity piled up in the inner core region of resultant state vortex originating from the elliptic vortex and the vorticity in spiral band mainly from the successive stretch and rupture of the eccentric vortex.     

正压无辐散模式中双涡的相互作用

本文在无环境流场的情况下,利用正压无辐散模式对双涡的相互作用以及β效应的影响进行了数值模拟研究。一系列的试验结果表明:双涡的相对运动对双涡间的初始距离及双涡的相对强度是十分敏感的,双涡间的非线性涡度平流可导致两个系统的气旋隆互旋;同时可造成两个系统的相互吸引和合并或相互排斥,吸引或排斥的临界距离取决于双涡的结构及相对强度:"合并"的快慢取决于双涡的联合强度,联合强度越强越难于"合并"β效应对双涡的相互作用具有显著的影响。它可以改变双涡相互吸引或排斥的性质,还可以使两个相互吸引的同等强度的涡旋"合并"后较平直地向西北方向漂移,而使两个不同强度的涡旋"合并"后的运动表现为β漂移和陀螺运动的叠加。      

华南涡旋暴雨的物理对比分析

低涡型暴雨是华南地区一种重要的暴雨类型,它常常发生在对流层低层天气尺度切变线上,虽难从气压场上找到,但它所造成的暴雨却很强。我们发现,常规天气图上似乎很弱的这类涡旋,却有较强的流场涡度和典型的散度分布,构成了强降水过程的必要物理条件。本文把它与热带气旋发展过程中的物理结构、能量变化和转换特征进行了诊断、对比分析,指出它们不仅三维物理量场分布差异较大,其发展过程中能量变化也有很大差异。热带气旋的K,值远大于切变线低涡,但K_φ的变化则相反,无论是其绝对值或它占总动能的比值,都不      

Dependence of Tropical Cyclone Intensification on the Latitude under Vertical Shear

The sensitivity of tropical cyclone (TC) intensification to the ambient rotation effect under vertical shear is investigated. The results show that the vortices develop more rapidly with intermediate planetary vorticity, which suggests an optimal latitude for the TC development in the presence of vertical shear. This is different from the previous studies in which no mean flow is considered. It is found that the ambient rotation has two main effects. On the one hand, the boundary layer imbalance is largely controlled by the Coriolis parameter. For TCs at lower latitudes, due to the weaker inertial instability, the boundary inflow is promptly established, which results in a stronger moisture convergence and thus greater diabatic heating in the inner core region. On the other hand, the Coriolis parameter modulates the vertical realignment of the vortex with a higher Coriolis parameter, favoring a quicker vertical realignment and thus a greater potential for TC development. The combination of these two effects results in an optimal latitude for TC intensification in the presence of a vertical shear investigated.     

Simulations of the motion of tropical cyclone-like vortices in the presence of synoptic and mesoscale circulations

Initial mesoscale vortex effects on the tropical cyclone(TC) motion in a system where three components coexist(i.e.,an environmental vortex(EV),a TC,and mesoscale vortices) were examined using a barotropic vorticity equation model with initial fields where mesoscale vortices were generated stochastically.Results of these simulations indicate that the deflection of the TC track derived from the initial mesoscale vortices was clearly smaller than that from the beta effect in 60% of the cases.However,they may have a more significant impact on the TC track under the following circumstances.First,the interaction between an adjacent mesoscale vortex and the TC causes the emergence of a complicated structure with two centers in the TC inner region.This configuration may last for 8 h,and the two centers undergo a cyclonic rotation to make the change in direction of the TC motion.Second,two mesoscale vortices located in the EV circulation may merge,and the merged vortex shifts into the EV inner region,intensifying both the EV and steering flow for the TC,increasing speed of the TC.     

Coherent Structures near the Surface in a Strongly Sheared Convective Boundary Layer Generated by Large-Eddy Simulation

Well-developed low speed and high temperature streaks in association with the alignment of convection cells are observed in a large-eddy-simulation (LES) generated strongly sheared convective boundary-layer flow, which is driven by a geostrophic wind speed of 15 m s^-1 and a surface kinematic heat flux of 0.05 K m s^-1. Vortices that drive streaky structures are identified through an eigenvalue method (lambda;₂method) near the surface. These vortices are highly elongated along the quasi-streamwise direction alternating sign of the x-component of vorticity (_x). By conditional sampling of fully developed vortices, a statistically significant coherent structure is educed. The educed vortex is elongated to the streamwise direction with the elevation angle of about 17° above the horizontal surface. However, the horizontal tilting is not clearly demonstrated in the present simulation. Fluctuation fields in the domain of the educed vortex show the existence of a low speed and high temperature streak as a direct consequence of momentum and heat transport by vortical motions. The strong ejection(upward transport of low momentum or high temperature)occurring at the higher level than that of the strong sweep (downward transport of high momentum and low temperature) can be explained from the spatial distribution of the fluctuationfields of velocity and temperature. The contribution of ejection to the Reynolds stress at z/h₁ = 0.18 is about 75%, which is slightly greater than that (70% at z/h₁ = 0.173) for the neutrally stratified atmospheric boundary layer. Ejection is also found to be dominant for the turbulent heat flux.     

随机分布的小尺度涡对涡旋自组织影响的研究

以往双涡相互作用的动力学一般都在决定性的框架内研究。文中用一个平流方程模式,实施积分时间为30 h的8组试验,分析决定性和随机性共存系统中双涡相互作用和涡旋自组织的问题。随机性通过以下方式引入模式:先用Iwayama方案生成随机分布的小尺度涡,再将这些小尺度涡加入初始场。试验中,初始随机分布小尺度涡的强度参数K分别取0.0、0.4、0.6、0.8和1.0。结果表明,没有小尺度涡的条件下(K=0.0),初始分离的两个β中尺度涡逆时针互旋,其准终态流型是两个分离的涡;引进小尺度涡后,K取0.8、1.0时,初始分离强度相同的两个β中尺度涡,逐渐形成主次之分。主涡将次涡拉伸成为螺旋带,其准终态流型是一个自组织起来的类似于台风环流的涡旋。准终态涡中心的相对涡度值随K值的加大而加大。结果还表明,准终态流型不仅与初始小尺度涡的强度参数有关,而且与初始小尺度涡的分布有关。此外,在相同初始场的情况下,还实施了3类不同边畀条件的试验:第1类,在东西边界取周期条件,在南北边界取固定条件;第2类,在所有边界均取固定条件;第3类,在所有边界均取周期条件。这3类试验的准终态流型相同,都显示出一个类似于台风涡旋的环流。根据这些结果可以初步认为,涡旋自组织的研究从决定性动力学向随机动力学的过渡是值得探索的。     

The interaction of ellipsoidal vortices with background shear flows in a stratified fluid

We show that an arbitrarily oriented ellipsoid of uniform potential vorticity, embedded in a background flow described by a quadratic streamfunction, is an exact solution of the quasigeostrophic equations governing motion in a uniformly stratified, unbounded fluid. This type of flow includes plane horizontal shear and strain as well as uniform vertical shear of a unidirectional horizontal flow. We derive ordinary differential equations describing the motion of such a vortex and discuss some aspects of their solutions. We note the existence of steady states (solutions in which the vortex is in equilibrium with the background flow), of periodic solutions near these steady states, of non-periodic trajectories which nervertheless remain in the vicinity of the steady states, and of solutions which represent the shearing out of the vortex by the background flow. We try to use this information to propose partial answers to the question of when a given horizontal or vertical shear flow is likely to destroy a vortex and when a vortex might survive external shear and strain.     

An Investigation into Effect of Randomly Distributed Small Scale Vortices on Vortex Self-Organization

Previous studies concerning the interaction of dual vortices have been made generally in the determin-istic framework. In this paper, by using an advection equation model, eight numerical experiments whose integration times are 30 h are performed in order to analyze the interaction of dual vortices and the vortex self-organization in a coexisting system of deterministic and stochastic components. The stochastic compo-nents are introduced into the model by the way that the Iwayama scheme is used to produce the randomly distributed small-scale vortices which are then added into the initial field. The different intensity of the small-scale vortices is described by parameter K being 0.0, 0.4, 0.6, 0.8, and 1.0, respectively. When there is no small-scale vortex (K=0.0), two initially separated meso-beta vortices rotate counterclockwise mutu-ally, and their quasi-final flow pattern is still two separated vortices; after initially incorporating small-scale vortices (K=0.8, 1.0), the two separated meso-beta vortices of initially same intensity gradually evolve into a major and a secondary vortex in time integration. The major vortex pulls the secondary one, which gradually evolves into the spiral band of the major vortex. The quasi-final flow pattern is a self-organized vortex with typhoon-like circulation, and the relative vorticity at its center increases with increasing in K value, suggesting that small-scale vortices feed the self-organized vortex with vorticity. This may be a pos-sible mechanism responsible for changes in the strength of the self-organized vortex. Results also show that the quasi-final pattern not only relates with the initial intensity of the small-scale vortices, but also with their initial distribution. In addition, three experiments are also performed in the case of various boundary conditions. Firstly, the periodic condition is used on the E-W boundary, but the fixed condition on the S-N boundary; secondly, the fixed condition is set on all the boundaries; and thirdly, the periodic condition is chosen on all the boundaries. Their quasi-final flow patterns in the three experiments are the same with each other, exhibiting a larger scale typhoon-like circulation. Based on these results mentioned above, authors think that the transition of vortex self-organization study from the deterministic system to the coexisting system of deterministic and stochastic components is worth exploring.     

涡群中双涡相互作用的研究

在涡旋自组织动力学的框架内，数值研究了涡群中双涡相互作用的问题，对比了弱环境流与涡群环境流两类条件下双涡作用的异同。指出：弱环境流条件下双涡合并的过程，在涡群环境条件下不再存在；同时，涡群环境流的引进可使涡强度显著增强。     

守恒系统中台风强度变化及其可能因子的数值研究

用一个高分辨率的 f平面正压涡度方程模式 ,实施了时间积分为 36h的 2 1组试验 ,研究相邻中尺度涡旋与台风涡旋的相互作用。结果指出 :这种相互作用能否导致台风加强 ,取决于两类因子 :一是台风涡旋最大风速的取值以及圆形基流切变的强弱 ;二是切变基流中的中尺度涡旋的自身条件 ,包括中尺度涡旋的分布、尺度、强度和结构。台风强度与初始中尺度涡旋的尺度、强度之间存在着非线性的联系     

Interaction between an eddy and a zonal jet : Part II. Two-and-a-half-layer model

In a two-and-a-half-layer quasi-geostrophic model, a process study is conducted on the interaction between a vortex and a zonal jet, both with constant potential vorticity. The vortex is a stable anticyclone, initially located north of the eastward jet. The potential vorticity of the jet is allowed to have various vertical structures, while the vortex is concentrated in only one layer. The flow parameters are set to values characteristic of the Azores region.First, the jet is stable. Weak vortices steadily drift north of the jet without crossing it while strong vortices can cross the jet and tear off a cyclone with which they pair as a heton (baroclinic dipole). This heton often breaks later in the shear exerted by the jet; the two vortices finally drift apart. When crossed by deep anticyclones, the jet develops meanders with 375 km wavelength. These results exhibit a noticeable similarity with the one-and-a-half-layer case studied in Part I.Secondly, the jet is allowed to be linearly unstable. In the absence of the vortex, it develops meanders with 175 km wavelength and 25-day e-folding time on the β-plane. For various vertical structures of the jet, baroclinic instability is shown to barely affect jet–vortex interaction if the linear growth rate of unstable waves is smaller than 1/(14 days). Further simulations with a linearly unstable, nonlinearly equilibrated jet evidence its strong temporal variability when crossed by a deep vortex on the β-plane. In particular, long waves can dominate the spectrum for a few months after jet crossing by the vortex. Again in this process, the deep vortex couples with a surface cyclone and both drift southwestward.     

An Investigation into Effect of Randomly Distributed Small Scale

Previous studies concerning the interaction of dual vortices have been made generally in the deterministic framework. In this paper, by using an advection equation model, eight numerical experiments whose integration times are 30 h are performed in order to analyze the interaction of dual vortices and the vortex self-organization in a coexisting system of deterministic and stochastic components. The stochastic components are introduced into the model by the way that the Iwayama scheme is used to produce the randomly distributed small-scale vortices which are then added into the initial field. The different intensity of the small-scale vortices is described by parameter K being 0.0, 0.4, 0.6, 0.8, and 1.0, respectively. When there is no small-scale vortex （K=0.0）, two initially separated meso-beta vortices rotate counterclockwise mutually, and their quasi-final flow pattern is still two separated vortices; after initially incorporating small-scale vortices （K=0.8, 1.0）, the two separated meso-beta vortices of initially same intensity gradually evolve into a major and a secondary vortex in time integration. The major vortex pulls the secondary one, which gradually evolves into the spiral band of the major vortex. The quasi-final flow pattern is a self-organized vortex with typhoon-like circulation, and the relative vorticity at its center increases with increasing in K value, suggesting that small-scale vortices feed the self-organized vortex with vorticity. This may be a possible mechanism responsible for changes in the strength of the self-organized vortex. Results also show that the quasi-final pattern not only relates with the initial intensity of the small-scale vortices, but also with their initial distribution. In addition, three experiments are also performed in the case of various boundary conditions. Firstly, the periodic condition is used on the E-W boundary, but the fixed condition on the S-N boundary; secondly, the fixed condition is set on all the boundaries; and thirdly, the periodic conditio