CONTOUR DYNAMICS FOR THE MOTION OF MULTIPLE RING VORTICES*

This paper generalizes the contour dynamics for single ring vortices to that for multiple ring vortices, wherein six sets of numerical computation are performed. The phenomenon of the counterclockwise loop of a moving vortex is clearly shown in the computational results and the asymmetric change with time of the vortex structure may serve as a precursor for the phenomenon. Besides, we also discuss the dependence of the motion direction of a vortex upon the degree of its contour denseness, and the dependence of the westward component of vortex motion upon its asymmetric structure. The results are fairly consistent with those of previous dynamical analyses and numerical experiments.     

多圈涡旋等值线动力学的研究

将单圈涡旋等值线动力学推广到多圈涡旋的等值线动力学。在等值线动力学的框架内,实施了6组计算。结果显示出涡旋移行过程中逆时针打转的现象,该现象有清楚的前兆可寻。讨论了涡旋松紧程度对涡旋移向的影响以及涡旋非对称结构与涡旋移速之间的联系。这些结果与以往数值试验或动力学分析的结果较为一致。     

On the bogusing of tropical cyclones in numerical models: The influence of vertical structure

Summary In this study, idealised conditions are used to study the influence of vertical structure of the bogus vortex on its motion in numerical models by comparing the resultant forecast tracks. Two vortices were used: one has a cyclonic circulation throughout the troposphere and the other has an upper tropospheric anticyclone. Both vortices have the same structure in the middle and lower troposphere. The two vortices were inserted into four different environmental flows on a beta-plane: (a) a resting atmosphere; (b) a uniform flow; (c) a horozontal shear flow and (d) a vertical shear flow. The results show that the forecast tracks are very sensitive to the vertical structure of the bogus vortex, especially when the environmental flow is very weak, or is westerly and has a cyclonic horizontal shear. However, this sensitivity is reduced in moderate vertical shear. This motion sensitivity is found to arise from the vertical coupling mechanism by which the upper-and lower-level circulations interact with each other when a horizontal displacement occurs between them.The vertical structure of the bogus vortex can also affect the intensity of the model cyclone, depending on the configuration of the environmental flow. In general, the bogus vortex without an upper-level anticyclone will intensify quicker and will develop more intense than the one with an upper-level anticyclone. The vertical coupling mechanism can result in different asymmetric rainfall pattern in cyclone core region depending on the vertical structure of the bogus vortex. The asymmetric divergent flow associated with these convective asymmetries may in turn further influence the vortex motion. It is suggested that care needs to be taken in determining the vertical structure of the bogus vortex in numerical models.With 14 Figures     

A numerical study of multiple vortex self-organization as forced by mesoscale topography

Summary There exists a common observational phenomenon over the offshore areas of the northwest Pacific, that is, when several mesoscale vortices evolve suddenly into a larger scale typhoon-like vortex within one day, often with serious consequences. In this paper a series of numerical experiments has been designed and performed to emulate this evolution. The model is based on the Charney-Hasegawa-Mima equation, where there are around 40 initial meso-β vortices with parabolic profiles whose central positions, dimensions and intensities are all set stochastically. The self-organization process of these stochastically-distributed multiple meso-β vortices can be divided into two phases. During the first phase, a larger scale vortex similar to a typhoon-like vortex forms near the computational center through the gradual stretching and merging of adjacent meso-β vortices while there are more than 10 isolated vortices surrounding this typhoon-vortex. During the second phase, the isolated vortices are stretched and drawn into the typhoon-vortex circulation and become its spiral arms which are gradually incorporated into the inner area of the typhoon. This is then repeated as new isolated vortices are stretched and become new spiral arms until all the isolated vortices are drawn into the typhoon-vortex. The center of the self-organized typhoon-vortex rotates counterclockwise around the computational center when no topography is involved and is thus a transient vortex. When topography is present the vortex remain in the NE quadrant of the model domain, locked by the topography, and this quasi-steady vortex is thus capable of causing local disasters. Correspondence: Chongjian Liu, Chinese Academy of Meteorological Sciences (CAMS), State Key Labaratory of Severe Weather, 46 Zhongguancum South Avenue, 100081 Beijing, P.R. China     

CONTOUR DYNAMICS FOR VORTEX MOTION INFLUENCED BY THE CORIOLIS FORCE*

The computational formulae are given for single-contour constant-value vortex motion influenced by the Coriolis force in the framework of contour dynamics,by which four numerical computations are performed,the result exhibiting their validity.     

CONTOUR DYNAMICS FOR VORTEX MOTION INFLUENCED BY THE CORIOLIS FORCE

The computational formulae are given for single-contour constant-value vortex motion influenced by the Coriolisforce in the framework of contour dynamics,by which four numerical computations are performed,the result exhibitingtheir validity.     

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。     

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.     

Two-dimensional asymmetric vortex merger: merger dynamics and critical merger distance

Two-dimensional asymmetric merger of two like-signed vorticity monopoles with different sizes and vorticities is examined by combining simplified analytical models and contour dynamics experiments. The model results can capture the key dynamics and hence allow the prediction of the critical merger distance in a number of the situations. The models ignore deformation of one of the two vortices, replacing it with a point vortex, and employ a corotating frame of reference with a rotation rate estimated by point vortices. Thus, the two vortex problem becomes two separate problems of a single vortex in a background shear flow. Vortex merger is found to happen when the vortex cannot resist the background shear flow. Vortex merger and merging processes depend on the centroid distance d, the circulation ratio, (q_i and r_i are the vorticity and radius, respectively) and initial conditions. In the lowest order, the background flow is approximated by a uniform shear field, and the behavior of an elliptical vortex can be described by the Kida (1981) equation supplemented with one describing the time evolution of the centroid distance. This model reveals that merger takes place because the natural rotation of an elliptical vortex is overcome by the background uniform shear flow; the ellipse inversely rotates and is drawn out by the background straining field. The vortex deformation in a background flow field induces an inward flow at the position of the other vortex; as a result, the centroid distance decreases and two vortices merge. The critical merger distance from this model agrees quite well with the results from contour dynamics experiments for two vortices. Inclusion of higher order non-uniform shear in the background flow extends the critical merger distance, which gives almost perfect estimates for the experiment. In the non-uniform shear flow, partial merger occurs, where the vortex sheds off a filament, but the remaining part of the vortex resumes its natural rotation.     

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     

边缘区域扰动演变对台风结构的影响

在台风环流边缘区域给出不稳定模态的扰动四波分布作为初始场，用准地转正压模式实施四组数值积分，研究了边缘区域扰动演变及其对台风非对称结构及外区流型的影响。结果表明:线性平流对于外缘区域扰动的发展起主要作用。β项导致一个气旋—反气旋涡旋对和非对称结构的形成。非线性平流则使外缘区域较小尺度的涡旋破碎，形成更小尺度的涡旋。在线性平流、β项和非线性平流的共同作用下，台风结构与外区形成象螺旋云系的分布。外缘区域扰动引起的结构变化，进而能影响到台风的移动路径。     

1998年夏季西南低涡活动与长江上游暴雨

应用天气学和统计学方法，分析了1998年盛夏西南低涡活动的主要特征。指出该年夏季西南低涡活动偏强，该年长江上游暴雨偏多与此有关。     

Typhoon Vortex Self-Organization in a Baroclinic Environment

Self-organization of typhoon vortex in a baroclinic environment is studied based on eight numerical experiments with the fifth-generation Pennsylvania State University/National Center for Atmospheric Research （PSU/NCAR） Mesoscale Model （MM5）. The results show that, when there are only two 400-km-away mesoscale axisymmetric vortices with a radius of 500 km in the initial field, the two vortices move away from each other during co-rotating till the distance between them greater than a critical distance named co-rotating critical distance. Then, they stop co-rotating. The situation is changed when a small vortex with a radius of 80 kin is introduced in between the two vortices in the initial field, with the two initially separated vortices approaching each other during their co-rotation, and finally self-organizing into a typhoon-like vortex consisting of an inner core and spiral bands. This result supports both Zhou Xiuji＇s view in 1994 and the studies in the barotropic framework concerning the interactions between the same and different scales of vortices. Six other experiments are carried out to study the effects of the initial vortex parameters, including the initial position of the small-scale vortex, the distance and intensity of the initially axisymmetric binary mesoscale vortices. It is found that the distance between the initial axisymmetrie mesoscale vortices is the most important parameter that influences the self-organizing process of the final typhoon-like vortex. This conclusion is similar to that obtained from barotropical model experiments.     

Low-Order Point Vortex Models of Atmospheric Blocking

Summary Conceptual models of blocking structures are constructed by reducing the two-dimensional atmospheric vorticity field to a few point vortices. The flow is assumed to be barotropic and divergence-free, and a blocking event is represented by a point vortex dipole. The focus is here on the motion of the blocking dipole under the influence of the zonal mean flow. This is modelled in three different ways: A dipole embedded in a latitude-dependent zonal mean flow exhibits neutrally stable oscillations; their period is estimated analytically. A cyclonic point vortex approaching from upstream can either pass the dipole or break it up, so that an Ω-shaped pattern of three vortices emerges. The stationarity of a blocking between two troughs is modelled by four point vortices. These low-order point vortex models are compared with the dynamics of real blockings in case studies. Despite their high degree of simplification, those models reproduce the kinematics of blocking events properly. This results from the discretization of the flow to its actual physical states, the vortices, in contrast to the common, purely mathematical discretization to grid points. Thus, point vortex dynamics are proposed to be a powerful completion of continuous fluid dynamics in explaining blocking events. Received August 30, 1999 Revised December 22, 1999     

Effect of Baroclinicity on Vortex Axisymmetrization.Part Ⅱ：Baroclinic Basic Vortex

The effect of baroclinicity on vortex axisymmetrization is examined within a two-layer dynamical model.Three basic state vortices are constructed with varying degrees of baroclinicity：（i） barotropic,（ii） weak baroclinic,and （iii） strong baroclinic.The linear and nonlinear evolution of wavenumber-2 baroclinic disturbances are examined in each of the three basic state vortices.The results show that the radial propagating speed of the vortex Rossby wave at the lower level is larger with the stronger baroclinicity,resulting in a faster linear axisymmetrization process in the stronger baroclinic vortex.It is found that the nonlinear axisymmetrization process takes the longest time in the strongest baroclinic vortex among the three different basic vortices due to the weaker kinetic energy transfer from asymmetric to symmetric circulations at the lower level.A major finding in this study is that the same initial asymmetric perturbation can have different effects on symmetric vortices depending on the initial vortex baroclinicity.In numerical weather prediction models,this implies that there exists a sensitivity of the subsequent structural and intensity change solely due to the specification of the initial vertical shear of the tropical cyclone vortex.     

Mesoscale cyclones over the Black Sea

Considered are the results of the numerical analysis of two mesoscale cyclonic vortices generated over the Black Sea near the Caucasian coast on August 3, 2007 and August 7, 2010. It is demonstrated for the axially symmetric and more long-lived vortex occurred in 2007 that the Caucasian vortices are two-dimensional structures dying out rapidly due to the turbulent friction in the near-water boundary layer, and the deviation from the strictly two-dimensional motion is associated with the presence of the secondary circulation. The difference is demonstrated in the mechanisms of the origin of vortices in 2007 and 2010. In the first case, this is the formation of cyclonic circulation over the eastern part of the Black Sea limited by the Anatolian and high Caucasian Mountains, at the intrusion of the airflow of northwestern direction. In the second case, these are the processes of the generation of cyclonic vorticity at the baroclinic airflow running around the northwestern edge of the mountain range over the land.     

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.     

Effect of the Interaction of Different Scale Vortices on the Structure and Motion of Typhoons

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小尺度系统对涡旋自组织的影响

在涡旋自组织动力学的框架内,利用．厂平面准地转正压模式讨论小尺度涡旋系统对两个中β尺度涡旋的自组织过程的影响。4组数值试验表明：小尺度涡旋的存在,可能会改变双涡相互作用的终态,使原本不合并的两个涡旋组织起来;双涡相互作用的终态对小尺度涡旋的初始位置敏感;存在“Z”型敏感区域,当小尺度涡旋出现在这一区域时,就有可能改变双涡相互作用的终态;小尺度涡旋对双涡相互作用产生影响需具备4个条件,即初始位于敏感区内,有足够的强度,距离适当且生存时间足够长。     

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.