CONTOUR DYNAMICS FOR THE MOTION OF MULTIPLE RING VORTICES Luo Zhexian Nanjing Institute of Meteorology,Nanjing 210044

contour dynamics;;multiple ring vortex;;Coriolis force;;nonlinearity     

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     

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。     

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

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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.     

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.     

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.     

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     

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     

DYNAMIC ANALYSIS OF INHERENT CAUSES FOR DEVIATION OF TROPICAL CYCLONE TRACKS

To have a clearer picture of mechanisms responsible for the deviation of tropical cyclone (to be simplified as TC hereafter) tracks, the current work assumes the TC as a circular vortex with a radius of R. A general motion equation of TC is then determined by averaging its horizontal motion equation over the sentire region of TC. In the meantime, with the moving track of TC assumed as a characteristic arc, the curvature equation is derived for the track of movement and patterns of its deviation due to TC structure and variation are discussed. The result shows that the scale, size, maximum wind speed and radius are factors causing the deviation of TC tracks. In addition, asymmetric structure of TC is also important for the deviation of tracks. The results, achieved with hypothesis, agree with facts in some cases but disagree with them in others, which are to be verified with more observations or numerical simulations.     

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。     

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.     

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.     

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     

一次高原低涡过程的数值模拟与结构特征分析

利用非静力中尺度数值模式MM5,模拟了2009年7月29～31日的一次高原低涡过程,结果表明,TBB卫星资料显示出在低涡发展过程中具有同热带气旋类低涡相似的涡眼结构.MM5模式能较好地模拟出低涡的降水落区、强度以及内部结构,正位涡区随着低涡的东移而东移.在动力结构上,低涡发展过程中,涡心处散度和涡度的变化不大,垂直速度...     

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。     

Effect of tropical cyclone intensity and instability on the evolution of spiral bands

The evolution of spiral-band-like structures triggered by asymmetric heating in three tropical-cyclone-like vortices of different intensities is examined using the Three-Dimensional Vortex Perturbation Analyzer and Simulator （3DVPAS） model. To simulate the spiral bands, asymmetric thermal perturbations are imposed on the radius of maximum wind （RMW） of vortices, which can be considered as the location near the eyewall of real tropical cyclones （TCs）. All the three vortices experience a hydrostatic adjustment after the introduction of thermal asymmetries. It takes more time for weaker and stable vortices to finish such a process. The spiral-band-like structures, especially those distant from the vortex centers, form and evolve accompanying this process. In the quasi-balance state, the spiral bands are gradually concentrated to the inner core, the wave behavior of which resembles the features of classic vortex Rossby （VR） waves. The unstable vortices regain nonhydrostatic features after the quasi-balance stage. The spiral bands further from the vortex center, similar to distant spiral bands in real TCs, form and maintain more easily in the moderate basic-state vortex, satisfying the conditions of barotropic instability. The widest radial extent and longest-lived distant bands always exist in weak and stable vortices. This study represents an attempt to determine the role of TC intensity and stability in the formation and evolution of spiral bands via hydrostatic balance adjustment, and provides some valuable insights into the formation of distant spiral rainbands.