与海南岛秋季暴雨有关的一类热带中尺度涡旋的动力学分析

对惯性重力内波方程组分别通过线性和非线性求解探讨造成2010年10月海南岛一次特大暴雨中一类热带中尺度涡旋生成发展的动力、热力机制,研究发现：（1）在副热带高压和大陆冷高压南侧反气旋性纬向水平风切变大值区、静力不稳定大气层结、积云对流潜热释放、低空急流、适当强度的冷空气有利于热带中尺度涡旋的形成和发展;（2）非线性惯性重力内波的孤立波解与这类热带中尺度涡旋有很好的联系,在静力不稳定的大气层结下,热带中尺度涡旋的形态主要由对流凝结潜热加热所决定,即潜热加热下的孤立波解要求热带中尺度涡旋在垂直方向是一个浅薄的涡旋系统;另外强盛的对流凝结潜热对热带中尺度涡旋垂直运动振幅的增强起主要作用,更有利于涡旋的发展和维持。基于天气事实分析的理论研究为深化影响海南的热带中尺度涡旋乃至南海中尺度对流系统的机理认识进行了探索。     

A simple model of dry convective helical vortices (with applications to the atmospheric dust devil)

An asymptotic solution of inviscid Boussinesq equations for a ‘dry convective Rankine vortex’ with prescribed buoyant forcing is given. The obtained vortex solution demonstrates monotonic growth with height of the vortex core radius, which becomes infinite at a certain critical altitude, and the corresponding attenuation of the vertical vorticity. This idealized vortex is then embedded in a convectively unstable boundary layer; the resulting approximate vortex solution has been applied to determine the maximum rotational wind speed and diameter of dry convective dust-devil-like vortices.     

The effect of ageostrophy on the stability of thin oceanic vortices

This paper examines the stability of vortices in a two-layer ocean on the f-plane. The mean depth of the upper layer is assumed to be much smaller than the depth of the lower layer. Using the primitive equations, we derive an asymptotic criterion for baroclinic instability of compensated (i.e. confined to the upper layer) vortices. Surprisingly, it coincides exactly with a similar criterion derived from the quasigeostrophic equations [Benilov, E.S., 2003. Instability of quasigeostrophic vortices in a two-layer ocean with thin upper layer. J. Fluid Mech. 475, 303–331]. Thus, to leading order in , ageostrophy does not affect the stability properties of thin compensated vortices. As a result, whether a vortex is stable or not, depends on its shape, not amplitude (although the growth rate of an unstable vortex does depend on its amplitude).     

CHANGES OF TYPHOON INTENSITY AND ITS POSSIBLE INFLUENCING FACTORS IN AN f-PLANE BAROTROPIC QUASIGEOSTROPHIC MODEL

By using an f-plane barotropic quasigeostrophic model with the grid-spacing being 5 km,21 experiments whose integration time is 36 h are performed in this paper in order to investigate interactions between a typhoon vortex and its adjacent mesoscale vortices.Results show that whether the interaction leads to the intensification of the typhoon vortex depends on two kinds of factors:one is the value of the maximum wind speed of the typhoon vortex and the intensity of the shearing of circular basic flow:and the other is the condition of mesoscale vortices in the shearing basic flow,such as the spatial distribution,scale,intensity and structure of mesoscale vortices. There is the nonlinear relation between typhoon intensity and the scale and intensity of initial mesoscale vortices.     

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.     

Vortex Rossby waves on smooth circular vortices: Part I. Theory

A complete theory of the linear initial-value problem for Rossby waves on a class of smooth circular vortices in both f-plane and polar-region geometries is presented in the limit of small and large Rossby deformation radius. Although restricted to the interior region of barotropically stable circular vortices possessing a single extrema in tangential wind, the theory covers all azimuthal wavenumbers. The non-dimensional evolution equation for perturbation potential vorticity is shown to depend on only one parameter, G, involving the azimuthal wavenumber, the basic state radial potential vorticity gradient, the interior deformation radius, and the interior Rossby number.In Hankel transform space the problem admits a Schrödinger’s equation formulation which permits a qualitative and quantitative discussion of the interaction between vortex Rossby wave disturbances and the mean vortex. New conservation laws are developed which give exact time-evolving bounds for disturbance kinetic energy. Using results from the theory of Lie groups a nontrivial separation of variables can be achieved to obtain an exact solution for asymmetric balanced disturbances covering a wide range of geophysical vortex applications including tropical cyclone, polar vortex, and cyclone/anticyclone interiors in barotropic dynamics. The expansion for square summable potential vorticity comprises a discrete basis of radially propagating sheared vortex Rossby wave packets with nontrivial transient behavior. The solution representation is new, and for this class of swirling flows gives deeper physical insight into the dynamics of perturbed vortex interiors than the more traditional approach of Laplace transform or continuous-spectrum normal-mode representations. In general, initial disturbances are shown to excite two regions of wave activity. At the extrema of these barotropically stable vortices and for a certain range of wavenumbers, the Rossby wave dynamics are shown to become nonlinear for all initial conditions. Extensions of the theory are proposed.     

高原低涡移出高原的观测事实分析

应用天气学、统计学原理,结合TRMM资料,分析了1998—2004年5—9月移出高原的低涡的活动特征。结果指出:6—8月是高原低涡移出高原影响中国东部天气的主要时段,它与高原低涡在高原上的活动特征及西南低涡移出高原特征均不同;移出高原的高原低涡的涡源主要在曲麻莱附近、德格附近,这与高原上产生低涡的涡源不同;移出高原的高原低涡的移动路径多数是随低槽的活动而向东、向东南移动,这与高原低涡在高原上多数是沿切变线移向东北不同,高原低涡移出高原后,不仅影响中国的范围广,还可能影响到朝鲜半岛、日本;高原低涡移出高原后涡的强度、性质会有变化,在高原以东活动时间长(≥36 h)的高原低涡,移出高原前多数为暖性低涡,移出高原后多数为斜压性低涡,低涡加强、多数可产生暴雨、大暴雨;高原低涡移出高原后移到海洋上,往往因下垫面不同而变化,出海后都有降水加强、多数位势高度下降的现象;移出高原后的高原低涡因东面海上热带气旋活动而少动,与其南面热带气旋活动相向而行,因季风低压少动而少动的现象。     

一种新的梅雨锋上中尺度涡旋识别方法

中尺度涡旋的发生、发展对梅雨锋暴雨常具有直接作用,客观准确地识别中尺度涡旋有助于提高暴雨预报的准确性。本研究提出一种从格点风场中自动识别中尺度涡旋中心的客观方法。利用美国国家环境预报中心(NCEP)提供的全球模式分析资料,选取2013—2014年梅雨期间两次暴雨个例,考察新方法识别中尺度涡旋的能力,并与现有的两种识别方法(分别基于相对涡度场与基于高度场)进行比较分析。结果表明,由于较小尺度的系统不遵守地转风规则,梅雨锋上许多涡旋的风场环流中心、涡度中心与低压中心位置不重合,影响通过涡度识别或气压识别方法的准确性。新方法从风场出发,可准确识别出大多数涡旋中心,误判率低,定位精度高于无人工辅助下的另外两种方法。接着利用新方法分析了两次暴雨个例中不同中尺度涡旋的垂直结构与时间演变。分析表明,新方法无需人工辅助,无特定层高和时间限制,可在短时间内识别出区域内所有中尺度涡旋的位置、三维结构与时间演变,可用于梅雨期间静止锋上中尺度涡旋的识别和路径的追踪,有助于预报员实时分析与预报暴雨。     

The thermodynamic speed limit and its violation in axisymmetric numerical simulations of tornado‐like vortices

Abstract

Processes that regulate the central pressure and maximum wind speeds of tornado‐like vortices are explored with an axisymmetric numerical model. The model consists of a rotating cylinder of fluid enclosed within rigid boundaries. The momentum diffusivity is a fixed function of height. In the rotating reference frame, relative motion is induced by a buoyancy force in the vicinity of the rotation axis, leading to the formation of a central vortex. The work done by the central buoyancy force on a parcel rising along the axis defines theoretical and empirical wind speed bounds on both the updraft and the low‐level vortex. Certain processes are found that allow for the vortex to greatly exceed this wind speed bound, or the so‐called thermodynamic speed limit; however, in most of the parameter space the vortex wind speeds are close to the thermodynamic speed limit.

The most effective limit‐breaking process involves a supercritical end‐wall vortex with an axial jet. In steady state, the supercritical vortex sustains wind speeds 2.0 times the speed limit. A transient end‐wall vortex, with the vortex breakdown travelling rapidly downwards toward the surface, is able to achieve wind speeds 5.0 times the speed limit. Warming of the subsiding vortex core past the vortex breakdown increases the maximum steady‐state azimuthal wind speed by about 20% from what it would be otherwise. Axial momentum diffusion is not found to significantly enhance the surface pressure deficit in any of the simulations.     

Numerical modeling studies of lee mesolows,mesovortices and mesocyclones with application to the formation of Taiwan mesolows

Summary Numerical experiments are performed for inviscid flow past an idealized topography to investigate the formation and development of lee mesolows, mesovortices and mesocyclones. For a nonrotating, low-Froude number flow over a bell-shaped moutain, a pair of mesovortices form on the lee slope move downstream and weaken at later times. The advection speed of the lee vortices is found to be about two-thirds of the basic wind velocity, which is due to the existence of a reversed pressure gradient just upstream of the vortices. The lee vortices do not concur with the upstream stagnation point in time, but rather form at a later time. It is found that a pair of lee vortices form for a flow withFr=0.66, but take a longer time to form than in lower-Froude number flows. Since the lee vortices are formed rather progressively, their formation may be explained by the baroclinically-induced vorticity tilting as the mountain waves become more and more nonlinear.A stationary mesohigh and mesolow pressure couplet forms across the mountain and is produced in both high and low-Froude number flows. The results of the high Froude number simulations agree well with the classical results predicted by linear, hydrostatic mountain wave theory. It is found that the lee mesolow is not necessarily colocated with the lee vortices. The mesolow is formed by the downslope wind associated with the orographically forced gravity waves through adiabatic warming. The earth's rotation acts to strengthen (weaken) the cyclonic (anticyclonic) vortex and shifts the lee mesolow to the right for an observer facing downstream. The cyclonic vortex then develops into a mesocyclone with the addition of planetary vorticity at later times. For a flow over a steeper mountain, the disturbance is stronger even though the Froude number is kept the same.For a southwesterly flow past the real topography of Taiwan, there is no stagnation point or lee vortices formed because the impinging angle of the flow is small. A major mesoscale low forms to the southeast of the Central Mountain Range (CMR), while a mesohigh forms upstream. For a westerly flow past Taiwan, a stagnation point forms upstream of the mountain and a pair of vortices form on the lee and move downstream at later times. The cyclonic vortex then develops into a mesocyclone. A mesolow also forms to the southeast of Taiwan. For a northeasterly flow past Taiwan, the mesolow forms to the northwest of the mountain. Similar to flows over idealized topographies, the Taiwan mesolow is formed by the downslope wind associated with mountain waves through adiabatic warming. A conceptual model of the Taiwan southeast mesolow and mesocyclone is proposed.With 16 Figures     

Observed and simulated precursors of stratospheric polar vortex anomalies in the Northern Hemisphere

The Northern Hemisphere stratospheric polar vortex is linked to surface weather. After Stratospheric Sudden Warmings in winter, the tropospheric circulation is often nudged towards the negative phase of the Northern Annular Mode (NAM) and the North Atlantic Oscillation (NAO). A strong stratospheric vortex is often associated with subsequent positive NAM/NAO conditions. For stratosphere?Ctroposphere associations to be useful for forecasting purposes it is crucial that changes to the stratospheric vortex can be understood and predicted. Recent studies have proposed that there exist tropospheric precursors to anomalous vortex events in the stratosphere and that these precursors may be understood by considering the relationship between stationary wave patterns and regional variability. Another important factor is the extent to which the inherent variability of the stratosphere in an atmospheric model influences its ability to simulate stratosphere?Ctroposphere links. Here we examine the lower stratosphere variability in 300-year pre-industrial control integrations from 13 coupled climate models. We show that robust precursors to stratospheric polar vortex anomalies are evident across the multi-model ensemble. The most significant tropospheric component of these precursors consists of a height anomaly dipole across northern Eurasia and large anomalies in upward stationary wave fluxes in the lower stratosphere over the continent. The strength of the stratospheric variability in the models was found to depend on the variability of the upward stationary wave fluxes and the amplitude of the stationary waves.     

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。     

Vortex–ridge interaction in a rotating fluid

The evolution of barotropic vortices interacting with a topographic ridge on a f-plane is studied by means of laboratory experiments in a rotating tank and numerical simulations. The initial condition in all experiments is a cyclonic vortex created at a certain distance from the ridge. The results are presented in two main scenarios: (a) weak interactions, which occur at early stages of the experiments, when the vortex is far from the ridge, and thus weakly experiences the influence of the topography. In these situations, the vortex slowly drifts towards the ridge with a leftward inclination due to the ascending slope of the topography. Such a behaviour is similar to the “northwestern” motion of cyclones over a weak sloping bottom. The circular shape of the monopolar vortex is preserved. (b) Strong interactions, in which the vortex core reaches the ridge and presents a more complicated evolution. The cyclone “climbs” to the top of the topography and crosses to the other side. Once the vortex experiences the opposite slope, it moves backwards trying to return to the original side of the ridge. For strong enough vortices, this process may be repeated a number of times until the vortex is dissipated by viscous effects. During these interactions the shape of the vortex is strongly deformed and several filaments are produced. In some cases the vortex is cleaved in two parts when crossing the ridge, one at each side of it and moving in opposite directions.Weak and strong interactions are numerically simulated by using a quasi-two-dimensional model. The results confirm that the vortex behaviour is governed by stretching and squeezing effects associated with changes in depth over the ridge and, at latter stages, by Ekman damping due to the solid bottom. The main results observed during strong interactions on a f-plane are also found on preliminar topographic β-plane experiments.     

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.     

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.     

冷空气对高原低涡移出青藏高原的影响

在对1998—2004年冷空气影响高原低涡移出青藏高原 (以下简称高原) 观测事实分析的基础上, 利用NCEP再分析资料对2002年8月12—14日托勒低涡移出高原的位涡进行诊断分析, 并通过数值试验揭示了托勒低涡移出高原的冷空气侵入特征和影响机理。结果表明:这次托勒低涡是受我国东北冷空气影响, 有高位涡空气伸入低涡区, 使冷空气迫近暖湿空气, 低涡处在斜压不稳定增强情况下移出高原的。在低涡区域没有冷空气或我国东北不存在冷温度槽情况下, 将会使伸向高原东北部的冷空气主力偏东、减弱, 使低涡受到我国东北冷空气影响减弱, 斜压不稳定减弱, 从而使高原低涡移出高原的速度减慢, 低涡强度减弱, 尤其是我国东北冷温度槽的影响更为明显, 在我国东北没有冷温度槽存在的情况下, 低涡24 h内西退, 在高原边缘徘徊。     

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     

Experimental Study on Effects of Ground Roughness on Flow Characteristics of Tornado-Like Vortices

The three-dimensional wind velocity and dynamic pressure for stationary tornado-like vortices that developed over ground of different roughness categories were investigated to clarify the effects of ground roughness. Measurements were performed for various roughness categories and two swirl ratios. Variations of the vertical and horizontal distributions of velocity and pressure with roughness are presented, with the results showing that the tangential, radial, and axial velocity components increase inside the vortex core near the ground under rough surface conditions. Meanwhile, clearly decreased tangential components are found outside the core radius at low elevations. The high axial velocity inside the vortex core over rough ground surface indicates that roughness produces an effect similar to a reduced swirl ratio. In addition, the pressure drop accompanying a tornado is more significant at elevations closer to the ground under rough compared with smooth surface conditions. We show that the variations of the flow characteristics with roughness are dependent on the vortex-generating mechanism, indicating the need for appropriate modelling of tornado-like vortices.     

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.     

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