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.     

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

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     

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.     

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.     

地形对涡旋自组织影响的初步研究

用一个带有地形项的f平面准地转正压涡度方程，实施5组积分时间长度为72h的试验，研究了中尺度地形对涡旋自组织的影响。结果指出：无地形时，准终态涡是一个带有螺旋带的类似台风的涡旋；有地形时，准终态涡是一个无螺旋带但有两个低涡量区的准圆形涡旋。有无地形两个准终态涡中心的位置可以相距100km以上。     

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。      

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.     

Numerical simulation of a heavy rainfall event in China during July 1998

Summary A detailed analysis associated with this case has been carried out (Zhao et al., 2001). In order to conduct further research on the meso-β scale system, which is the directly influencing system, the heavy rainfall that occurred in Wuhan (Station no.: 57494) and Huangshi (Station no.: 58407), Hubei Province during July 1998 are simulated using higher resolution and more complete initial data, after the large scale fields and rainfall areas have been simulated successfully. The simulation results indicate that there are meso-β scale weather systems which developed and dissipated near Wuhan and Huangshi during 1800 UTC 20 July to 0600 UTC 21 July and 1800 UTC 21 July to 0600 UTC 22 July in 1998, respectively. The life cycle of the meso-scale system is about 12 hours and its horizontal scale is from 100 to 200 km. These are characteristic of a typical meso-β scale system. By analyzing the vertical section of wind field and other physical variables during the mentioned-above two periods, it is found that horizontal convergence, ascending motion and positive vorticity of the middle and lower troposphere are strengthened during the heavy rainfall periods near the above mentioned two places. In addition, the wind disturbance in middle and lower troposphere may be a possible triggering mechanism for the occurrence of the meso-β weather system. A budget analysis of the meso-scale system indicates that the sources of moisture and positive vorticity are different during the different stages of the meso-scale systems. Finally, a three dimensional conceptual model of the meso-β scale systems causing the sudden heavy rainfall in Wuhan and Huangshi is suggested. Received November 4, 2001 Revised December 28, 2001     

青藏高原上中尺度对流系统(MCS)的数值模拟

A mesoscale convective system (MCS) developing over the Qinghai-Xizang Plateau on 26 July 1995 issimulated using the fifth version of the Penn State-NCAR nonhydrostatic mesoscale model (MM5). Theresults obtained are inspiring and are as follows. (1) The model simulates well the largescale conditionsin which the MCS concerned is embedded, which are the well-known anticyclonic Qinghai-Xizang PlateauHigh in the upper layers and the strong thermal forcing in the lower layers. In particular, the modelcaptures the meso-α scale cyclonic vortex associated with the MCS, which can be analyzed in the 500 hPaobservational winds; and to some degree, the model reproduces even its meso-β scale substructure similarto satellite images, reflected in the model-simulated 400 hPa rainwater. On the other hand, there aresome distinct deficiencies in the simulation; for example, the simulated MCS occurs with a lag of 3 hoursand a westward deviation of 3-5° longitude. (2) The structure and evolution of the meso-α scale vortexassociated with the MCS are undescribable for upper-air sounding data. The vortex is confined to thelower troposphere under 450 hPa over the plateau and shrinks its extent with height, with a diameter of4° longitude at 500 hPa. It is within the updraft area, but with an upper-level anticyclone and downdraftover it. The vortex originates over the plateau, and does not form until the mature stage of the MCS. Itlasts for 3-6 hours. In its processes of both formation and decay, the change in geopotential height fieldis prior to that in the wind field. It follows that the vortex is closely associated with the thermal effectsover the plateau. (3) A series of sensitivity experiments are conducted to investigate the impact of varioussurface thermal forcings and other physical processes on the MCS over the plateau. The results indicatethat under the background conditions of the upper-level Qinghai-Xizang High, the MCS involved is mainlydominated by the low-level thermal forcing. The simulation described here is a good indication that itmay be possible to reproduce the MCS over the plateau under certain large-scale conditions and with theincorporation of proper thermal physics in the lower layers.     

A study of the effect of topography on the merging of vortices

Eight sets of numerical experiments are performed in 48 hours of integtation by using a barotropic primitive equation model with a topographic term so as to investigate the effect of topography on the merging of vortices. It is pointed out that the introduction of topography may change the track of vortices,and it causes the low vortices and vorticity lumps to be detained on the southeast side of the topography,thus creating a favorable condition for the merging of the low vortex and vorticity lumps. It is also shown that the effect of topography may cause double mergers of vortices in a horizontally shearing basic flow,and it can strengthen the low vortex remarkably.     

大地形上空偶极子东移对热带气旋路径的影响

With a quasi-geostrophic barotropic model on the β-plane with a topography term, 16 experiments were performed with an integration period of 6 days. The interaction between tropical cyclone tracks and 500 kin-scale vortices originating from the western part ora large-scale topography is investigated. It is suggested that this kind of interaction may have a significant impact on the moving speed and direction of tropical cyclones. Under certain conditions, this interaction may be a factor in causing an abnormal tropical cyclone track. Furthermore, the effect of large-scale topography plays an important role in the formation of unusual tropical cyclone tracks.     

Semi-Implicit Scheme for the DWD Lokal-Modell

Summary  The fourth generation of numerical weather prediction (NWP) models is currently under development at the Deutscher Wetterdienst (DWD) consisting of a global grid point model (GME) and limited-area Lokal-Modell (LM). The nonhydrostatic fully compressible LM has been designed to meet high-resol ution regional fore-cast requirements at meso-β and meso-γ scales. The initial LM implementation is based on the NCAR/Penn State MM5 with the addition of a novel generalized terrain-following coordinate and rotated lat-lon grid. A fully 3D semi-implicit time-stepping scheme has been implemented by retaining the full buoyancy term instead of the approximate form found in MM5. In contrast with earlier schemes, mass-lumping is not applied to simplify the elliptic operator on an Arakawa-C/Lorenz grid. The resulting variable-coefficient elliptic problem is solved using a minimal residual Krylov iterative method with line relaxation preconditione rs. The new semi-implicit scheme is compared with a variant of the Klemp–Wilhelmson split-explicit scheme (horizontal explicit, vertical implicit) on the basis of computational efficiency and accuracy at resolutions ranging from 7 km to 400 m. Both idealized 3D mountain wave flows and naturally occuring flows are analyzed. Below the tropopause, the 3D semi-implicit scheme can be more efficient for low Mach number M ≪ 1 flows when the number of small time steps Δt _s of the split-explicit approach increases with the sound-speed Courant number. Revised October 7, 1999     

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21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。     

长江下游梅汛期中尺度涡旋特征分析

利用2006～2009 年日本再分析资料对长江下游地区梅汛期间(5～7 月)边界层内中尺度涡旋进行普查,并分类统计分析了边界层内中尺度涡旋与暴雨、低空急流的关系。研究结果表明:每年的5～7 月该地区经常在对流层低层或(和)边界层内出现中尺度扰动涡旋,根据中尺度涡旋最初生成的高度不同,可划分为边界层中尺度涡旋、对流层低层中尺度涡旋和对流层低层—边界层中尺度涡旋三类。边界层中尺度涡旋中与暴雨有密切关系的中尺度涡旋称为边界层中尺度扰动涡旋(PMDV),根据涡旋前或后6 小时累积雨量,可以进一步将其分成两类:第一类是暴雨的直接制造者中尺度对流系统(MCS)先于边界层中尺度扰动涡旋发生(MCS-PMDV);第二类是边界层中尺度涡旋产生后,激发了中尺度对流,造成了暴雨过程(PMDV-MCS)。PMDV-MCS 类涡旋暴雨的特点是在对流层低层850 hPa 是一条切变线,其南侧有一支西南低空急流,边界层925 hPa 则是一个闭合的涡旋,暴雨区主要落在涡旋的东北面和东南面。     

An Analysis of a Meso-β System in a Mei-yu Front Using the Intensive Observation Data During CHeRES 2002

The conventional and intensive observational data of the China Heavy Rain Experiment and Study (CHeRES) are used to specially analyze the heavy rainfall process in the mei-yu front that occurred during 20-21 June 2002, focusing on the meso-β system. A mesoscale convective system (MCS) formed in the warm-moist southwesterly to the south of the shear line over the Dabie Mountains and over the gorge between the Dabie and Jiuhua Mountains. The mei-yu front and shear line provide a favorable synoptic condition for the development of convection. The GPS observation indicates that the precipitable water increased obviously about 2-3h earlier than the occurrence of rainfall and decreased after that. The abundant moisture transportation by southwesterly wind was favorable to the maintenance of convective instability and the accumulation of convective available potential energy (CAPE). Radar detection reveals that meso-β and -γ systems were very active in the MαCS. Several convection lines developed during the evolution of the MαCS, and these are associated with surface convergence lines. The boundary outflow of the convection line may have triggered another convection line. The convection line moved with the mesoscale surface convergence line, but the convective cells embedded in the convergence line propagated along the line. On the basis of the analyses of the intensive observation data, a multi-scale conceptual model of heavy rainfall in the mei-yu front for this particular case is proposed.     

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.     

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     

地面感热对青藏高原低涡流场结构及发展的作用

考虑热带气旋类青藏高原低涡为受加热和摩擦强迫并满足热成风平衡的轴对称涡旋系统,通过求解线性化的柱坐标系中涡旋模式的初值问题,分析了地面感热对高原低涡流场结构及发展的影响,给出了高原低涡眼壁内、外侧水平流场和垂直流场的结构特征,讨论了低涡发展与其水平尺度、垂直厚度、所处纬度以及热量总体输送系数和加热强度的关系.结果表明:地面感热对低涡的生成及发展具有重要作用,但这种作用是否有利于低涡的发展与低涡中心和感热加热中心的配置有关.