Three－dimensional Global Scale Permanent－wave Solutions of the Nonlinear Quasigeostrophic Potential Vorticity Equation and Energy Dispersion

The three-dimensional nonlinear quasi-geostrophic potential vorticity equation is reduced to a linear form in the stream function in spherical coordinates for the permanent wave solutions consisting of zonal wavenumbers from 0 to n and rn vertical components with a given degree n. This equation is solved by treating the coefficient of the Coriolis parameter square in the equation as the eigenvalue both for sinusoidal and hyperbolic variations in vertical direction. It is found that these solutions can represent the observed long term flow patterns at the surface and aloft over the globe closely. In addition, the sinusoidal vertical solutions with large eigenvalue G are trapped in low latitude, and the scales of these trapped modes are longer than 10 deg. lat. even for the top layer of the ocean and hence they are much larger than that given by the equatorial β-plane solutions. Therefore such baroclinic disturb-ances in the ocean can easily interact with those in the atmosphere.Solutions of the shallow water potential vorticity equation are treated in a similar manner but with the effective depth H = RT / g taken as limited within a small range for the atmosphere.The propagation of the flow energy of the wave packet consisting of more than one degree is found to be along the great circle around the globe both for barotropic and for baroclinic flows in the atmosphere.     

APPLICATION OF ADVECTIVE VORTICITY EQUATION TO TYPHOON FUNG-WONG

The momentum advection vorticity equation in the form of cross multiplication is introduced, in which the divergence term in the classic vorticity equation does not appear explicitly. This equation includes the rotation effect of the horizontal wind advection, which are not explicitly included in the classic vorticity equation. The vorticity and its tendency of Typhoon Fung-Wong (0808) that occurred in July 2008 are analyzed. The computed results show that the rotation effect of the advection of the horizontal wind is a leading factor in determining the change of vertical vorticity for Fung-Wong during its life cycle, especially in the period leading up to landfall. The advection term represents the tendency variation of the vertical vorticity, and the positive-value region of the vertical vorticity tendency is almost in accord with the track of Fung-Wong, which may be taken as a factor to locate the key observational region of Fung-Wong. The equation provides a supplementary diagnostic tool for the systems related with strong advection of horizontal wind.     

APPLICATION OF GENERALIZED CONVECTIVE VORTICITY VECTOR IN A RAINFALL PROCESS CAUSED BY A LANDFALLING TROPICAL DEPRESSION

A heavy rainfall process, which occurred in Shanghai during 5-6 August, 2001 from a landfalling tropical depression (TD),is examined with a control numerical experiment based on MM5 model. It is found that the contours of generalized equivalent potential temperature (θ*) are almost vertical with respect to horizontal surfaces near the TD center and more densely distributed than those of equivalent potential temperature (θe).Because the atmosphere is non-uniformly saturated in reality, θ* takes the place of θe in the definition of convective vorticity vector (CVV) so that a new vector, namely the generalized convective vorticity vector (CVV*), is applied in this study. Since CVV* can reflect both the secondary circulation and the variation of horizontal moist baroclinicity, the vertical integration of vertical component of CVV* is found, in this study, to represent the rainfall areas in the TD case better than potential vorticity (PV), moist potential vorticity (MPV), generalized moist potential vorticity (Pm), and CVV, with high-value area of CVV* corresponding to heavy-rainfall area. Moreover, the analysis from CVV* implies that the Hangzhou Bay might play an important role in the heavy rain process. A sensitivity experiment without the Hangzhou Bay is then designed and compared with the control run. It is found that the CVV* becomes weaker than that in the control run, implying that the elimination of Hangzhou Bay results in reduced rainfall. Further analyses show that the Hangzhou Bay provides sufficient water vapor and surface heat flux to the TD system, which is very important to the genesis and development of mesoscale cloud clusters around the TD and the associated heavy rainfall.     

A MECHANISM FOR EFFECTS OF THE LARGE-SCALE MOTION AND HORIZONTAL INHOMOGENEITY OF THE MOIST STATIC INSTABILITY ON MCS AT MIDLATITUDES

Under the influence of the synoptic-scale environmental flows, the implicit nonthermal windvorticity imbalance with ξ_T>0 may arise when the change in the vertical shear vorticity of the flows,which is caused by the change of vorticity advection with altitude, is larger than that in the thermalwind vorticity of temperature fields, which is caused by the horizontal inhomogeneity of temperatureadvection. This kind of implicit imbalance will cause ascending motion to develop in the adjustmentprocess. If the static stratification is horizontally inhomogeneous with the presence of its mesoscalehigh-value regions or the conditionally unstable region where moisture can be fully provided, thedevelopment of mesoscale disturbance with scale L_m may result from the coupling of the ascendingmotion on synoptic scale L_1 with the parameter field of static stratification on mesoscale L_2. The disturbance possesses such a vertical structure as ascending motion in the center, horizontaldivergence in the upper and convergence in the lower atmosphere. This developmental process of insta-bility may be one of the most important processes responsible for the growing of heavy rains in summerhalf year in China.     

Hurricane Forecasts in the FSU Models

A brief account of our studies on the hurricane forecast problem is presented here. This covers recent prediction results from the Florida State University (FSU) regional and global numerical weather prediction models. The regions covered are the Indian and the Pacific Oceans. The life cycle of the onset vortex (a hurricane) of the summer monsoon, typhoons over the western Pacific Ocean and tropical cyclones over the Bay of Bengal (Andhra Pradesh and the Bangladesh storms) are covered here. The essential elements in the storm formaton are the strong horizontal shear in the cyclogenetic areas, a lack of vertical shear and warn sea surface temperatures. The storm motion has a steering component largely described by the advection of vorticity by a vertically averaged layer mean wind, the recurvature of a storm appears to invoke physical processes via the advection of divergence by the divergent part of the wind especially in the outflow layers of the storm. Very high resolution global models seem to be abl     

Shearing wind helicity and thermal wind helicity

Helicity is defined as H ： V ω, where V and ω are the velocity and vorticity vectors, respectively. Many works have pointed out that the larger the helicity is, the longer the life cycle of the weather system is. However, the direct relationship of the helicity to the evolution of the weather system is not quite clear. In this paper, the concept of helicity is generalized as shearing wind helicity （SWH）. Dynamically, it is found that the average SWH is directly related to the increase of the average cyclonic rotation of the weather system. Physically, it is also pointed out that the SWH, as a matter of fact, is the sum of the torsion terms and the divergence term in the vorticity equation. Thermal wind helicity （TWH）, as a derivative of SWH, is also discussed here because it links the temperature field and the vertical wind field. These two quantities may be effective for diagnosing a weather system. This paper applies these two quantities in cylindrical coordinates to study the development of Hurricane Andrew to validate their practical use. Through analyzing the hurricane, it is found that TWH can well describe the characteristics of the hurricane such as the strong convection and release of latent heat. SWH is not only a good quantity for diagnosing the weather system, but also an effective one for diagnosing the development of the hurricane.     

Finescale Spiral Rainbands Modeled in a High-Resolution Simulation of Typhoon Rananim （2004）

Finescale spiral rainbands associated with Typhoon Rananim(2004)with the band length ranging from 10 to nearly 100 km and band width varying from 5 to 15 km are simulated using the Fifth-Generation NCAR/Penn State Mesoscale Model(MM5).The finescale rainbands have two types:one intersecting the eyewall and causing damaging wind streaks,and the other distributed azimuthally along the inner edge of the eyewall with a relatively short lifetime.The formation of the high-velocity wind streaks results from the interaction of the azimuthal flow with the banded vertical vorticity structure triggered by tilting of the horizontal vorticity.The vertical advection of azimuthal momentum also leads to acceleration of tangential flow at a relatively high altitude.The evolution and structures of the bands are also examined in this study. Further investigation suggests that the boundary inflection points are related tightly to the development of the finescale rainbands,consistent with previous findings using simple symmetric models.In particular,the presence of the level of inflow reversal in the boundary layer is a crucial factor controlling the formation of these bands.The near-surface wavy peaks of vertical vorticity always follow the inflection points in radial flow.The mesoscale vortices and associated convective updrafts in the eyewall are considered to strengthen the activity of finescale bands,and the updrafts can trigger the formation of the bands as they reside in the environment with inflow reversal in the boundary layer.     

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.     

INTERACTIONS OF MULTIPLE TYPHOONS AND RELATIONSHIPS OF HORIZONTAL AND VERTICAL VORTICITY

Three typhoons, Goni, Morakot and Etau which were generated in Western Pacific in 2009, are successfully simulated by the WRF model. The horizontal and vertical vorticity and their interaction are analyzed and diagnosed by using the simulation results. It is shown that their resultant vectors had a fixed pattern in the evolution process of the three typhoons: The horizontal vorticity converged to the tropical cyclone (TC) center below 900 hPa level, flowed out from it at around 900 to 800 hPa, and flowed in between 800 hPa and 700 hPa. If multiple maximum wind speed centers showed up, the horizontal vorticity converged to the center of the typhoon below the maximum wind speed center and diverged from the TC center above the maximum wind speed center. At low levels, the three typhoons interacted with each other through vertical circulation generated by the vortex tube. This circulation was mainly generated by the eastward or westward horizontal vorticity vectors. Clouds and precipitation were generated on the ascending branch of the vertical circulation. The vortex tubes often flowed toward the southwest of the right TC from the northeast of the left TC. According to the full vorticity equation, the horizontal vorticity converted into the vertical vorticity near the maximum wind speed center below 850 hPa level, and the period of most intense conversion was consistent with the intensification period of TC, while the vorticity advection was against the intensification. The vertical vorticity converted into the horizontal vorticity from 800 hPa to 600 hPa, and the wind speed decreased above the maximum wind speed region at low levels.     

Dynamical and Thermal Problems in Vortex Development and Movement. Part I: A PV–Q View

Based on the Lagrangian change equation of vertical vorticity deduced from the equation of threedimensional Ertel potential vorticity(PV e),the development and movement of vortex are investigated from the view of potential vorticity and diabatic heating(PV-Q).It is demonstrated that the asymmetric distribution in the vortex of the non-uniform diabatic heating in both vertical and horizontal can lead to the vortex’s development and movement.The theoretical results are used to analyze the development and movement of a Tibetan Plateau(TP) vortex(TPV),which appeared over the TP,then slid down and moved eastward in late July 2008,resulting in heavy rainfall in Sichuan Province and along the middle and lower reaches of the Yangtze River.The relative contributions to the vertical vorticity development of the TPV are decomposed into three parts:the diabatic heating,the change in horizontal component of PV e(defined as PV 2),and the change in static stability θ z.The results show that in most cases,diabatic heating plays a leading role,followed by the change in PV 2,while the change of θ z usually has a negative impact in a stable atmosphere when the atmosphere becomes more stable,and has a positive contribution when the atmosphere approaches neutral stratification.The intensification of the TPV from 0600 to 1200 UTC 22 July 2008 is mainly due to the diabatic heating associated with the precipitation on the eastern side of the TPV when it uplifted on the up-slope of the northeastern edge of the Sichuan basin.The vertical gradient of diabatic heating makes positive(negative) PV e generation below(above) the maximum of diabatic heating;the positive PV e generation not only intensifies the low-level vortex but also enhances the vertical extent of the vortex as it uplifts.The change in PV e due to the horizontal gradient of diabatic heating depends on the vertical shear of horizontal wind that passes through the center of diabatic heating.The horizontal gradient of diabatic heating makes positive(negative) PV e generation on the right(left) side of the vertical shear of horizontal wind.The positive PV e generation on the right side of the vertical shear of horizontal wind not only intensifies the local vertical vorticity but also affects direction of movement of the TPV.These diagnostic results are in good agreement with the theoretic results developed from the PV-Q view.     

Vortex boundary layer under quadratic surface stress

The influences of the quadratic surface stress on the two-dimensional structure of boundary-layer flows in hurricane-like and tornado-like vortices are investigated by solving the nonlinear boundary-layer equations in the vertical direction through power series expansion and expressing the expansion coefficients in terms of parameters of the vortex profile. It is found that the series solutions converge rapidly and the vertical velocity w_bcreated by the boundary-layer flow is upward everywhere for the hurricane type vortex, with the maximum vertical velocity w_bmoccurring inside the radius of maximum tangential wind. This result is of utmost importance for the hurricane development problem on account of the organizing influence of w_bon cumulus convection and latent heat release in the conditionally unstable tropical atmosphere. On the other hand, the vertical velocity created by the boundary layer of the pure potential vortex with zero absolute vorticity is downward.     

螺旋度及螺旋度方程的讨论

文中从无摩擦的运动方程出发 ,利用量纲分析的方法 ,导出简化了的螺旋度方程和不同方向上的螺旋度方程 ,并对影响它们变化的各因子进行了讨论。分析结果表明 ,除了Lilly在 1986年研究中强调的浮力效应外 ,压力梯度与涡度共同作用项和力管项对螺旋度的变化也有重要影响 ,甚至比浮力效应更大 ,且力管作用、水平压力梯度与水平涡度共同作用主要影响水平螺旋度 ,浮力效应、垂直压力梯度与垂直涡度共同作用主要影响垂直螺旋度 ;螺旋度的输送和大气的辐散、辐合对螺旋度变化的影响较弱 ;地转偏向力 (无论是在水平方向还是垂直方向 )的作用要在系统水平尺度较大时才能体现出来。水平和垂直方向上的螺旋度既相互区别在暴雨、强对流天气过程中表现出不同的作用 ,又相互联系。一方面 ,水平螺旋度更具预示性 ,对预报强风暴有指示意义 ,而垂直螺旋度更倾向为能反映系统的维持状况和系统发展、天气现象的剧烈程度的一个参数。另一方面 ,大的正水平螺旋度有助于垂直螺旋度的增长 ,而与垂直螺旋度对应的运动可能对水平螺旋度产生影响。将中尺度模式和螺旋度计算结合起来可能可以提高风暴路径和雨区的预报准确度。     

The mesoscale balance and imbalance and the corresponding potential vorticity inversion from the view of helicity

The static balance and the geostrophic balance are the common balances in meteorology.All the synoptic systems and most of the mesoscale systems satisfy the above two balances.However,due to the strong convection and non-geostrophic feature,many mesoscale systems usually present as static imbalance,and the quasi-geostrophic approximation is no longer attainable.This paper tried to find out a kind of balance that exists for mesoscale convective system.To do this,the concrete mathematics definitions for balance and imbalance equations were defined.Then,it is proposed that the new balance equation should include the divergence,vorticity,and vertical motion simultaneously,and the helicity equation was a good choice for the basis.Finally,the mesoscale balance and imbalance equations were constructed,as well as a new balance model that was based on the helicity,horizontal divergence,vertical vorticity,continuity,and thermal dynamic equations under same approximations.Moreover,the corresponding potential vorticity(PV)inversion technique was introduced.It was pointed out that by using the PV conservation and the potential temperature conservation,the flows of the mesoscale balance model can be deduced,and their comparison with the real fields would give the degree of the imbalance.     

切变风螺旋度和热成风螺旋度在东北冷涡暴雨中的应用

引入切变风螺旋度和热成风螺旋度, 并将其应用于东北冷涡暴雨的诊断分析。理论上, 切变风螺旋度定义为风速垂直切变与绝对涡度矢量的点积, 表示风速垂直方向的分布不均匀对涡管的扭转效应, 由扭转项和垂直涡度的辐合辐散项两部分组成。热成风螺旋度是在切变风螺旋度的基础上利用地转关系和热成风关系得出的简化形式, 其强度和符号取决于上升气流和暖湿空气的配置。相对于切变风螺旋度, 热成风螺旋度的计算只需要单平面层的资料即可, 避免了垂直差分计算, 这大大弥补了台站观测中垂直层密度稀疏或者边界层的处理等问题的不足, 使得计算大大简化, 便于业务应用。在以上定义和理论分析的基础上, 选取一次东北冷涡降水过程进行数值模拟, 利用模式输出的中尺度资料, 诊断分析这次降水过程中的切变风螺旋度和热成风螺旋度。分析表明, 降水中心位于切变风螺旋度的正值和负值区的边界, 与降水的强度变化一致; 而作了热成风近似后的切变风螺旋度中的扭转项 (即热成风螺旋度), 与切变风螺旋度相似, 也能较好地诊断降水和对流 (尤其是强降水和强对流) 的发展, 而且其对暴雨的诊断优于传统的螺旋度。     

飓风中的涡旋罗斯贝波

文中从柱坐标系下的正压无辐散涡度方程出发,用WKBJ方法求解方程,发现在飓风中存在类似于行星罗斯贝波的涡旋罗斯贝波,这种波的形成主要是由于飓风中基态涡度垂直分量的径向梯度所决定。利用一次飓风过程的精确数值模拟所输出高分辨的资料,计算了飓风中径向涡度梯度的分布,指出这类波动主要存在于眼墙和眼心中。波动结构分析表明,波动能量具有径向频散,这有可能是飓风暖心结构的一种形成机制。最后用波射线法讨论了定常涡旋罗斯贝波的径向频散     

基于螺旋度的中尺度平衡方程及非平衡流诊断方法

在回顾大尺度准地转平衡理论、各种平衡方程、平衡模式及非平衡流诊断工具的基础上,对平衡方程、非平衡方程给出了具体的定义.并在此基础上,进一步考虑中尺度强对流天气系统的特征,指出中尺度也有平衡运动的存在.但是由于中尺度对流系统中强烈的辐散风效应以及不可忽略的垂直运动的作用,以散度方程为基础的各种近似平衡方程不足以描述中尺度强对流天气系统的平衡运动,进而提出了从能够同时考虑旋转、辐散及垂直运动作用的螺旋度方程出发,寻找中尺度的平衡方程.在所得的平衡方程基础上,给出了相应的平衡模式和非平衡方程.并进一步将非平衡方程分解,用来诊断非平衡过程的平衡破坏和平衡恢复两个阶段,同时将它们与水平螺旋度和垂直螺旋度联系起来.     

Simulation of formation of a near-equatorial typhoon Vamei (2001)

Summary A community mesoscale model is used to simulate and understand processes that led to the formation and intensification of the near-equatorial typhoon Vamei that formed in the South China Sea in December, 2001. The simulated typhoon resembles the observed in that it had a short lifetime and a small size, formed near the equator (south of 2° N), and reached category-one intensity. The formation involved the interactions between the scales of the background cyclonic circulation (the Borneo Vortex of order ∼100 km) and of mesoscale convective vortices (MCVs, in the order ∼10 km). Before tropical cyclone formation MCVs formed along a convergent, horizontal shear vorticity line on the eastern edge of an exceptionally strong monsoonal northerly wind surge. The typhoon genesis is marked by three rapid intensification periods, which are associated with the rapid growth of potential vorticity (PV). A vorticity budget analysis reveals that the increases in low-level vorticity during the rapid intensification periods are attributed to enhanced horizontal vorticity fluxes into the storm core. The increase of the horizontal vorticity flux is associated with the merging of areas of high PV associated with MCVs into the storm core as they are advected by background cyclonic flows. The increases in PV at upper levels are associated with the evaporation of upper level stratiform precipitation and increases of vertical potential temperature gradient below the maximum stratiform cloud layer. It appears that two key sources of PV at upper and lower levels are crucial for the build up of high PV and a deepening of a cyclonic layer throughout the troposphere.     

对流涡度矢量在暴雨诊断分析中的应用研究

位涡在诊断分析中是一个常用且有效的物理量, 但在深对流系统中由于湿等熵面的倾斜变得较弱。因此, 本文利用高守亭等(2004)提出的新矢量——对流涡度矢量(简称CVV)来研究深对流系统, 并用对流涡度矢量诊断华北一次大范围的大到暴雨天气过程。结果表明, CVV垂直分量在中纬度对流性暴雨中有很好的指示性, 它的高值区与云中水凝物和地面降水有较好的对应关系, 暴雨区位于CVV垂直分量高值区附近及其北侧的梯度大值区内。CVV垂直分量是与云相联系的参数, 暴雨区垂直积分和区域平均的CVV垂直分量和云中水凝物混合比的相关系数为0.92, 与降水率的相关系数为0.71, 比湿位涡与云中水凝物的相关系数高很多。CVV垂直分量反映了水平涡度和水平相当位温梯度的相互作用, 可以把中纬度深对流系统中的中尺度动力过程和热力过程与云微物理过程密切联系起来, 有助于理解环流和云相互作用促使对流发展的机制, 可以很好地追踪暴雨系统的发展和演变。     

热力适应、过流、频散和副高II.水平非均匀加热与能量频散

利用位涡方程和热力适应原理，讨论了因非绝热加热的空间不均匀性导致的大气 动力特征的变化，进一步阐明了副热带地区的深对流凝结潜热加热的垂直非均匀性使副热带高压在中低空出现在热源区以东，在高空出现在热源区以西。在此基础上，深入研究了水平非均匀加热对大气环流的影响。结果表明加热区以北，虽然非绝热加热消失，但存在加热的水平梯度在西风环流的背景下在高低层造成深厚的负涡度强迫。因而高层热源北部边界附近的西风向南偏转进入加热区，造成加热区北部边界及其以北发生次级辐散；低层热源区的南风发生反气旋偏转，汇入加热区外的西风气流中，造成低层加热区北部边界及其以北发生次级辐合。结果该区域产生了垂直上升运动及负的涡度强迫源，对应着异常强烈的反气旋环流。该负涡度强迫源还通过能量频散，在西风带中以Rossby波的形式向中高纬传播，影响中高纬地区的异常环流型。