Discussion on the complete-form vorticity equation and slantwise vorticity development

The complete form of the vertical vorticity tendency equation (the complete-form vorticity equation) is derived from the Ertel potential vorticity equation to contain thermodynamic factors. In this study, a new complete-form vorticity equation, which has the same form as the original complete-form vorticity equation, is deduced from the absolute vorticity vector equation combined with the continuity equation and the expression of three-dimensional (3D) entropy gradient. By comparing the complete-form vorticity equation with the classical vertical vorticity equation, it is found that regardless of whether or not the isentropic surface is tilting, the two vorticity equations are in essence the same. The “baroclinic term” of the complete-form vorticity equation is exactly equal to the solenoidal term of the classical one, and there is a significant amount of cancellation between the two baroclinic items (the “slantwise term” and the horizontal vorticity change term) in the complete-form vorticity equation. In operational weather analysis, the tilt of the isentropic surface can be diagnosed according to the density of the isotherm on the upper-level isobaric map. For synoptic-scale motion, the vertical vorticity produced by the tilt of the isentropic surface is due to the contribution of atmospheric baroclinicity, which is measured by the solenoid. The 3D solenoid is parallel to the isentropic surface, so the more tilted the isentropic surface, the bigger the projection of the 3D solenoid in the vertical direction. The baroclinic contribution can be interpreted based on the PV thinking theory, but the relationship between the vorticity field and the potential vorticity field is not immediate.     

一次暴雨中尺度涡旋发展机制诊断分析研究

中尺度涡旋可以持续激发新对流,是造成局地持续性降水的重要系统。基于经典涡度方程的诊断无法描述热力信息对于涡旋发展的贡献。本文采用Boussinesq近似对涡度方程进行整理,将方程唯一强迫项定义为垂直速度位涡,其形式与位涡类似,利用垂直速度替换位温。进一步在垂直速度位涡倾向方程中,以气压水平梯度的形式引入热力过程的间接作用,定量描述动热力配置的贡献。以2021年6月15日发生在南疆的一次极端暴雨为例,利用高分辨率数值模拟资料,初步分析了低层动热力强迫作用向垂直涡度的传递。结果表明,垂直速度位涡的局地变化主要来自热力强迫项中低层垂直风切变与低层冷池的耦合作用,两者在降水区前侧产生大范围的正值区。该区域与垂直速度位涡的正值区重叠,促进垂直速度位涡的增长,进而维持降水前缘的正涡度,有利于产生较强的上升运动,触发新对流并造成持续性降水。     

变化涡动沾性系数的Ekman动量近似模式风场结构

在边界层动力学中，涡动粘性系数是影响边界层风场结构的一个重要参数。本文利用边界层动力学中的Ekman动量近似理论，给出了涡动粘性系数随高度缓变条件下的Ekman动量近似边界层模式解，着重讨论了边界层的风场结构、水平散度、垂直涡度以及边界层顶部的垂直速度。结果分析表明：与常值涡动粘性系数情况相比，在边界层低层随高度增加的涡动粘性系数可以导致低层边界层风速随高度迅速增加，即风速垂直切变增加，同时风速矢与地转风之间的夹角减小。惯性项作用可以导致上述作用在气旋性区域减小、而在反气旋性区域增大。随高度增加的涡动粘性系数导致水平散度绝对值、垂直涡度绝对值以及边界层顶部的垂直速度绝对值在气旋性区域减小，而在反气性旋区域增大。涡动粘性系数与惯性之间的非线性相互作用是边界层动力学中重要过程。     

A NOVEL METHOD FOR CALCULATING VERTICAL VELOCITY: A RELATIONSHIP BETWEEN HORIZONTAL VORTICITY AND VERTICAL MOVEMENT

The present work provides a novel method for calculating vertical velocity based on continuity equations in a pressure coordinate system.The method overcomes the disadvantage of accumulation of calculating errors of horizontal divergence in current kinematics methods during the integration for calculating vertical velocity,and consequently avoids its subsequent correction.In addition,through modifications of the continuity equations,it shows that the vorticity of the vertical shear vector(VVSV) is proportional to-ω,the vertical velocity in p coordinates.Furthermore,if the change of ω in the horizontal direction is neglected,the vorticity of the horizontal vorticity vector is proportional to-ω.When ω is under a fluctuating state in the vertical direction,the updraft occurs when the vector of horizontal vorticity rotates counterclockwise;the downdraft occurs when rotating clockwise.The validation result indicates that the present method is generally better than the vertical velocity calculated by the ω equation using the wet Q-vector divergence as a forcing term,and the vertical velocity calculated by utilizing the kinematics method is followed by the O'Brien method for correction.The plus-minus sign of the vertical velocity obtained with this method is not correlated with the intensity of d BZ,but the absolute error increases when d BZ is =40.This method demonstrates that it is a good reflection of the direction of the vertical velocity.     

一次桂北暴雨过程中低涡的发展维持机制

利用常规观测、卫星数据及ERA5再分析数据,从动力和热力角度对引发2020年5月24-25日广西北部暴雨过程的低涡发展维持机制进行了诊断分析。结果表明：低涡在滇黔桂交界一带生成,随后逐渐发展东移,对流云团及降水落区主要分布在低涡东侧及南侧。涡度方程诊断表明,低涡的发展维持主要受涡度平流项和水平散度项影响。水平风场对涡度的输送使得局地涡度减小,而水平风场的辐合效应使得局地涡度增大。将原始风场分解为地转风和非地转风分量后发现,非地转风分量主导了局地涡度的变化,非地转风水平散度项正贡献最大,扭转项次之,两者是造成低涡发展维持的主要原因。在热力作用方面,低涡发展移动过程中对流层中层附近的潜热加热正反馈也有利于低层低涡的发展维持。     

On the determination of the absolute velocity of steady flows of a baroclinic fluid with applications to ocean currents

The problem of determining the absolute velocity of marine currents, including its barotropic component, is revisited. A generalization of the classical Needler’s formula is discussed for a Boussinesq fluid and it is shown that the steady flow solution can be deduced from a variational principle that uses the constants of motion existing in the problem. A simple model of a steady flow is considered when the Bernoulli function consists of two terms. The first term is proportional to the square of Ertel’s potential vorticity and the second term is a quadratic function of the fluid buoyancy. This model is applied to mimic the circulation in the western Mediterranean Sea near the African coast. Alternatively, “potential temperature – salinity” coordinates are applied to construct the stream-tubes and infer the steady flow velocity in the simplest case of the Bernoulli function being proportional to the product of the above two variables.     

东北冷涡下一次飑线和MCV的形成与水平涡度的关系

利用WRF中尺度数值模式,NCEP/NCAR分析资料,多普勒雷达观测资料等,对2016年7月25日一次东北冷涡下的飑线过程进行数值模拟,研究了飑线形成和维持与水平涡度的关系及飑线过程中中尺度对流涡旋(MCV)的形成机制,分析发现,高低层水平涡度逆时针旋转对本次飑线的形成和维持有很好的指示意义。(1)飑线发生前,高层渤海湾西侧出现水平涡度的逆时针旋转中心,并有较强的辐散配合,低层水平涡度为逆时针弯曲,为飑线产生提供了有利的上升运动条件。随后高层多个对流单体的水平涡度气旋式涡旋合并形成较大范围的气旋式涡旋结构,触发低层的上升运动,同时低层对流区前部形成一致的气旋式弯曲使得对流单体组织成带状结构,形成飑线。(2)飑线成熟时期高层水平涡度表现为统一大范围气旋式涡旋结构,低层则呈现典型的S型弯曲结构,水平涡度x方向的分量沿对流带从南至北表现为正负正,y方向的分量始终为正,并由对流带的中心向两侧减小,显示出水平涡度矢量旋转的方向对飑线影响的重要性。(3)由垂直涡度方程的分析得出,在飑线发展中期,MCV形成前,雷达反射率回波在500 hPa左右表现出明显的旋转,此时主要与500 hPa以上强的正涡度水平平流项及中层倾侧项和水平散度项有关,之后,在这几项的作用下使得中层风场产生气旋式旋转,形成MCV。      

由台风低压倒槽引发的山东暴雨过程研究

2004年8月26-28日发生在山东省的大到暴雨过程主要是由"艾莉"台风减弱的低压和西风带冷空气远距离相互作用造成的,台风倒槽的发展与低空东南气流的加强及台风低压外围热量和动量的向北输送密切相关.采用双向三重嵌套网格非静力模式MM5对这一过程进行了数值模拟,研究了台风倒槽的中尺度结构特征,并通过涡度收支探讨了台风倒槽及中尺度低涡发生发展的物理过程.结果表明,强降水是在台风倒槽顶部强风中心与弱风中心之间的强辐合作用下触发的,台风倒槽的增强和中尺度低涡的形成是低空急流及其动力作用的结果,降水的非绝热加热也起着重要作用.涡度方程的收支诊断表明,对流层低层的散度项、对流层中层的水平平流项和铅直输送项是正涡度的主要贡献者,在同一等压面上散度项和水平平流项的作用是相反的.对流层中层铅直输送项的贡献为正,扭转项为负贡献,涡度变化的总趋势是它们相互作用的净结果.等压面上相对涡度的变化趋势并不是均匀的,中尺度低涡的东南象限相对涡度局地变化较强,这是强降水发生在此的重要原因.低层正涡度的增加是由水平辐合引起的,而高层正涡度的增加是涡度由低层向高层垂直输送的结果.因此台风倒槽的发展和中尺度低涡的形成主要是由于低层的涡度制造,另一方面来自中低层涡度的垂直输送.     

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.     

A Study on a Heavy Rainfall Event Triggered by an Inverted Typhoon Trough in Shandong Province

A heavy rainfall event that occurred in Shandong Province in 26 28 August 2004 was caused mainly by Typhoon Acre and cold air activities related to a westerly trough. The event was triggered by an inverted typhoon trough, which was closely associated with the intensification of the low-level southeasterly flow and the northward transport of heat and momentum in the periphery of the typhoon low. A numerical simulation of this event is performed using the nonhydrostatic mesoscale model MM5 with two-way interactive and triply-nested grids, and the structure of the inverted typhoon trough is studied. Furthermore, the formation and development mechanism of the inverted typhoon trough and a mesoscale vortex are discussed through a vorticity budget analysis. The results show that the heavy rainfall was induced by the strong convergence between the strong and weak winds within the inverted typhoon trough. Dynamic effects of the low-level jet and the diabatic heating of precipitation played an important role in the development of the inverted typhoon trough and the formation of the mesoscale vortex. The vorticity budget analysis suggests that the divergence term in the low troposphere, the horizontal advection term, and the convection term in the middle troposphere were main contributors to positive vorticity. Nonetheless, at the same pressure level, the effect of the divergence term and that of the adveetion term were opposite to each other. In the middle troposphere, the vertical transport term made a positive contribution while the tilting term made a negative contribution, and the total vorticity tendency was the net result of their counteractions. It is found that the change tendency of the relative vorticity was not uniform horizontally. A strong positive vorticity tendency occurred in the southeast of the mesoscale vortex, which is why the heavy rainfall was concentrated there. The increase of positive vorticity in the low （upper） troposphere was caused by horizontal convergence （upward transport of vorticity from the lower troposphere）. Therefore, the development of the inverted typhoon trough and the formation of the mesoscale vortex were mainly attributed to the vorticity generated in the low troposphere, and also the vertical transport of vorticity from the low and middle troposphere.     

天山山区及邻近地区夏季降水的环境场特征与涡度平衡

本文对天山山区及其邻近地区夏季降水过程的环境场特征、水热收支和涡度平衡做了诊断分析。结果表明，降水发生前的环境场有利于降水系统的发展。Ｑ１，Ｑ２和涡度平衡在降水发生前与降水期有一定的差异，降水期水热收支中起主作用的是水平平流项潜热和热基本上被冷平流所平衡；水汽的水平输送为降水的主要水汽来源，垂直输送也起一定的作用，涡度平衡中主要是水平平流累积的正涡度与散度项制造的负涡度相平衡，与副热带锋区上急流相     

广义Ertel-Rossby不变量在北京“7.21”暴雨过程分析中的应用

在绝热无摩擦大气中,具有守恒性及可反演性的Ertel位涡(PV)在大尺度天气系统分析中有广泛应用。由于忽略了力管项的作用,PV用于分析中小尺度天气系统演变时受到局限。从广义速度推导得到的广义Ertel-Rossby不变量(GERI)除了包含有PV的守恒性,还包含了螺旋度效应及力管项的作用,对于分析研究快变流型的中小尺度系统演变有一定优势。用GERI分析2012年7月21日北京地区的特大暴雨过程,表明GERI在暴雨区有明显的异常出现,其异常基本与暴雨出现时间同位相,表明GERI的定义涵盖了螺旋度和PV,也包含了暴雨发生时的旋转斜压大气的力管项效应,确实能体现暴雨过程中的流型快变的特点,可以作为独立的变量来分析和揭示造成暴雨的低涡系统的动力结构,为诊断和预报暴雨落区提供新的动力物理量。     

BAROCLINITY AND NONLINEAR EKMAN PUMPING DYNAMICS

With the Ekman momentum approximation,the influence of atmospheric baroclinity on the dynamics of boundarylayer is studied.Some new results are obtained.These results show that the atmospheric baroclinity plays an importantrole in altering the horizontal velocity of Ekman boundary layer and its angle with the horizontal wind velocity compo-nent near the surface.There are three different physical factors affecting the nonlinear Ekman suction,the vertical mo-tion at the top of boundary layer:first,barotropic geostrophic relative vorticity at the ground;second,the thermal windvorticity induced by the baroclinity;and third,the nonlinear interaction between the barotropic geostrophic relativevorticity and the baroclinic thermal wind vorticity.These results may provide a better physical basis for theparameterization of boundary layer and the interpretation of the numerical modeling results.     

Vorticity budget investigation of a simulated long-lived mesoscale vortex in South China

A vorticity budget investigation is performed using the output data from a numerical simulation of a typical MCV (mesoscale convectively generated votex) case in South China. Results suggest that the divergence caused by convection in the low troposphere is the main producer of positive vorticity, while vertical vorticity transferred by the tilting term from the horizontal vorticity compensates the upward output of cyclonic vorticity. Scale analyses of the vorticity equation suggest that the advection of planetary vorticity can be neglected owing to the low latitude, which is different from the larger scale systems in high latitude areas. In addition, the distribution of relative vorticity tendency on pressure level is not uniform. A vortex will move along the vector from the negative to the positive vorticity tendency region. The mechanism of the phenomenon-that nearly all of the convectively ascending region is located southward/southeastward of the vortex center-is also discussed. Convergence with regard to latent heat release would be in favor of the spin-up of meso-vortex, however, the horizontal vorticity caused by windshear is tilted by vertical motion due to convection. Consequently, the negative and positive vorticity tendencies are located symmetrically about the convective center, which suggests that the vortex southward movement is dynamically driven by convection.     

高层冷涡对台风路径影响的数值模拟和动力分析

通过六层斜压干模式模拟了高层冷涡对台风运动的影响，并用涡度方程各动力项的诊断分析，证实了高层冷涡对台风运动的影响主要是通过改变台风中心周围的环流结构而达到的。分析还指出了总涡度倾向和台风运动的直接联系以及这种联系的持续稳定性。同时也发现总涡度倾向主要来自于涡度水平平流和散度场的贡献。说明台风运动主要由正压性动力因子控制。     

THE RELATIONSHIP BETWEEN HORIZONTAL VORTICITY INDUCED BY VERTICAL SHEAR AND VERTICAL MOTION DURING A SQUALL LINE PROCESS

The horizontal vorticity equation used in this study was obtained using the equations of motion in the pressure coordinate system without considering friction, to reveal its relationship with vertical shear. By diagnostically analyzing each term in the horizontal vorticity equation during a squall line process that occurred on 19 June 2010, we found that the non-thermal wind term had a negative contribution to the local change of upward movement in the low-level atmosphere, and that its impact changed gradually from negative to positive with altitude, which could influence upward movement in the mid- and upper-level atmosphere greatly. The contribution of upward vertical transport to vertical movement was the largest in the low-level atmosphere, but had negative contribution to the upper-level atmosphere. These features were most evident in the development stage of the squall line. Based on analysis of convection cells along a squall line, we found that in the process of cell development diabatic heating caused the subsidence of constant potential temperature surface and non- geostrophic motion, which then triggered strong convergence of horizontal acceleration in the mid-level atmosphere and divergence of horizontal acceleration in the upper-level atmosphere. These changes of horizontal wind field could cause a counterclockwise increment of the horizontal vorticity around the warm cell, which then generated an increase of upward movement. This was the main reason why the non-thermal wind term had the largest contribution to the strengthening of upward movement in the mid- and upper-level atmosphere. The vertical transport of large value of horizontal vorticity was the key to trigger convection in this squall line process.     

太行山地形在“7·19”华北持续性低涡暴雨中的作用北大核心

本文对2016年“7·19”华北特大暴雨进行观测分析和数值模拟,并设置了改变地形高度的敏感性试验,以探究该过程降水系统的发生发展机制以及太行山地形的作用。结果表明:(1)本次强降水过程发生在“东高西低”的有利环流形势下,受太行山地形和平原环流系统影响,低层东风急流造成强的对流性降水和低涡作用的叠置造成“7·19”华北地区持续性暴雨的维持和加强;(2)第一阶段为对流性降水,太行山东麓大气对流不稳定能量释放,大气逐渐转为稳定层结;第二阶段为低涡降水,涡度收支分析表明水平散度项和扭转项对低涡维持和发展起到了主要的正贡献,同时伴随有较强的上升运动和垂直风切变,垂直风切变的增强促使水平涡度向垂直涡度转变;(3)太行山地形在持续性暴雨中对两阶段降水、低涡和水汽的作用存在差异。地形高度敏感性试验中,地形高度增高对低层气流的阻挡和强迫抬升作用增强,使得地形降水增强,低涡路径东移,且强度增大。水平散度项使得对流层低层辐合上升运动增强,造成涡度的垂直输送,这是低涡发展和维持的重要原因之一。太行山地形阻挡截留东部平原水汽,且水汽回流加强,有利于太行山东麓水汽的输送与辐合。     

水平涡度与夏季风环流变化

在斜压涡度发展理论的基础上，讨论了大尺度大气运动中水平涡度向垂直涡度转化的情况，并用以刻划夏季风变动。将声坐标中涡度方程的有关项在2坐标中分离出水平涡度向垂直涡度转化的主要项，经尺度分析得出，在对流层中、高层，这些转化项中的水平分量是大尺度大气斜压性涡度发展的主要因子。通过对1998年4—8月的GAME(GEWEX Asian Monsoon Experiment，全球能量和水分循环试验(GEWEX)的子试验：亚洲季风试验，简称GAME)再分析资料进行实际计算发现，转化项在东亚夏季风上升支的600 hPa及以上层次对P坐标垂直涡度的局地变化贡献很大，不能忽略。同时发现水平涡度向垂直涡度的转化对南海季风爆发和江淮梅雨入梅及其发展过程均有指示性意义。南海季风爆发以后，在中国东南部地区，转化项的大小与夏季风的活跃和中断等活动吻合，转化项的变化反映了西太平洋副高在中国大陆的活动规律。     

Kinetic equations and stationary energy spectra of weakly nonlinear internal gravity waves

An ensemble of random-phase internal gravity waves is considered in the dynamical framework of the Euler–Boussinesq equations. For flows with zero mean potential vorticity, a kinetic equation for the mean spectral energy density of the waves is obtained under hypothesis of Gaussian statistics with zero correlation length. Stationary scaling solutions of this equation are found for almost vertically propagating waves. The resulting spectra are anisotropic in vertical and horizontal wave numbers. For flows with small but non-zero mean potential vorticity, under the same statistical hypothesis applied to the wave part of the flow, it is shown that the vortex part and the wave part decouple. The vortex part obeys a limiting slow dynamics equation exhibiting vertical collapse and layering which may contaminate the wave-part spectra. Relation of these results to the in situ atmospheric measurements and previous work on oceanic gravity waves is discussed.     

斜压性与非线性Ekman抽吸的动力特征

本文利用Ekman动量近似研究了斜压性对Ekman层动力学的影响,得到了一些新的结果。大气斜压性对Ekman层的水平风速分布及近地面的风速矢的水平分量夹角有重要的改变作用。斜压边界层顶部的非线性Ekman抽吸(垂直运动)由三个不同的物理因子决定,第一、正压性的地面地转涡度,第二、斜压性作用产生的热成风涡度,第三、正压性的地面地转涡度与斜压性的热成风涡度的非线性相互作用。这些理论结果为边界层的参数化及数值模拟结果的解释提供物理基础。