Based on the barotropic equations regarding terrain in the z coordinate system, obtaining the first-order approximation by using the small parameter method, and then analyzed shear wave and vortex wave and the relationship between them in theory. It was concluded that the wave caused by the wind shear includes the shear wave, the inertial wave and the gravity external wave, which belong to the two-way scattered wave. When considering terrain slope, the necessary condition of wave stability is related to the square of wave number, the contribution of terrain slope to stability fluctuation depends on the zonal distribution of the basic flow. Without considering terrain slope, the basic flow exists north-south shear and the wavelength is longer, there will be wave instability. Vortex wave instability is a special case of shear wave instability, which means the wave of the shear line develops into low vortex through the unstable development of the fluctuation, and shows that the shear line under certain conditions can induce low vortex, which is conducive to the formation of the extreme weather events.
[1]Chen G, Li G P. 2014. Dynamic and numerical study of waves in the Tibetan Plateau vortex[J]. Adv Atmos Sci, 31(1):131-138
[2]Chen L S, Luo Z X. 2003. A preliminary study of the dynamics of eastward shifting cyclonic vortices[J]. Adv Atmos Sci, 20(3):323-332.
[3]Gao S T, Zhou Y S. 2001. The instability of the vortex sheet along the shear line[J]. Acta Meteor Sinica, 59(4):393-404.<br/>高守亭, 周玉淑. 2001.水平切变线上涡层不稳定理论[J].气象学报, 59(4):393-404.
[4]Gu Q Y, Shi R, Xu H M. 2010. Comparison analysis of the circulation characteristics of plateau vortex moving out of and not out of the plateau[J]. Meteor Mon, 36(4):7-15.<br/>顾清源, 师锐, 徐会明. 2010.移出与未移出高原的两类低涡环流特征的对比分析[J].气象, 36(4):7-15.
[5]Hao L P, Zhou J, Kang L. 2016. Weather analyses and numerical study of Southwest China vortex and its induced heavy rainfall[J]. Plateau Meteor, 35 (5):1182-1190. DOI:10.7522/j.issn. 1000-0534.2015.00046.<br/>郝丽萍, 周瑾, 康岚. 2016.西南涡暴雨天气过程分析和数值模拟试验[J].高原气象, 35(5):1182-1190.
[6]He G B. 2013. Review of the plateau shear-line studies[J]. Plateau Mountain Meteor Res, 33(1):90-96.<br/>何光碧. 2013.高原切变线研究回顾[J].高原山地气象研究, 33(1):90-96.
[7]He G B, Gao W L, Tu N N. 2009. The observational analysis of shear line and low vortex over the Tibetan Plateau in summer from 2000 to 2007[J]. Plateau Meteor, 28(3):549-555.<br/>何光碧, 高文良, 屠妮妮. 2009.2000-2007年夏季青藏高原低涡切变线观测事实分析[J].高原气象, 28(3):549-555.
[8]Li G P, Luo X P, Chen T, et al. 2011. Preliminary theorotical study of waves in the Tibetan Plateau vortex[J]. Plateau Meteor, 30(3):553-558.<br/>李国平, 罗喜平, 陈婷, 等. 2011.高原低涡中涡旋波动特征的初步分析[J].高原气象, 30(3):553-558.
[9]Li S S, Li G P. 2017a. Evolution and mechanism analysis of a plateau vortex and plateau shear line[J]. Chinese J Atmos Sci, 41(4):713-726. DOI:10.3878/j.issn. 1006-9895.1611.16179.<br/>李山山, 李国平. 2017a.一次高原低涡与高原切变线演变过程与机理分析[J].大气科学, 41(4):713-726.
[10]Li S S, Li G P. 2017b. Diagnostic analysis based on wet <i>Q</i>-vector of a shear line with rain on the east side of Qinghai-Tibetan Plateau under the saddle pattern circulation background field[J]. Plateau Meteor, 36 (2):317-329. DOI:10.7522/j.issn. 1000-0534.2016.00025.<br/>李山山, 李国平. 2017b.一次鞍型场环流背景下高原东部切变线降水的湿<i>Q</i>矢量诊断分析[J].高原气象, 36(2):317-329.
[11]Li Z L, Wan J. 1995. Stability of the nonlinear waves on the horizontal shear-line of wind with the geostrophic momentum approximation[J]. Acta Meteor Sinica, 53(3):289-298.<br/>李子良, 万军. 1995.准地转动量近似下风速切变线上的波动[J].气象学报, 53(3):289-298.
[12]Liu S S. 1991. Unstable theory on the formation and development of tropical cyclone[J]. J Trop Ocean, 10(2):1-9.<br/>刘式适. 1991.热带气旋发生、发展的不稳定理论[J].热带海洋学报, 10(2):1-9.
[13]Liu S S, Bai J Y, Chen H. 2000. Rossby wave affected by large-scale topography of Qinghai-Xizang Plateau[J]. Plateau Meteor, 19(3):331-338.<br/>刘式适, 柏晶瑜, 陈华. 2000.青藏高原大地形作用下的Rossby波[J].高原气象, 19(3):331-338.
[14]Liu S S, Liu S D. 2011. Atmospheric Dynamics[M]. Beijing:Peking University Press, 166-167.<br/>刘式适, 刘式达. 2011.大气动力学[M].北京:北京大学出版社, 166-167.
[15]Liu S S, Tan B K. 1988. Nonlinear Rossby waves forced by topography[J]. Applied Mathematics and Mechanics, 9(3):229-240.<br/>刘式适, 谭本馗. 1988.地形作用下的非线性Rossby波[J].应用数学和力学, 9(3):229-240.
[16]Liu X R, Li G P. 2006. Review and prospect of research on the Tibetan Plateau vortex[J]. Arid Meteor, 24(1):60-66.<br/>刘晓冉, 李国平. 2006.青藏高原低涡研究的回顾与展望[J].干旱气象, 24(1):60-66.
[17]Long X, Cheng L S. 2004. Numerical simulation and analysis for "99·6" Meiyu front rainstorm and the low vortex with shear line[J]. Chinese Journal of Atmospheric Sciences, 28(3):342-356.<br/>隆霄, 程麟生. 2004. "99·6"梅雨锋暴雨低涡切变线的数值模拟和分析[J].大气科学, 28(3):342-356.
[18]Lü K L. 1986a. The influences of large orography on instability of Rossby waves in shear currents[J]. Chinese J Atmos Sci, 10(3):327-331.<br/>吕克利. 1986a.大地形对切变基流上罗斯贝波稳定性的影响[J].大气科学, 10(3):327-331.
[19]Lv K L. 1986b. The large-scale orography and the stability of Rossby wave in the barotropic atmosphere[J]. Acta Meteor Sinica, 44(3):275-281.<br/>吕克利. 1986b.大地形和正压Rossby波的稳定性[J].气象学报, 44(3):275-281.
[20]Ma L, Zhang Q M, Zhao C N, et al. 2003. The forming and forecasting of winter snow-disaster weather in eastern pastoral-area of Qinghai-Xizang Plateau[J]. J Natural Disaster, 12(3):61-68.<br/>马林, 张青梅, 赵春宁, 等. 2003.青藏高原东部牧区春季雪灾天气的形成及其预报[J].自然灾害学报, 12(3):61-68.
[21]Qiao Q M, Tan H Q. 1984. The structure of 500mb shear line and large-scale circulation over Qingzang Plateau in summer[J]. Plateau Meteor, 3 (3):50-57.<br/>乔全明, 谭海清. 1984.夏季青藏高原500毫巴切变线的结构与大尺度环流[J].高原气象, 3(3):50-57.
[22]Lhasa Group of Tibetan Plateau Meteorology Research. 1981. Research of 500 mb vortex and shear lines over the Tibetan Plateau in summer[M]. Beijing:Science Press, 120-155.<br/>青藏高原气象科学研究拉萨会战组. 1981.夏半年青藏高原500毫巴低涡切变线研究[M].北京:科学出版社, 120-155.
[23]Shi R, He G B. 2011. Contrast analysis on background circulation of plateau shear line moving out and not moving out of the Tibetan Plateau[J]. Plateau Meteor, 30(6):1453-1461.<br/>师锐, 何光碧. 2011.移出与未移出高原的高原切变线背景环流对比分析[J].高原气象, 30(6):1453-1461.
[24]Tu N N, He G B. 2010. Case analysis on two low vortexes induced by Tibetan Plateau shear line[J]. Plateau Meteor, 29(1):90-98.<br/>屠妮妮, 何光碧. 2010.两次高原切变线诱发低涡活动的个例分析[J].高原气象, 29(1):90-98.
[25]Wang Z, Chen Y Y. 2007. Analyses on major effect systems and typical atmospheric circulation triggering mountain torrential disasters in Chongqing[J]. Plateau Meteor, 26(3):609-614.<br/>王中, 陈艳英. 2007.触发重庆山洪灾害的典型环流和影响系统分析[J].高原气象, 26(3):609-614.
[26]Wu R S. 1964. On the influences of mountain range on the instability of disturbances[J]. Acta Meteorologica Sinica, 34(1):11-19.<br/>伍荣生. 1964.大地形与扰动的不稳定[J].气象学报, 34(1):11-19.
[27]Wu R S. 1982. The effects of basic flow and topography on the barotropic disturbances[J]. Acta Meteor Sinica, 40(2):129-138.<br/>伍荣生. 1982.基本气流和大地形对于正压波动的作用[J].气象学报, 40(2):129-138.
[28]Xie Y B, Huang Y L. 1964. A preliminary theoretical study about the instability of the waves along the intertropical convergence zone[J]. Acta Meteor Sinica, 34(2):198-210.<br/>谢义炳, 黄寅亮. 1964.赤道辐合带上扰动不稳定性的简单理论分析[J].气象学报, 34(2):198-210.
[29]Yao X P, Sun J Y, Kang L, et al. 2014. Advances on research of shear convergence line over Qinghai-Xizang Plateau[J]. Plateau Meteor, 33(1):294-300. DOI:10.7522/j.issn. 1000-0534.2013.00164.<br/>姚秀萍, 孙建元, 康岚, 等. 2014.高原切变线研究的若干进展[J].高原气象, 33(1):294-300.
[30]Yu J, Zhang J Q, Zhu J, et al. 2017. Relation between kinetic energy gradient and geostrophic deviation in barotropic atmosphere and diagnosis of torrential rain[J]. J Meteor Sci, 37(2):265-271.<br/>于杰, 张继权, 朱娟, 等. 2017.正压大气动能梯度与地转偏差的关系及其对暴雨的诊断[J].气象科学, 37(2):265-271.
[31]Yu S H, Gao W L, Peng J. 2013. Statistical analysis of shearline activity in QXP and its influence on rainfall in China in recent 13 years[J]. Plateau Meteor, 32(6):1527-1537. DOI:10.7522/j.issn. 1000-0534.2012.00149.<br/>郁淑华, 高文良, 彭俊. 2013.近13年青藏高原切变线活动及其对中国降水影响的若干统计[J].高原气象, 32(6):1527-1537.