波射线理论在大气正压不稳定中的应用
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摘要
应用球面上Rossby波射线理论初步探讨了基本流为急流的大气中正压扰动的动力学行为,对正压不稳定的条件进行了再思考,指出存在一个准地转位势涡度梯度bM的负区,在这个区域中向北传播的扰动振幅增长很大,为扰动发展的不稳定区,此外扰动能量无法穿越β_M=0的线,据此称之为陷波线.在90°E,20°N给定一个初始扰动,应用包含急流的理想风速廓线分析指出,对于非定常波,扰动的行为依赖于初始的纬向波数k和经向波数l.k值较小的大气长波经向传播范围大,向北传播容易被陷波线捕获,而尺度较小的短波不能到达陷波线,因此能够在西风中南北振荡并向下游传播.对k=1,l=8的大气长波,向北传播时波能量增加,在急流以北波能量达到最大值,当靠近陷波线时能量迅速减小,最终在陷波线中能量衰减为零.向北传播时波能量的增大,意味着扰动从急流以南的基本风场中获得的能量传到急流以北,在陷波线附近能量又还给了基本流,完成了大气中能量的南北输送.进一步计算了1和6月500 hPa上实际纬向风速廓线下扰动能量的传播,其结果大体和理想基流的结果相同,不同之处在于冬季低纬度向南的扰动容易被东风带阻挡,不能传播到南半球;而夏季低纬非定常扰动可以穿越东风带到达南半球,并且在东风带中形成西传的波动.
Based on the spherical Rossby wave ray theory,dynamic characteristics of the barotropic disturbances associated with the westerly jet are discussed,and the barotropic instability conditions are reconsidered.The well-known Rayleigh-Kuo instability criterion indicates that the gradient of potential vorticity must change sign in the unstable area.Kuo uses the method of eigenvalues by assuming disturbances to be simple harmonic waves;however,in this work we assume the atmosphere to be a slowly varying medium,and calculate the amplitude of the Rossby wave by ray tracing.We find a band where the quasi-geostrophic potential vorticity gradient(β_M) is negative,and the amplitude of the northward perturbation grows substantially in this area,making it an unstable region for northward perturbations.In addition the perturbations cannot cross the line of β_M=0,and therefore,this is referred to as the "trapped line".Characteristics of the nonstationary Rossby wave are first analyzed using an ideal zonal mean wind profile u=30sin~8(2φ)+0.2,with the "trapped line" located at 58°N and 70°N,and β_M<0 between 58°N and 70°N.We put the wave source at 90°E,20°N with meridional wave number l = 8,but with different zonal wave numbers k.The results suggest that the behavior of the disturbances depends on the initial wave numbers k and l.Northward disturbances with smaller k can propagate further,while disturbances with larger k cannot reach high latitudes and turn back towards the south at turning points β_M/(u_M-δ/k)-k~2=0.As such,only long Rossby waves with small k values can reach the"trapped line",while short Rossby waves with larger k values cannot reach it.Long Rossby waves with k = 1,l = 8,first propagate northwest,and then turn eastwards at the "trapped line".Their energy increases while propagating northward,reaching its maximum in the northern part of the jet stream,and then decays rapidly to zero near the "trapped line".The energy increases during northward propagation,which means the disturbance obtains energy from the base flow in the southern part of the jet stream,and gives it back to the base flow near the "trapped line",which completes energy transport from south to north.Further,we also calculated the energy evolution with realistic January and June wind profiles using NCEP data.We conclude that long waves with k<3 are easily trapped by the "trapped line" in both winter and summer,while the propagation of short waves differs substantially between winter and summer.The non-stationary disturbances at low latitudes are easily blocked by easterly winds during winter;however,they can cross easterlies and then propagate to the southern hemisphere in summer,forming a westward wave in the easterlies.It is known that stationary Rossby waves cannot propagate in the easterlies,because only non-stationary waves that meet many conditions can propagate in the easterlies;therefore,this scenario will not be detailed in this paper.
Based on the spherical Rossby wave ray theory,dynamic characteristics of the barotropic disturbances associated with the westerly jet are discussed,and the barotropic instability conditions are reconsidered.The well-known Rayleigh-Kuo instability criterion indicates that the gradient of potential vorticity must change sign in the unstable area.Kuo uses the method of eigenvalues by assuming disturbances to be simple harmonic waves;however,in this work we assume the atmosphere to be a slowly varying medium,and calculate the amplitude of the Rossby wave by ray tracing.We find a band where the quasi-geostrophic potential vorticity gradient(β_M) is negative,and the amplitude of the northward perturbation grows substantially in this area,making it an unstable region for northward perturbations.In addition the perturbations cannot cross the line of β_M=0,and therefore,this is referred to as the "trapped line".Characteristics of the nonstationary Rossby wave are first analyzed using an ideal zonal mean wind profile u=30sin~8(2φ)+0.2,with the "trapped line" located at 58°N and 70°N,and β_M<0 between 58°N and 70°N.We put the wave source at 90°E,20°N with meridional wave number l = 8,but with different zonal wave numbers k.The results suggest that the behavior of the disturbances depends on the initial wave numbers k and l.Northward disturbances with smaller k can propagate further,while disturbances with larger k cannot reach high latitudes and turn back towards the south at turning points β_M/(u_M-δ/k)-k~2=0.As such,only long Rossby waves with small k values can reach the"trapped line",while short Rossby waves with larger k values cannot reach it.Long Rossby waves with k = 1,l = 8,first propagate northwest,and then turn eastwards at the "trapped line".Their energy increases while propagating northward,reaching its maximum in the northern part of the jet stream,and then decays rapidly to zero near the "trapped line".The energy increases during northward propagation,which means the disturbance obtains energy from the base flow in the southern part of the jet stream,and gives it back to the base flow near the "trapped line",which completes energy transport from south to north.Further,we also calculated the energy evolution with realistic January and June wind profiles using NCEP data.We conclude that long waves with k<3 are easily trapped by the "trapped line" in both winter and summer,while the propagation of short waves differs substantially between winter and summer.The non-stationary disturbances at low latitudes are easily blocked by easterly winds during winter;however,they can cross easterlies and then propagate to the southern hemisphere in summer,forming a westward wave in the easterlies.It is known that stationary Rossby waves cannot propagate in the easterlies,because only non-stationary waves that meet many conditions can propagate in the easterlies;therefore,this scenario will not be detailed in this paper.
引文
1 Rossby C G.Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action.J Mar Res,1939,2:38-55
2 Jaw J J.The formation of the semi-permanent center of action in relation to the horizontal solenoidal field.J Meteorol,1946,3:103-144
3 Kuo H L.Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere.J Meteorol,1949,6:105-122
4 Charney J G.The dynamics of long waves in a baroclinic westerly current.J Meteorol,1947,4:135-163
5 Eady E T.Long waves and cyclone waves.Tellus,1949,1:33-52
6 Pedlosky J.Geophysical Fluid Dynamics.Berlin:Springer-Verlag,1979.624
7 Chao J P,Wang X L.Energy propagation of Rossby wave in a baroclinic atmosphere(in Chinese).In:Collection of Atmospheric Sciences.Nanjing:Nanjing University Press,1993.49-61[巢纪平,王晓丽.斜压大气中能量传播的射线理论.见:大气科学文集.南京:南京大学出版社,1993.49-61]
8 Chao J P,Ye D Z.The spiral-like planetary waves in the barotropic atmosphere(in Chinese).Chin J Atmos Sci,1997,1:81-88[巢纪平,叶笃正.正压大气中的螺旋行星波.大气科学,1977,1:81-88]
9 Liu S S,Yang D S.The spiral structure of the planetary waves in the earth atmosphere(in Chinese).Acta Meteorol Sin,1979,1:14-27[刘式适,杨大升.地球大气行星波的螺旋结构.气象学报,1979,1:14-27]
10 Chen J K.The variation mechanism of the spiral structure of the spherical planetary waves in a barotropic atmosphere(in Chinese).Sci Meteorol Sin,1980,Z1:27-41[陈久康.正压大气球面行星波螺旋结构变化的机制.气象科学,1980,Z1:27-41]
11 Ye D Z,Zhu B Z.Some Basic Problems in Atmospheric Circulation(in Chinese).Beijing:Science Press,1958[叶笃正,朱抱真.大气环流中的若干基本问题.北京:科学出版社,1958]
12 Ji J J.Spiral planetary waves and the transfer processes of angular momentum in the baroclinic atmosphere(in Chinese).Acta Meteorol Sin,1979,37:90-96[季劲钧.斜压球面螺旋行星波和角动量输送.气象学报,1979,37:90-96]
13 Chen Y Y,Chao J P.Conservation of wave action and development of spiral Rossby waves(in Chinese).Sci China Ser B,1983,7:663-672[陈英怡,巢纪平.螺旋Rossby波的波密度守恒和稳定性.中国科学B辑,1983,7:663-672]
14 Liu F,Chao J P,Huang G,et al.A semi-analytical model for the propagation of Rossby waves in slowly varying flow.Chin Sci Bull,2011,56:2727-2731
15 Rossby C G.On the propagation of friquencies and energy in certain types of ocean and atmospheric waves.J Meteorol,1945,2:187-204
16 Whitham G.A note on group velocity.J Fluid Mech,1960,9:347-352
17 Hoskins B J,Karoly D J.The steady linear response of a spherical atmosphere to thermal and orographic forcing.J Atmos Sci,1981,38:1179-1196
18 Karoly D J.Rossby wave propagation in a barotropic atmosphere.Dyn Atmos Oceans,1983,7:111-125
19 Hoskins B J,Ambrizzi T.Rossby wave propagation on a realistic longitudinally varying flow.J Atmos Sci,1993,50:1661-1671
20 Xu X D,Miao Q J.The low fequency dynamics on the wave ray propagation of tropical atmosphere energy dispersion(in Chinese).Acta Meteorol Sin,2000,58:534-544[徐祥德,苗秋菊.热带大气能量频散波射线的低频动力学特征.气象学报,2000,58:534-544]
21 Li Y J,Li J P.Propagation of planetary waves in the horizontal non-uniform basic flow(in Chinese).Chin J Geophys,2012,55:361-371[李艳杰,李建平.水平非均匀基流中行星波的传播.地球物理学报,2012,55:361-371]
22 Kalnay E,Kanamitsu M,Kistler R,et al.The NCEP/NCAR 40-year reanalysis project.Bull Amer Meteorol Soc,1996,77:437-471
23 Branstator G.Horizontal energy propagation in a barotropic atmosphere with meridional and zonal structure.J Atmos Sci,1983,40:1689-1708
24 Branstator G.Circumglobal teleconnections,the jet stream waveguide,and the North Atlantic Oscillation.J Clim,2002,15:1893-1910
25 Ding Q,Wang B.Circumglobal teleconnection in the Northern Hemisphere summer.J Clim,2005,18:3483-3505
26 Liu F,Wang B.Mechanisms of global teleconnections associated with the Asian summer monsoon:An intermediate model analysis.JClim,2013,26:1791-1806
27 Li Y J,Li J P,Jin F F,et al.Interhemispheric propagation of stationary Rossby waves in a horizontally nonuniform background flow.JAmos Sci,2015,72:3233-3256
2 Jaw J J.The formation of the semi-permanent center of action in relation to the horizontal solenoidal field.J Meteorol,1946,3:103-144
3 Kuo H L.Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere.J Meteorol,1949,6:105-122
4 Charney J G.The dynamics of long waves in a baroclinic westerly current.J Meteorol,1947,4:135-163
5 Eady E T.Long waves and cyclone waves.Tellus,1949,1:33-52
6 Pedlosky J.Geophysical Fluid Dynamics.Berlin:Springer-Verlag,1979.624
7 Chao J P,Wang X L.Energy propagation of Rossby wave in a baroclinic atmosphere(in Chinese).In:Collection of Atmospheric Sciences.Nanjing:Nanjing University Press,1993.49-61[巢纪平,王晓丽.斜压大气中能量传播的射线理论.见:大气科学文集.南京:南京大学出版社,1993.49-61]
8 Chao J P,Ye D Z.The spiral-like planetary waves in the barotropic atmosphere(in Chinese).Chin J Atmos Sci,1997,1:81-88[巢纪平,叶笃正.正压大气中的螺旋行星波.大气科学,1977,1:81-88]
9 Liu S S,Yang D S.The spiral structure of the planetary waves in the earth atmosphere(in Chinese).Acta Meteorol Sin,1979,1:14-27[刘式适,杨大升.地球大气行星波的螺旋结构.气象学报,1979,1:14-27]
10 Chen J K.The variation mechanism of the spiral structure of the spherical planetary waves in a barotropic atmosphere(in Chinese).Sci Meteorol Sin,1980,Z1:27-41[陈久康.正压大气球面行星波螺旋结构变化的机制.气象科学,1980,Z1:27-41]
11 Ye D Z,Zhu B Z.Some Basic Problems in Atmospheric Circulation(in Chinese).Beijing:Science Press,1958[叶笃正,朱抱真.大气环流中的若干基本问题.北京:科学出版社,1958]
12 Ji J J.Spiral planetary waves and the transfer processes of angular momentum in the baroclinic atmosphere(in Chinese).Acta Meteorol Sin,1979,37:90-96[季劲钧.斜压球面螺旋行星波和角动量输送.气象学报,1979,37:90-96]
13 Chen Y Y,Chao J P.Conservation of wave action and development of spiral Rossby waves(in Chinese).Sci China Ser B,1983,7:663-672[陈英怡,巢纪平.螺旋Rossby波的波密度守恒和稳定性.中国科学B辑,1983,7:663-672]
14 Liu F,Chao J P,Huang G,et al.A semi-analytical model for the propagation of Rossby waves in slowly varying flow.Chin Sci Bull,2011,56:2727-2731
15 Rossby C G.On the propagation of friquencies and energy in certain types of ocean and atmospheric waves.J Meteorol,1945,2:187-204
16 Whitham G.A note on group velocity.J Fluid Mech,1960,9:347-352
17 Hoskins B J,Karoly D J.The steady linear response of a spherical atmosphere to thermal and orographic forcing.J Atmos Sci,1981,38:1179-1196
18 Karoly D J.Rossby wave propagation in a barotropic atmosphere.Dyn Atmos Oceans,1983,7:111-125
19 Hoskins B J,Ambrizzi T.Rossby wave propagation on a realistic longitudinally varying flow.J Atmos Sci,1993,50:1661-1671
20 Xu X D,Miao Q J.The low fequency dynamics on the wave ray propagation of tropical atmosphere energy dispersion(in Chinese).Acta Meteorol Sin,2000,58:534-544[徐祥德,苗秋菊.热带大气能量频散波射线的低频动力学特征.气象学报,2000,58:534-544]
21 Li Y J,Li J P.Propagation of planetary waves in the horizontal non-uniform basic flow(in Chinese).Chin J Geophys,2012,55:361-371[李艳杰,李建平.水平非均匀基流中行星波的传播.地球物理学报,2012,55:361-371]
22 Kalnay E,Kanamitsu M,Kistler R,et al.The NCEP/NCAR 40-year reanalysis project.Bull Amer Meteorol Soc,1996,77:437-471
23 Branstator G.Horizontal energy propagation in a barotropic atmosphere with meridional and zonal structure.J Atmos Sci,1983,40:1689-1708
24 Branstator G.Circumglobal teleconnections,the jet stream waveguide,and the North Atlantic Oscillation.J Clim,2002,15:1893-1910
25 Ding Q,Wang B.Circumglobal teleconnection in the Northern Hemisphere summer.J Clim,2005,18:3483-3505
26 Liu F,Wang B.Mechanisms of global teleconnections associated with the Asian summer monsoon:An intermediate model analysis.JClim,2013,26:1791-1806
27 Li Y J,Li J P,Jin F F,et al.Interhemispheric propagation of stationary Rossby waves in a horizontally nonuniform background flow.JAmos Sci,2015,72:3233-3256