波射线理论在大气正压不稳定中的应用  

On the barotropic instability using wave ray theory

作　　者：亢妍妍 李耀锟[3] 

机构地区：[1]北京大学物理学院,北京100871 [2]国家海洋环境预报中心国家海洋局海洋灾害预报技术研究重点实验室,北京100081 [3]北京师范大学全球变化与地球系统科学研究院,北京100875

出　　处：《科学通报》2016年第34期3718-3725,共8页Chinese Science Bulletin

基　　金：国家重点基础研究发展计划(2014CB953903;2015CB953601);国家自然科学基金(41505042)资助

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 mean

关 键 词：正压不稳定 波射线 ROSSBY波 位势涡度梯度 急流 

分 类 号：P424[天文地球—大气科学及气象学]