基态位涡径向分布对浅水涡旋系统动力稳定性的影响分析

Impacts of the basic state Potential Vorticity(PV) profiles on the stability of shallow-water vortices

本文基于正压浅水模型,分析基态位涡(Potential Vorticity:PV)结构对热带气旋(Tropical Cyclone:TC)类涡旋系统稳定性及其波动特征的影响.通过引入基态PV结构参数:宽度δ(眼墙内外边界涡度发生陡变的半径长度之比)和中空度γ(眼心相对涡度与内核区域平均相对涡度之比),设计具有相同基流最大切向风速和最大风速半径的170组不同基态PV环结构的敏感性试验,并讨论了不同基态PV结构下涡旋系统最不稳定波数(the most unstable wavenumber:MUWN)和系统最不稳定模态(the most unstable mode of System:MUMS)的特征频率及其不稳定增长率的大小.结果指出:当PV环较宽,系统表现为低波数最不稳定,相应的MUMS为低频波且增长率小;当PV环较窄,系统表现为高波数不稳定,且PV环越实最不稳定波数越高;当PV环窄且空时,MUMS均为中高频波动,且不稳定增长率随PV环的宽度变窄和中空度变空而明显增大.分析典型PV结构下系统演变特征可知,当PV环较宽,MUMS表现为具有平衡约束的低频波动的线性不稳定特征;当PV环趋向窄且空时,MUMS的平衡性约束趋向弱化,同时不稳定增长表现为明显的指数型增长.进一步讨论系统内部非对称结构的形成和传播机制发现,对于弱不稳定的PV环来说,低波数波最不稳定的特征波动具有典型涡旋Rossby波特征;而对于强不稳定的PV环来说,高波数不稳定的特征波动混合波性质明显.

In this study,the effect of the shape of basic-state potential vorticity（PV）profile on the stability and wave characteristics of the tropical cyclone（TC）-like vortices is discussed in a two-dimensional（2 D）shallow water barotropic model.A sequence of 170 numerical simulations are conducted by setting two structural parameters of basic-state PV under the premise of the same basic-state maximum wind and the radius of maximum wind（RMW）,with the first parameter defining the thickness of the ring（i.e.,the ratio of the inner and outer radii of the ring）and the second parameter defining the hollowness of the ring（i.e.,the ratio of eye vorticity to inner-corerelative vorticity）.The most unstable wavenumber（MUWN）as well as the eigenfrequency and growth rate of the most unstable mode in systems（MUMSs）with different the basic-state PV profiles are examined.The results show that the MUWN for thicker rings are more prone to lower wavenumber（WNs）,and the corresponding MUMSs possess lower intrinsic frequencies and small growth rates,while thinner rings are more prone to higher wavenumber growth.As the ring becomes more filled,there is a tendency for the MUWN to be at higher wavenumber.For thin and hollow rings,MUMSs possess high frequencies and large growth rates.The evolution of perturbation kinetic energy for vortices,possessing different typical PV rings are analyzed.It is found that the MUMSs for thick rings present the algebraically growing instability under the equilibrium constraint.However,as the PV rings tend to be thin and hollow,the MUMSs are exponentially growing,as well as equilibrium constraint weakening.The dynamics of the asymmetric structure in the inner core of TC-like vortices are further advanced,indicating that the wave structure of MUMSs for weakly unstable ring have typical characteristics of Vortex Rossby Waves（VRWs）,while the wave structure of MUMSs for strongly unstable ring possess typical mix waves.