中文摘要：

利用Fourier变换方法，研究准地转近似下beta平面上绝热、无摩擦、无强迫耗散的正压大气Rossby波扰动能量在有限时段内的快速发展和衰减情形．给出线性正压位势涡度方程扰动流函数的解析解，并进一步分析扰动能量与东西波数、南北波数、基流切变和黏性系数之间的关系．

英文摘要：

Fourier-transformed method is used to investigate the problem of the rapid growth and decay of the disturbance energy of Rossby wave in barotropic atmosphere on the assumption that this kind of atmosphere is adiabatic, non-frictional, unforced, non-dissipative and quasigeostrophic on a beta plane. The analytical solution of linear barotropic potential vorticity equation is obtained for the first time and we go a step further to discuss the relations between the disturbance energy and the initial perturbation flow wave numbers, shear of basic flow and viscid coefficient by using the above analytical solution.