The stability properties of the equilibria with constant wind shear (both in vertical and horizontal direction) andthe non-constant static stability in bounded, inviscid and adiabatic atmosphere were investigated by u...The stability properties of the equilibria with constant wind shear (both in vertical and horizontal direction) andthe non-constant static stability in bounded, inviscid and adiabatic atmosphere were investigated by using normalmode method. The results show that the stability property is determined by Richardson number R, as well as the absolute vorticity. When the absolute vorticity F is positive, i.e. F > 0, (where F = f+ vx ) the sufficient condition forsymmetric stability is Ri > f/ F and when F < 0, the equilibria are unstable for all possible normal mode disturbances. In addition, the most unstable growth rate was also obtained here.展开更多
The general property of zonally symmetric stability of quasi-homogeneous and incompressible rotating ocean can be determined by a nondimensional parameter R. which is similar to the Richardson number in Howard's p...The general property of zonally symmetric stability of quasi-homogeneous and incompressible rotating ocean can be determined by a nondimensional parameter R. which is similar to the Richardson number in Howard's paper. The results indicate that the rotating effect leads to stabilize the basic flows and the horizontal shear effect leads to destabilize the basic flows.In addition, the most unstable growth rate is obtained and,the semicircle and semiellipse theorem about the distributions of the unstable phase velocity are given in this paper.展开更多
The average variational principle was employed in this paper to study the evolution of large-scale and slowly varying Rossby wave packet with basic flow both in barotropic and baroclinic atmospheres. The evolution of ...The average variational principle was employed in this paper to study the evolution of large-scale and slowly varying Rossby wave packet with basic flow both in barotropic and baroclinic atmospheres. The evolution of the structure of Rossby wave packet with both time and space was studied. The results obtained in this paper are similar to the results of by WKBJ method. In addition, the dispersive process of the wave packet was analysed by taking Gaussian type wave packet as an initial disturbance. The valid time scale for application of wave packet theory in the atmosphere was obtained.展开更多
Since Arnold (1965) used variational principle to study the nonlinear stability of ideal inviscid fluid, there have been many papers published in this field. Holm (1985) reviewed the recent results. There are also som...Since Arnold (1965) used variational principle to study the nonlinear stability of ideal inviscid fluid, there have been many papers published in this field. Holm (1985) reviewed the recent results. There are also some papers in which this method is used to study the nonlinear stability of geophysical fluid dynamics including the papers of Bulman, Mclntyre, Zeng Qingcun, Zeng Qingcun & Mu Mu. Zeng’s work made a big progress compared with the work before. By using the conservation of angular momentum, he put this method into the case that the basic flow is unsteady.展开更多
Normal mode method is an important tool in the study of fluid mechanics and the results of some research work show that if we applied this method in the fluid mechanics without considering some suitable conditions, th...Normal mode method is an important tool in the study of fluid mechanics and the results of some research work show that if we applied this method in the fluid mechanics without considering some suitable conditions, then the conflict results would appear. This was pointed out by Hφland, Case from theoretical point of view for non-rotating barotropic flow. They concluded that normal mode is not complete for describing all the possible disturbance, and in order to solve the stability problem completely, we must take it as an initialboundary value problem.展开更多
文摘The stability properties of the equilibria with constant wind shear (both in vertical and horizontal direction) andthe non-constant static stability in bounded, inviscid and adiabatic atmosphere were investigated by using normalmode method. The results show that the stability property is determined by Richardson number R, as well as the absolute vorticity. When the absolute vorticity F is positive, i.e. F > 0, (where F = f+ vx ) the sufficient condition forsymmetric stability is Ri > f/ F and when F < 0, the equilibria are unstable for all possible normal mode disturbances. In addition, the most unstable growth rate was also obtained here.
文摘The general property of zonally symmetric stability of quasi-homogeneous and incompressible rotating ocean can be determined by a nondimensional parameter R. which is similar to the Richardson number in Howard's paper. The results indicate that the rotating effect leads to stabilize the basic flows and the horizontal shear effect leads to destabilize the basic flows.In addition, the most unstable growth rate is obtained and,the semicircle and semiellipse theorem about the distributions of the unstable phase velocity are given in this paper.
文摘The average variational principle was employed in this paper to study the evolution of large-scale and slowly varying Rossby wave packet with basic flow both in barotropic and baroclinic atmospheres. The evolution of the structure of Rossby wave packet with both time and space was studied. The results obtained in this paper are similar to the results of by WKBJ method. In addition, the dispersive process of the wave packet was analysed by taking Gaussian type wave packet as an initial disturbance. The valid time scale for application of wave packet theory in the atmosphere was obtained.
文摘Since Arnold (1965) used variational principle to study the nonlinear stability of ideal inviscid fluid, there have been many papers published in this field. Holm (1985) reviewed the recent results. There are also some papers in which this method is used to study the nonlinear stability of geophysical fluid dynamics including the papers of Bulman, Mclntyre, Zeng Qingcun, Zeng Qingcun & Mu Mu. Zeng’s work made a big progress compared with the work before. By using the conservation of angular momentum, he put this method into the case that the basic flow is unsteady.
基金Project supported by the National Natural Science Foundation of China.
文摘Normal mode method is an important tool in the study of fluid mechanics and the results of some research work show that if we applied this method in the fluid mechanics without considering some suitable conditions, then the conflict results would appear. This was pointed out by Hφland, Case from theoretical point of view for non-rotating barotropic flow. They concluded that normal mode is not complete for describing all the possible disturbance, and in order to solve the stability problem completely, we must take it as an initialboundary value problem.
