The optimality of a nonlinear stability criterion of motions of two_layer Phillips model is investigated. The result shows that for a given zonal periodical channel, there exist cases that there is no normal mode whic...The optimality of a nonlinear stability criterion of motions of two_layer Phillips model is investigated. The result shows that for a given zonal periodical channel, there exist cases that there is no normal mode which grows exponentially even if the sufficient conditions of the criterion are destroyed. On the other hand, the above criterion is optimal in the following sense: when the sufficient conditions of the criterion are destroyed, except some critical cases, there exists a finite zonal periodical channel, in which there is a zonal normal mode growing exponentially.展开更多
A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case o...A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′<SUB> i </SUB>at any time.展开更多
We investigate the instability of two-layer Phillips model in this paper, which is a prototypical geophysical fluid model. Using the results of Guo and Strauss et al, we obtained linear instability implies nonlinear i...We investigate the instability of two-layer Phillips model in this paper, which is a prototypical geophysical fluid model. Using the results of Guo and Strauss et al, we obtained linear instability implies nonlinear instability provided the linearized system has an exponentially growing solution.展开更多
现有电力系统稳定分析主要考虑励磁系统主环电压控制,而忽略励磁辅助控制环节(简称励磁辅环控制)的影响。现场运行经验表明,励磁系统辅环控制对发电机组动态品质及电网稳定性有着重要影响。以国内主流励磁调节器EXC9100为例,在分别建立...现有电力系统稳定分析主要考虑励磁系统主环电压控制,而忽略励磁辅助控制环节(简称励磁辅环控制)的影响。现场运行经验表明,励磁系统辅环控制对发电机组动态品质及电网稳定性有着重要影响。以国内主流励磁调节器EXC9100为例,在分别建立了含欠励限制、伏赫兹限制和过励限制这三种辅环控制的扩展Heffron-Phillips模型的基础上,采用阻尼转矩分析方法从理论上推导了这三种辅环控制的重要参数对电力系统稳定器(Power System Stabilizer, PSS)所提供的附加阻尼转矩以及其自身所提供的阻尼转矩的影响规律。最后结合发电机组实际运行工况,通过典型算例的仿真测试验证了所得规律的正确性和有效性。展开更多
On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is...On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance展开更多
On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is inve...On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.展开更多
文摘The optimality of a nonlinear stability criterion of motions of two_layer Phillips model is investigated. The result shows that for a given zonal periodical channel, there exist cases that there is no normal mode which grows exponentially even if the sufficient conditions of the criterion are destroyed. On the other hand, the above criterion is optimal in the following sense: when the sufficient conditions of the criterion are destroyed, except some critical cases, there exists a finite zonal periodical channel, in which there is a zonal normal mode growing exponentially.
基金This project was supported jointly by the National Natural Science Foundation of China under Grant Nos. 49455007, 40075011, and 40075014, and the China Postdoctoral Science Foundation,
文摘A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′<SUB> i </SUB>at any time.
基金Supported by the National Natural Science Foundation of China(No.10871097)National Basic Research Program of China(973 Program)(No.2013CB834100)
文摘We investigate the instability of two-layer Phillips model in this paper, which is a prototypical geophysical fluid model. Using the results of Guo and Strauss et al, we obtained linear instability implies nonlinear instability provided the linearized system has an exponentially growing solution.
文摘现有电力系统稳定分析主要考虑励磁系统主环电压控制,而忽略励磁辅助控制环节(简称励磁辅环控制)的影响。现场运行经验表明,励磁系统辅环控制对发电机组动态品质及电网稳定性有着重要影响。以国内主流励磁调节器EXC9100为例,在分别建立了含欠励限制、伏赫兹限制和过励限制这三种辅环控制的扩展Heffron-Phillips模型的基础上,采用阻尼转矩分析方法从理论上推导了这三种辅环控制的重要参数对电力系统稳定器(Power System Stabilizer, PSS)所提供的附加阻尼转矩以及其自身所提供的阻尼转矩的影响规律。最后结合发电机组实际运行工况,通过典型算例的仿真测试验证了所得规律的正确性和有效性。
文摘On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance
文摘On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.
