On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the thi...On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.展开更多
The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate s...The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.展开更多
Using the T63L16 analysis data with the resolution of 1.875╳1.875 degree of latitude and lon-gitude obtained from National Meteorological Center (NMC) and the real central position information of tropi-cal cyclone (r...Using the T63L16 analysis data with the resolution of 1.875╳1.875 degree of latitude and lon-gitude obtained from National Meteorological Center (NMC) and the real central position information of tropi-cal cyclone (referred to as TC hereafter) numbered by NMC, the basic environmental geostrophic flow at 126 time levels of 25 TCs in 1996 are calculated. The vertical distribution features of the flows are analyzed. Be-sides, the deviation of real TC tracks from the flows (referred as steering deviation hereafter, namely, the de-viation between the real central position of TC and the position calculated according to the steering flow) is also investigated. The result shows that the steering deviation would be different if the domain used to calculate the steering flow is different. The present paper obtains the optimum domain size to calculate the steering flow. It is found that the steering deviation is related to the velocity of steering flow and the initial latitude and intensity of TC itself, and that TC motion has relationship with the vertical shear structure of environmental geostrophic flow. The result also shows that the optimum steering flow is the deep-layer averaged basic flow from 1000 hPa to 200 hPa. Having the knowledge of these principle and features would help make accurate forecast of TC motion.展开更多
A nonlinear mathematic model taking the nutation and precession angles as variables for the coning motion of projectile was established according to a short period moment projection of the spining projectile. By intro...A nonlinear mathematic model taking the nutation and precession angles as variables for the coning motion of projectile was established according to a short period moment projection of the spining projectile. By introducing the generalized nutation angle and precession angular speed, the model that is difficult to be resolved can be transformed to a resolvable one. The interrelationship between nutation and precession was analyzed based on the linear model, and the stability condition was obtained for the spinning projectile. For the nonlinear model, the effects of the nutation and precession on the limit circle of the projectile's coning motion were investigated, and the analytical relations between the nutation angle and the precession angular speed in the steady coning motion of the spinning projectile were given.展开更多
基金Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006).
文摘On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.
基金Project supported by the National Natural Science Foundation of China(Nos.40175014,90411006)
文摘The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.
基金The Program of Research on Weather Forecasting Methods and Operational Systems by the National Meteorological Center (ZX95-02)
文摘Using the T63L16 analysis data with the resolution of 1.875╳1.875 degree of latitude and lon-gitude obtained from National Meteorological Center (NMC) and the real central position information of tropi-cal cyclone (referred to as TC hereafter) numbered by NMC, the basic environmental geostrophic flow at 126 time levels of 25 TCs in 1996 are calculated. The vertical distribution features of the flows are analyzed. Be-sides, the deviation of real TC tracks from the flows (referred as steering deviation hereafter, namely, the de-viation between the real central position of TC and the position calculated according to the steering flow) is also investigated. The result shows that the steering deviation would be different if the domain used to calculate the steering flow is different. The present paper obtains the optimum domain size to calculate the steering flow. It is found that the steering deviation is related to the velocity of steering flow and the initial latitude and intensity of TC itself, and that TC motion has relationship with the vertical shear structure of environmental geostrophic flow. The result also shows that the optimum steering flow is the deep-layer averaged basic flow from 1000 hPa to 200 hPa. Having the knowledge of these principle and features would help make accurate forecast of TC motion.
基金Sponsored by the National Science Foundation of China (10972034)
文摘A nonlinear mathematic model taking the nutation and precession angles as variables for the coning motion of projectile was established according to a short period moment projection of the spining projectile. By introducing the generalized nutation angle and precession angular speed, the model that is difficult to be resolved can be transformed to a resolvable one. The interrelationship between nutation and precession was analyzed based on the linear model, and the stability condition was obtained for the spinning projectile. For the nonlinear model, the effects of the nutation and precession on the limit circle of the projectile's coning motion were investigated, and the analytical relations between the nutation angle and the precession angular speed in the steady coning motion of the spinning projectile were given.
