大气中的Hamilton函数的构造和Lyspounov稳定性
THE CONSTRUCTION OF HAMILTONIAN FUNCTION AND LYAPOUNOV STABILITY IN THE ATMOSPHERE
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摘要: 本文对大气中的地转和非地转运动的Hamilton函数进行了构造,在此基础上得到了一个Lyapounov函数的不变量,同时我们还用Lyapounov函数的二阶变分找出了大气运动的稳定性判据。Abstract: In this paper, the Hamiltonian function of atmospheric motions is construtted, and on this base, the integral invariant of Lyapounov functons is obtained. Furthermore, the nonlinear Lyapounov stability criteria are obtained by applying the second variations of Lyapounov functions.
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Arnol'd, V. I, Conditions for nonlinear stability of stationary plane'curvilinear flows of an ideal fluid, Dokl. Akad. SSSR., 162, 975-978, 1965.
Bretherton, F. P, A note on Hamilton's principle for perfect fluids, J. Fluid Meclt., 44, 19-31,1970.
Abarbanel, H. D., and D. D. Holm, Nonlinear stability analysis of inviscid flows in three dimension:Incompressible fluid and barotropic fluids, Pltys. Fluids, 30, 11, 3369-3382, 1987.
Salmon, R., Practical use of Hamilton's principle, J. Fluid Mech.,32,431-444, 1983.
伍荣生、侯志明,局地势与涡度守恒原理,气象学报,47, 130-136, 1989. Mclntyre, M. E., and T. G. Shepherd, An exact local conservation theorem for finite-amplitude disturbance to non-parallel shear flow, with remarks on Hamiltonian structure and on Arnol'd's stability theorems, J. Fluid. Meck., 181,527-565, 1987.
Zeng Qingcun, Variational principle of instability of Atmospheric motion, Adv. Almos. Sci., 6,137-172, 1989.
Pedlosky, J., Geophyscical Fluid Dynamics, Sponger Verlag, New, York, 1979.
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