地球磁场长期变化动力学的Hamilton形式

ON THE DYNAMICS OF THE GEOMAGNETIC SECULAR VARIATION:THE HAMILTONIAN STRUCTURE

时间尺度O(1)—O(10~2)年的地球磁场长期变化,是由地球液核中导电流体的运动产生的.在合理的框架下,将支配地核流体的动力学方程组加以近似和简化,无论从正演还是反演的角度都是极为重要的.本文将理想地核流体的磁流体动力学方程组表述成Hamilton 形式,包括非正则动力学变量组U={V p,S,B},Hamilton 泛函H(u),Poisson 括号及与之等价的辛矩阵J.期望Hamilton 力学方法对地球磁场长期变化的动力学的研究有所裨益.

We used the equation of ideal magnetohydro dynamics to describe the behavior of the secularvaniation with time-scale O(1)—0(10~2)years.We studied the Hamiltonian structure consisting of theHamiltonian functional and Poisson braket as well as an alternative notion,i.e the symplectic form in thepolar spherical coordinate used in geomagnetism.