磁流体力学中的位涡
Potential Vorticity in Magnetohydrodynamics
摘要：
利用拉格朗日乘子的Noether第二定理，研究了磁流体力学中流体重标对称性守恒律。我们得到了一个新的广义位涡型守恒方程，它考虑了熵梯度和由电流${\bf J}$和磁感应${\bf B}$引起的作用在等离子体上的${\bf J}\times{\bf B}$力。这个新的守恒定律是利用Noether第二定理结合一类流体再标记对称性导出的，其中Lagrange标记变换的对称生成元在Lagrange标记空间中不平行于磁场感应。这是与一个阿贝尔李伪代数和一个叶相空间在拉格朗日标签空间。它包含了理想流体力学中的Ertel定理作为特例。一个独立的推导表明，新的守恒定律也适用于更一般的物理情况。
英文摘要：
A version of Noether's second theorem using Lagrange multipliers is used to investigate fluid relabelling symmetries conservation laws in magnetohydrodynamics (MHD). We obtain a new generalized potential vorticity type conservation equation for MHD which takes into account entropy gradients and the ${\bf J}\times{\bf B}$ force on the plasma due to the current ${\bf J}$ and magnetic induction ${\bf B}$. This new conservation law for MHD is derived by using Noether's second theorem in conjunction with a class of fluid relabelling symmetries in which the symmetry generator for the Lagrange label transformations is non-parallel to the magnetic field induction in Lagrange label space. This is associated with an Abelian Lie pseudo algebra and a foliated phase space in Lagrange label space. It contains as a special case Ertel's theorem in ideal fluid mechanics. An independent derivation shows that the new conservation law is also valid for more general physical situations.
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