Standard covariant formulation for perfect-fluid dynamics
Standard covariant formulation for perfect-fluid dynamics
复制标题
完美流体动力学的标准协变公式
DOI：
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发表时间：
1988
影响因子：
3.7
通讯作者：
B. Gaffet
中科院分区：
文献类型：
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作者：
B. Carter;B. Gaffet
在简要描述了牛顿运动学时空的伽利略不变性群的米尔恩推广之后，它表明如何广义欧拉动力学方程的运动的多组分完美（非导电）流体可以用电流4矢量与适当的4动量1形式的外部导数的内积来表示（其作用是在这种方法的核心）在一个完全协变的标准形式，其结构是相同的，在牛顿的情况下，相应的方程的情况下（特殊或一般）相对论完美流体力学。除了时空协方差，这个标准形式还表现出化学协方差，即在独立保守化学组分的数密度重新定义下，它在彼此的线性组合方面是明显不变的。它示出了如何，在严格保守的情况下，当没有化学反应发生时，这个标准的形式，可以使用（通过建设适当的广义Clebsch潜力）建立一个欧拉（定点）变分原理的形式，是同时有效的牛顿和相对论的情况下。
After a brief description of the Milne generalization of the Galilean invariance group for the space–time of Newtonian kinematics, it is shown how the generalized Eulerian dynamical equations for the motion of a multiconstituent perfect (nonconducting) fluid can be expressed in terms of interior products of current 4-vectors with exterior derivatives of the appropriate 4-momentum 1-forms (whose role is central in this approach) in a fully covariant standard form whose structure is identical in the Newtonian case to that of the corresponding equation for the case of (special or general) relativistic perfect fluid mechanics. In addition to space–time covariance, this standard form exhibits chemical covariance in the sense that it is manifestly invariant under redefinition of the number densities of the independent conserved chemical constituents in terms of linear combinations of each other. It is shown how, in the strictly conservative case when no chemical reactions occur, this standard form, can be used (via the construction of suitably generalized Clebsch potentials) for setting up an Eulerian (fixed-point) variation principle in a form that is simultaneously valid for both Newtonian and relativistic cases.