基矢量和坐标变量的随体导数公式及其应用

Formulae on the base vectors and the coordinate variables derivative going with fluid particle and their application

流体力学中随体导数的含义是指流体质点的某个物理量相对于时间的变化率,随体导数的运算符是DDt,如果把它看成是与普通导数ddt相似的一个运算符的话,当采用正交曲线坐标系研究流体力学问题时,在计算流体质点某个物理量的随体导数过程中,计算公式内就会出现正交曲线坐标系基矢量的随体导数DeiDt和坐标变量的随体导数DqiDt,用以前的随体导数概念不能解释这两项的含义,因它们不是流体质点的物理量,而是几何量.但对随体导数进行深入分析可以发现,随体导数的概念和计算公式完全可以应用到基矢量和坐标变量上去.导出了它们的计算公式并给出了应用实例.

The meaning of derivative going with fluid particle in hydrodynamics is the variety rate of physical quantity belonging to certain fluid particle relative to time. Theoperator is DDt.If we regards it as similar as the ordinary derivative ddt,when we study the hydrodynamics problems adopting perpendicular curve coordinate system, the base vectors and the coordinate variables derivative going with fluid particle which belong to perpendicular curve coordinate system De_iDt,Dq_iDtwill appear in the calculating formulae during calculating the derivative going with fluid particle of physical quantity belonging to certain fluid particle . The meanings of the above two terms can′t be explained, because they are not physical quantity belong to certain fluid particle, but are geometries. However when we analyze the concept of derivative going with fluid particle thorough, we will find that the concept and the formulae of derivative going with fluid particle can be applied to base vectors and the coordinate variables completely and educe the calculating formulae about them and present the applying examples.