流体力学中物质导数概念的推广

Extension of Material Derivative Concept in Fluid Mechanics

物质导数的定义是流体质点的某个物理量相对时间的变化率。但有时需计算不属于流体质点的某个非物理量的物质导数,如计算正交曲线坐标系基矢量和坐标变量的物质导数。严格说求这些量的物质导数在概念上不清楚。为解决此问题,对物质导数概念进行了深入剖析,结果发现可将这一概念推广,使之也适合于定义在流场中不属于流体质点的任何量,包括矢量、标量、物理量和非物理量。使得这一基本概念的定义更加精确,有关的理论问题的分析过程得以简化,也使得流体力学的理论体系更加严密和完整。

Material derivative is a basic concept in fluid mechanics.Its original definition is changing rate relative to the time of a physical quantity which belongs to a fluid particle.But when researching the problems of fluid mechanics,not only need to calculate the material derivative of a physical quantity which belongs to a fluid particle,but also need in some cases to calculate the material derivative of a certain quantity which dos not belong to a fluid particle.This kind of quantities includes physical quantity or non physical quantity,vector or scalar and so on,Such as calculating the material derivative of base vectors and coordinate variables of orthogonal curvilinear coordinates.Strictly speaking,the original definition of material derivative is not suitable for this kind of quantities,calculating material derivative of these quantities is not clear in concept.In order to solve this problem,thorough analysis about material derivative was made according to the original definition and calculation formula of material derivative.As a result it was founded that the concept of material derivative might be extended,So this concept could apply not only to a certain physical quantity which belonged to a fluid particle,but also to any quantity which did not belong to a fluid particle and was defined in the flow field,This kind of quantities included vector or scalar,physical quantity or non physical quantity and so on.The extension of material derivative made its definition more precise,made analysis process of related theoretical problems be simplified,and also made the theory system of fluid mechanics more strict and complete.This paper gave a specific example to illustrate the application of the extension.