Introduction

As we saw in Appendix A, many physical entities can be represented mathematically as either scalars or vectors, depending on their transformation properties under rotation of the coordinate axes. However, it turns out that scalars and vectors are particular types of a more general class of mathematical constructs known as tensors. In fact, a scalar is a tensor of order zero, and a vector is a tensor of order one. In fluid mechanics, certain important physical entities (i.e., stress and rate of strain) are represented mathematically by tensors of order greater than one. It is therefore necessary to supplement our investigation of fluid mechanics with a brief discussion of the mathematics of tensors. For the sake of simplicity, we shall limit this discussion to Cartesian coordinate systems. Tensors expressed in such coordinate systems are known as Cartesian tensors. For more information on Cartesian tensors see Jeffries 1961, Riley 1974, and Temple 2004.