Introduction

In this part of the text, for compactness, Cartesian coordinates and components will be used in the analysis. In specific examples, the clearer notation x, y, z, and u, v, w will be used

The summation convention will be used so that summation signs will not be written explicitly but will be implied by repeated indices; in scalar products or vectors.

and the divergence operator

Notations:

	Inst	mean	fluctuating
This text (usually)	u
Alternative -1	u	<u>
Alternative -2	u	U
Pope (2000)	U	<U>	u
Tennekes& Lumley (1972)		U	u