As a means of studying the structure of the turbulence, the time mean invariants, defined according to the theory of Lumley [3] has proven to be a useful and popular tool. According to the theory there is a domain, known as the Lumley triangle, within which all realizable Reynolds's stress invariants must lie. The borders of this domain describes different states of the turbulent stress tensor. It has been found that there is some confusion in the terminology used when describing these states. The confusion is related to whether the notation is used to describe the shape of the stress tensor or the eddies of the turbulence. Choi and Lumley [1] noted the same controversy in terminology, but since the confusion is still found to exist the current work describes the fundamental relationships which exist between the shape of the stress tensor and it's invariants. Also an analysis is given to clarify the existing terminology.

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