Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region

Abstract EN

The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows.

Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors S and Ω are studied.

The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω , in which the scalar coefficients depend on simultaneous invariants of these tensors.