The Turbulent Shear Flow around a Rotating Cylinder in a Quiescent Fluid : 2nd Report, An Interpretation of the Turbulent Field Expressed in the Wave Number Space

Abstract

Spectrum tensor equations are derived for ψ_{2, 1}, ψ_{2, 3}, and ψ_{1, 3}, and the roles of terms in the equations are studied. Some terms can be explained by the same concept of spectrum tensor (i=j), but others play different roles. The production terms depending upon Coriolis force and metric force occur, and they are not due to mean flow tensor. Particularly, the production terms appearing in equations for ψ_{2, 3} and ψ_{1, 3} have opposite functions. The role of pressure-velocity terms is transport of spectrum components. Viscosity terms perform destruction, and they are not dissipated into heat. ψ_{2, 1} is closely related to ψ_{1, 1}, ψ_{2, 2} and ψ_{3, 3}. The relationship between ψ_{2, 3}, and ψ_{1, 3} is also close due to production terms.