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

Abstract

The equations for spectral tensor ψ_{2, ψ1}, ψ_{2, 3} and ψ_1.3 are derived, and the roles of terms in the equations are studied. Some terms can be explained by the same concept of spectral tensor for i=j, but others play different roles. Production terms dependent on Coriolis force and metric force occur, and are not due to mean flow tensor. In particular, the production terms appearing in the equations for ψ_{2, 3} and ψ_{1, 3} have opposite functions. The role of the pressure-velocity terms is the transport of spectrum components. Viscosity terms play a destructive role, and they are not dissipated into heat. Spectral tensor 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.