Dynamic Effects of Centrifugal Forces on Turbulence

The dynamic effect of suddenly applied centrifugal forces on homogeneous and isotropic turbulence in the entrance region of a curved pipe is analyzed by a perturbation method. The model is for small-scale turbulence and is valid away from the pipe wall; hence is not restricted to a particular cross-sectional shape and can be applied even to external flows if the mean velocity profile is almost uniform, as in the region outside the turbulent boundary layer on a curved surface. The analysis indicates that the major effect of centrifugal forces is to generate pure turbulent shear and this effect is cumulative. Thus, an initially isotropic turbulence become anisotropic due to linear effects. This result is in contrast with the effect of solid-body rotation on isotropic turbulence, where rotation acts on an initially isotropic turbulence only through nonlinear interactions, and pure linear effects influence the double correlations only if the turbulence is initially anisotropic.