On the normalized dissipation parameter Cε in decaying turbulence

The Reynolds number dependence of the non-dimensional mean turbulent kinetic energy dissipation rate C-epsilon = epsilon L/u('3) (where epsilon is the mean turbulent kinetic energy dissipation rate, L is an integral length scale and u' is the velocity root-mean-square) is investigated in decaying turbulence. Expressions for C-epsilon in homogeneous isotropic turbulent (HIT), as approximated by grid turbulence, and in local HIT, as on the axis of the far field of a turbulent round jet, are developed from the Navier-Stokes equations within the framework of a scale-by-scale energy budget. The analysis shows that when turbulence decays/evolves in compliance with self-preservation (SP), C-epsilon remains constant for a given flow condition, e.g. a given initial Reynolds number. Measurements in grid turbulence, which does not satisfy SP, and on the axis in the far field of a round jet, which does comply with SP, show that C-epsilon decreases in the former case and remains constant in the latter, thus supporting the theoretical results. Further, while C-epsilon can remain constant during the decay for a given initial Reynolds number, both the theory and measurements show that it decreases towards a constant, C-epsilon,C-infinity, as Re-lambda increases. This trend, in agreement with existing data, is not inconsistent with the possibility that C-epsilon tends to a universal constant.