Energy dissipation rate in the inertial sublayer of turbulent channel flow at large but finite Re?

This paper presents a theory of the position dependence of the statistical average (epsilon) of the energy dissipation rate epsilon per unit mass in the inertial sublayer of turbulent channel flow. The theory gives (epsilon)y/u3 tau -1/K epsilon + Cp(y/h) + Cv(l tau/y) for small but finite ratios y/h and l tau/y, at large but finite friction Reynolds number Re tau = h/l tau, where y is the distance from the wall, h is the channel half-width, u tau and l tau are the friction velocity and length respectively, and K epsilon, Cp, and Cv are nondimensional constants. The theory agrees well with the data of a series of direct numerical simulations of turbulent channel flow with Re tau up to approximately 8000. The data suggest K epsilon eta 0.44, which is distinctively different from the widely accepted value (eta 0.40 or so) for the von Karman constant for the mean velocity in the log-law region of wall-bounded flows.

Automated summary

This paper presents a theory on the position dependence of the energy dissipation rate in the inertial sublayer of turbulent channel flow. The theory provides a formula for small but finite ratios of y/h and l tau/y, at a large but finite friction Reynolds number Re tau = h/l tau. The theory agrees well with the data from direct numerical simulations of turbulent channel flow.