The spectrum of energy in turbulent shear flow

Abstract

The spectrum of energy in isothermal turbulent shear flow at large wave numbers is studied following the phenomenological approach used by Tchen (1953), Hinze (1959), and Panchev (1968, 1969). The considered spectrum equation consists of the dissipation, the transfer, the production, and the diffusion spectrum function. Parametric solutions for the three-dimensional energy spectrum function, E(k) are obtained firstly by using Heisenberg's type of approximations for the transfer function. Much simpler solutions for E(k) are obtained with the modified Obukhov approximation (Ellison 1962). Some closed form solutions for E(k) are derived by using a vorticity approximation concept. It is shown that Tchen's k-l law cannot exist if diffusional effects are taken into account. Computed one - dimensional energy spectra (isotropic relations were used) show good agreement with measurements from the viscous region of a turbulent boundary layer.