Turbulent energy scale budget equations in a fully developed channel flow

Kolmogorov's equation, which relates second- and third-order moments of the velocity increment, provides a simple method for estimating the mean energ y dissipation rate [epsilon] for homogeneous and isotropic turbulence. Howe ver, this equation is usually not verified in small to moderate Reynolds nu mber flows. This is due partly to the lack of isotropy in either sheared or non-sheared hows, and, more importantly, to the influence, which is flow s pecific, of the inhomogeneous and anisotropic large scales. These shortcomi ngs are examined in the context of the central region of a turbulent channe l flow. In this case, we propose a generalized form of Kolmogorov's equatio n, which includes some additional terms reflecting the large-scale turbulen t diffusion acting from the walls through to the centreline of the channel. For moderate Reynolds numbers, the mean turbulent energy transferred at a scale r also contains a large-scale contribution, reflecting the non-homoge neity of these scales. There is reasonable agreement between the new equati on and hot-wire measurements in the central region of a fully developed cha nnel flow.