On the Karman constant in turbulent channel flow

Abstract

The Karman constant κ in the literature shows a notable variation of 15%, prompting claims that it is really not a constant. Here, we present a new interpretation of κ, based on a multi-layer analytical theory of Prandtl's mixing length function. It is shown that a central symmetry argument yields a new bulk structure of the channel flow and interprets κ as a global invariant of the outer region. With κ properly defined as such, a universal value of 0.45 is determined from mean velocity data over a wide range of Reynolds numbers.