Estimating von Kármán's constant from homogeneous turbulence

A celebrated universal aspect of wall-bounded turbulent flows is the von Kármán log-law-of-the-wall, describing how the mean velocity in the stream-wise direction depends on the distance from the wall. Although the log-law is known for more than 75 years, the von Kármán constant governing the slope of the log-law was not determined theoretically. In this letter we show that the von Kármán constant can be estimated from homogeneous turbulent data, i.e. without information from wall-bounded flows.