Numerical study of high-order Lagrangian structure functions in a turbulent channel flow with low Reynolds number

The scaling exponents of Lagrangian velocity structure functions from orders 1 to 10 in a low Reynolds number turbulent channel flow are investigated by using direct numerical simulation. The Reynolds number Reτ is 80 (based on friction velocity on the wall). The Lagrangian velocity structure functions are shown to obey the scaling relations <Δvq(τ)>∼τζL(q). The scaling exponents are normalized by ζL(2) (so-called ESS procedure). The coincidence between the theoretical predictions and numerical calculations is very good for the longitudinal scaling exponent in the channel center. It is also found that the high-order longitudinal scaling exponents agree with theoretical values better than those for the transverse direction.