The largest Lyapunov exponent and the turbulent fluctuation of the time series from air turbulent jets

Abstract

The velocity time series of round air jets are acquired with the hot-wire anemometer. We compute the largest Lyapunov exponent and the turbulent incoherent perturbation of the velocity signals at 939 ≤ Re ≤ 3758 using an analytical method of chaotic time series which is based on the invariant of the largest Lyapunov exponent. The results show that the largest Lyapunov exponent increases with exit Reynolds number, and decreases with the distance away from nozzle exit. The reciprocal of the largest Lyapunov exponent is positively correlated with correlation time. The incoherent perturbation of turbulence increases either with exit Reynolds number or with the distance away from nozzle exit. The incoherent perturbation of turbulence is negatively correlated with Kolmogorov scale.