Disturbance growth rate in turbulent wall flows

Disturbance development in turbulent wall flows is numerically investigated. The flows in a circular tube and in a plane channel are considered. The Navier-Stokes equations subjected to the condition of periodicity along the main flow are integrated in time until a statistically stationary turbulent flow regime is attained. Then the solution is disturbed and the further evolution of the disturbance is determined by comparing the two solutions, i.e., with and without the disturbance, which are calculated in parallel. It is shown that in the linear stage on average the solutions diverge exponentially. The main result of the study is that the small disturbance growth rate normalized by the wall time scale turns out to be constant, that is, dependent on neither the Reynolds number on the range considered nor the type of the flow: lambda(+) a parts per thousand 0.021. The estimate of the disturbance growth rate is consistent with the previously obtained results concerning downstream disturbance growth and the estimate for the highest Lyapunov exponent calculated for turbulent flow in a plane channel.