Perturbation Growth Rate in Turbulent Couette Flow

The evolution of small perturbations in turbulent Couette flow is investigated numerically at the Reynolds numbers Reτ from 35 to 125. Steady-state turbulent flows calculated on the basis of solving the Navier-Stokes equations are used as the basic flow to study the process of development of the perturbations against their background. The values of the senior Lyapunov exponent λ1 which characterizes the maximum growth rate of small perturbations in the stochastic systems are determined. It is found that the exponent, being normalized by the near-wall scales, is equal to λ1 ~ 0.02. This is in agreement with the results of the previous investigations of turbulent flows in the circular pipe and plane channel. It is shown that the λ1, whose value is smaller by three times and which was obtained earlier in calculating the Lyapunov spectrum in Couette flow at Reτ = 35 in the so-called “minimum channel”, can be explained by insufficient dimension of the computational domain but not by smallness of the Reynolds number.