Perturbation Growth Rate in Turbulent Couette Flow

Abstract

The evolution of small perturbations in turbulent Couette flow is investigated numerically at the Reynolds numbers Re_τ 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.