Characteristics of the leading Lyapunov vector in a turbulent channel flow

The values of the highest Lyapunov exponent (HLE) $\unicode[STIX]{x1D706}_{1}$ for turbulent flow in a plane channel at Reynolds numbers up to $Re_{\unicode[STIX]{x1D70F}}=586$ are determined. The instantaneous and statistical properties of the corresponding leading Lyapunov vector (LLV) are investigated. The LLV is calculated by numerical solution of the Navier–Stokes equations linearized about the non-stationary base solution corresponding to the developed turbulent flow. The base turbulent flow is calculated in parallel with the calculation of the evolution of the perturbations. For arbitrary initial conditions, the regime of exponential growth ${\sim}\exp (\unicode[STIX]{x1D706}_{1}t)$ which corresponds to the approaching of the perturbation to the LLV is achieved already at $t^{+}