Characteristics of the transition to turbulent motion

An elementary model of turbulence formation is considered which corresponds to Landau's concept of disruption of a stable limit cycle. Qualitative estimates are made of conditions for the onset of turbulent (stochastic) motion having the structure of a 'strange attractor'. It is shown that a strange attractor arises under conditions where the effective modulus of expansion of trajectories in phase space in the dissipationless case becomes larger than the effective diffusion coefficient. A detailed numerical experiment for this model is performed which clarifies the structure of the strange attractor, the transition process, local instability, the correlation function, and the steady-state distribution function in phase space.