Analysis of Lyapunov vectors of turbulent flows

In the perspective of predicting the formation of instabilities in turbulent flows, it is meaningful to characterize the formation and the propagation of disturbances. To this end, the Lyapunov theory provides a useful description of a turbulent flow field. On one hand, the computation of the Lyapunov spectrum provides the rate of growth of disturbances in a flow field and thereby quantifies the dimensionality of the strange attractor of the system. This is given by the Lyapunov exponents (LE) that have been the focus of numerous recent studies. On the other hand, the Lyapunov vectors (LV) can also be computed, but have been more overlooked since interpreting it is less obvious. In this work, the LV of several turbulent flows (1D Kuramoto Sivashinsky equation, homogeneous isotropic turbulence and turbulent channel flows) are computed, and their spatial structure is analyzed. It is shown that the LV exhibit non-trivial features for the vector associated with the null LE. In particular the concept of turbulent Lyapunov crisis is introduced and related to different turbulent forcing types.