Abstract:
As the two elementary structures in wall-bounded turbulence, streaks and streamwise vortices are of great importance in understanding the evolution of turbulence. In this paper, we first review the discovery and evolution of these coherent structures ranging from the near-wall region to the outer region and from low to high Reynolds numbers in fully-developed incompressible wall-bounded turbulence. A particular emphasis is placed on the two key characteristics of the structures, i.e., the self-similarity and the self-sustaining process (SSP). Then, a series of newly identified exact coherent states (ECSs) based on the SSP of turbulence is discussed. As the invariant solution of the N-S equations, the ECS gives an exact description of the coherent structure pair composed of streaks and streamwise vortices. The ECS has the two key characteristics, i.e., the self-similarity and the SSP, but with much lower dimension, thus it forms the skeleton of fully-developed turbulence and paves the way for the study of wall-bounded turbulence using the dynamical system theory. In recent years, the ECS study has also achieved a great success in explaining the subcritical transition by providing new views of this process. It is promising that the ECS may unify the two classical problems of turbulence and transition.