Transient growth of disturbances in near-wall region of turbulent channel flow

The transient growth of optimal disturbances has been suggested as a part of self-sustaining process of turbulent structures. It is generally accepted that the self-sustaining process is independent of the outer part of a boundary layer. In this study, we investigate the relationship between the optimally amplified disturbances in the near-wall region and turbulent structures in turbulent channel flows for $Re_{\tau}=180$ to $10000$. Optimal disturbances in a confined domain ($0y_{c}^{+}$ are damped out. The most amplified disturbances in a confined domain are streamwise velocity streaks that are induced by streamwise vortices. The wavelength, growth, and growth time of disturbances are almost independent of $Re_{\tau}$ when they are are normalized by viscous wall units. They increase with the domain height $y_{c}^{+}$. Especially, the optimal disturbance in $0