Transient growth of optimal disturbances with a turbulent mean velocity profile in a channel is investigated for Reynolds numbers, based on the wall-shear velocity and channel half height, of ${\mathrm{Re}}_{\tau }=180\sim 10000$. We consider optimal disturbances within near-wall regions ($0<y^{+}\le y_c^{+}$) by suppressing disturbances at $y^{+}>y_c^{+}$. The most amplified disturbances are streamwise velocity streaks induced by streamwise rolls. The wavelength and the growth time of these constrained optimal disturbances normalized in viscous wall units are nearly independent of ${\mathrm{Re}}_{\tau }$ but depend on the cutoff location $y_c^{+}$. The optimal disturbance corresponding to the cutoff location $y_c^{+}=40$, which is roughly the edge of the buffer layer, shows very similar characteristics to those of near-wall turbulence structures observed in turbulent channel flows, thus suggesting that the commonly observed turbulence structures are indeed the optimal disturbance within the buffer layer. The choice of this particular cutoff location, $y_c^{+}=40$, is justified from consideration of the shear rate parameter, $S^{*}=S{q}^2/\epsilon$, which is a measure of whether nonlinearity of turbulence can be neglected.

• Received 29 January 2016
• Revised 29 August 2016

DOI:https://doi.org/10.1103/PhysRevFluids.1.074403