“…The structure and dominant dimensions associated with the autonomous, near-wall cycle of turbulence have been known since the seminal experiments of Kline et al 45 Significant study of the dynamics of the flow in this region, performed by, e.g., Waleffe, 46 Jiménez and Pinelli, 47 and Schoppa and Hussain 48 using low Reynolds number data, revealed the well-known quasi-streamwise vortex and streamwise velocity streak structure, while experiments in the atmospheric surface layer 49 have demonstrated the Reynolds number independence of the streak spacing in viscous units at the near-wall scales identified above, namely, λ + x ≈ 1000 and λ + z ≈ 100. Comparison with the structure arising from our analysis requires the specification of an additional parameter, the phase velocity, c. For the dominant wavelengths associated with the near-wall cycle, the first singular mode is critical and attached to the wall, as identified in Figure 7, when c + = 10 − 15, the minimum convection velocity associated with energetic disturbances.…”