Revisiting streak reorientation in a turbulent channel flow subjected to spanwise oscillating walls

Streaks, existing as a distinct feature of wall turbulence, are closely related to the generation of friction drag. Quantifying and modeling the streak behaviors in controlled wall turbulence is fundamentally important for revealing the mechanism of drag reduction and advancing our understanding of the underlying physics. This paper reports a comprehensive investigation of the streak orientation in a turbulent channel flow subjected to spanwise oscillatory walls. An effective technique is developed to recognize the phase-averaged inclination angles of streaks from wall-parallel slices. The tangent of the streak angle, treated as a response signal driven by wall oscillation, is represented by a cosine function with a certain amplitude and relative phase. Two control parameters of the wall motion, including the maximum wall velocity (W m) and the activation period (T_a), are considered as influencing factors. The saturated response for sufficiently large T_a is discussed and explained based on the perspective of relative motion. Relations between the streak angle and various phase-averaged quantities are revealed. More importantly, it is found that the amplitude of the streak angle follows a univariate function of (Formula presented) for the near-wall region and (Formula presented) for the off-wall region. These two scalings reflect the dynamical self-similarity of the streak-angle response, which can be explained by dimensional analysis. A novel model, termed the window-averaged response model, is proposed to predict the streak-angle response based on the phase-averaged velocity profiles. The model works very well in predicting the streak-angle response for the near-wall region.