Convection velocity in high Reynolds number pipe flow

The convection velocity is an important topic in turbulence research, particularly in the context of Taylor’s frozen turbulence hypothesis. This hypothesis assumes that the convection velocity is equal to the local mean velocity. However, in many of flow field-including wall-bounded flows-this assumption does not hold. In the wall-bounded flow, while the convection velocity generally agrees with the local mean velocity in the outer region, it tends to be larger than the mean velocity near the wall (e.g. del Álamo and Jiménez, 2009). These observations, however, have been made primarily at low Reynolds numbers, and there has been no quantitative experimental investigation of the convection velocity scaling in wall-bounded flows at high Reynolds number. In this study, we experimentally investigate the convection velocity in high-Reynolds-number turbulent pipe flow. The experiments were conducted using the high Reynolds number flow facility (Hi-Reff). The convection velocity was determined from two-point correlations using two laser Doppler velocimetry (LDV). The Reynolds number based on friction velocity ranged from Re_τ=3000 to 20800, and profiles were obtained from y/R=0.002 up to the pipe center, where R is the pipe radius.

The measured convection velocity profile shows good agreement with the local mean velocity from the outer part of the logarithmic region to the pipe center. Closer to the wall, the convection velocity becomes nearly constant and exceeds the local mean. This profile exhibits clear inner scaling with respect to the wall-normal coordinate y⁺ and streamwise separation Δx⁺ between the two LDVs. Furthermore, we investigate the scale dependence of the convection. Previous studies have reported that the convection velocity of large-scale structures is faster than that of smaller ones. In this context, the convection velocity of very large-scale motions (VLSMs)- which become prominent at high Reynolds numbers and is identified only via spectral analysis in previous studies (e.g. Ono et al., 2025)- is of particular interest. In this study, we extract the VLSM convection velocity using scale-separated velocity fluctuations and find that it scales well with the bulk velocity U_b​, with a value around 0.85 U_b​.