Measurements of the structure of the Reynolds stress in a turbulent boundary layer

TLDR

It is suggested that many features of the fluctuating flow revealed by the measurements may be explained by convection past the measuring station of an evolving deterministic flow pattern such as the hairpin vorticity model of Willmarth & Tu (1967). The study uses the velocity at the edge of the viscous sublayer as a detector signal for bursts and sweeps, with the uv signal from an X‑wire probe conditionally sampled and sorted into four quadrants of the u, v plane. The experiments show that bursts occur when the edge‑sublayer velocity decreases, sweeps when it increases, and both have equal convection speeds (about 0.8 of the local mean velocity and 0.425 of free‑stream at y≈0.15δ*), bursts dominate the Reynolds stress, mean time intervals are constant across the layer, and their scaling with outer‑flow variables is confirmed.

Abstract

Additional experimental studies of the structure of Reynolds stress which supplement our previous work (Willmarth & Lu 1971) are reported. The velocity at the edge of the viscous sublayer is again used as a detector signal for bursts and sweeps. The signal uv obtained from an X-wire probe at various locations is conditionally sampled and sorted into four quadrants of the u, v plane. Using this method it is found that, when the velocity uw at the edge of the viscous sublayer becomes low and decreasing, a burst occurs. On the other hand, a sweep occurs when uw becomes large and increasing. The convection speeds of the bursts and the sweeps are found to be equal and are about 0·8 times the local mean velocity and 0·425 times the free-stream velocity at a distance y ≈ 0·15δ* from the wall (δ* is the displacement thickness). Throughout the turbulent boundary layer, the bursts are the largest contributors to from different events. Both mean time intervals are approximately equal and constant for most of the turbulent boundary layer. The scaling of the mean time interval between bursts with outer flow variables is confirmed. It is suggested that many of the features of the fluctuating flow revealed by the measurements may be explained by convection past the measuring station of an evolving deterministic flow pattern such as the hairpin vorticity model of Willmarth & Tu (1967).