Development of a Linear Mode in a Turbulent Boundary Layer

Abstract

An extraction method with an initial disturbance and an ensemble-average technique has been applied in order to investigate a coherent structure in a turbulent boundary layer. A linear mode is extracted from velocity data obtained with a hot-wire anemometer by the ensemble average based on the phase of the initial disturbance. A spatiotemporal diagram of the extracted structure clearly shows that the head of the elongated structure lifts away from the wall. This property and the dimensions of the structure are very similar to a hairpin vortex observed in wall-bounded shear flows. The structure of the linear mode is well-scaled by wall units and the dependence of the linear mode on the Reynolds number is very weak. Although the streamwise length is proportional to a period of the initial disturbance as a matter of course, the low-frequency initial disturbance makes the linear mode develop slightly slower than the high-frequency mode. These weak dependences of the initial disturbance frequency and Reynolds number suggest that the linear mode generated by the point-like disturbance is robust against the circumstances.