A study of the spatiotemporal structure of a turbulent boundary layer measured by the use of two hot-wire probes (Velocity time series patterns and Kolmogorov's structure function)

Abstract

The streamwise velocity at two points in a turbulent boundary layer under zero pressure gradient was measured using two hot-wire probes separated in the wall-normal direction. The time trace of the fluctuating velocity difference, probability density function, fluctuating vorticity, structure function, and the spatial correlation coefficient was obtained. First, the physical importance of structure functions was explained in some detail. Then, the results of the measurements were considered. When the spatial separation between two points is small, the fluctuating velocity difference decreases monotonically as the two points move away from the wall. On the other hand, as the spatial separation increases, the similarity between the two fluctuating velocities decreases. In addition, the fluctuating velocity at the nearer point from the wall becomes dominant. When moving away from the wall, the fluctuating velocity difference first increases, then reaches a maximum, and finally decreases. When both positions are within the logarithmic region or defect region, the velocity difference is made between similar fluctuating velocities. Hence, the probability density function distribution shape is symmetrical with respect to positive and negative values, close to the Gaussian distribution. The fluctuating vorticity decreases monotonically as it moves away from the wall, regardless of the spatial separation. The structure function increases as the separation increases. Away from the wall, the length over which the correlation is maintained increases, resulting in a large eddy.

Keywords

• boundary layer
• turbulence
• structure function
• spatial correlation
• spatiotemporal structure
• two-point velocity difference