Study on the Curvature of Lagrangian Trajectories in Thermal Counterflow

Abstract

Small particle trajectories are visualized in thermal counterflow using the particle tracking velocimetry technique, and the curvature of two-dimensional Lagrangian trajectories are studied. It is found that the probability density function of the curvature demonstrates a power-law tail similar to that of classical turbulence. The curvature distribution is classified into three regions with high, medium, and low values, and the particle velocity is averaged in each region. Furthermore, the particle velocity in the low curvature region clearly shows a bimodal distribution and agrees with the two-fluid model in the case of low heat flux. However, in the high curvature region, the particle velocity deviates from the theoretical value and exhibits a Gaussian distribution. We understand from the visualized particle trajectories that the high curvature region corresponds to a complex trajectory that interacts with a quantum vortex, but the low curvature region indicates an almost straight line.