Eulerian and Lagrangian statistics from particle tracking data

Jakob Mann and Søren Ott
Wind Energy Department, Risø National Laboratory, Denmark

Several hundreds flow-following particles are tracked with video cameras in approximately homogeneous and isotropic turbulence generated between oscillating grids. From these data several interesting statistical properties of turbulence can be inferred. The mean square separation of particles initially located close to each other will, according to Richardson and Obukhov, increase as C t3, where is the energy dissipation, as long as the separation is smaller than the integral scale. The constant C is determined to be approximately 0.5. Theoretical predictions of C range from 0.01 (from kinematic simulation) to more than 5 (Kraichnan). We attempt to explain why kinematic simulation gives a too small C. The spatio-temporal Eulerian velocity correlation RE(x,t) is compared to models, and the Corrsin hypothesis relating this to the Lagrangian autocorrelation function RL(t) is tested.