Numerical study of Lagrangian velocity structure functions from a spatial-temporal perspective

Lagrangian intermittency in turbulence is generally known to be stronger than its Eulerian counterpart, but the underlying physical mechanisms are not as well understood. A fundamental quantity for both physical understanding and modeling is the Lagrangian velocity increment $Delta_ au{mathbf u}(t)={mathbf u}^+(t+ au)-{mathbf u}^+(t)$, which is the difference between velocity fluctuations recorded at different time instants and different locations in space based on the instantaneous particle position. In this talk we discuss some physical insights that can be obtained by decomposing this increment into temporal and (randomized) spatial contributions, which bears resemblance to strong mutual cancellation between local and convective accelerations in the small $ au$ limit. The correlation between the temporal and spatial relative velocities plays an important role in the second order Lagrangian structure function, which appears to approach inertial range scaling at a time lag in less than 10 Kolmogorov time scales. A DNS code that scales extremely well with respect to particle count has been used to obtain results in isotropic turbulence at Taylor-scale Reynolds number exceeding 1000.