Stretching and tilting of material lines in turbulence: The effect of strain and vorticity

The Lagrangian evolution of infinitesimal material lines is investigated experimentally through three dimensional particle tracking velocimetry (3D-PTV) in quasihomogeneous turbulence with the Taylor microscale Reynolds number Reλ =50. Through 3D-PTV we access the full tensor of velocity derivatives ui' xj along particle trajectories, which is necessary to monitor the Lagrangian evolution of infinitesimal material lines l. By integrating the effect on l of (i) the tensor ui xj, (ii) its symmetric part sij, (iii) its antisymmetric part rij, along particle trajectories, we study the evolution of three sets of material lines driven by a genuine turbulent flow, by "strain only," or by "vorticity only," respectively. We observe that, statistically, vorticity reduces the stretching rate li lj sij l2, altering (by tilting material lines) the preferential orientation between l and the first (stretching) eigenvector λ1 of the rate of strain tensor. In contrast, sij, in "absence" of vorticity, significantly contributes to both tilting and stretching, resulting in an enhanced stretching rate compared to the case of material lines driven by the full tensor ui xj. The same trend is observed for the deformation of material volumes.