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 Re_λ=50. Through 3D-PTV we access the full tensor of velocity derivatives ∂u_i∕∂x_j 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 ∂u_i∕∂x_j, (ii) its symmetric part s_ij, (iii) its antisymmetric part r_ij, 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 l_il_js_ij∕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, s_ij, 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 ∂u_i∕∂x_j. The same trend is observed for the deformation of material volumes.