Streamlines in stationary homogeneous isotropic turbulence and fractal-generated turbulence

We compare streamline statistics in stationary homogeneous isotropic turbulence and in turbulence generated by a fractal square grid. We examine streamline segments characterised by the velocity difference u D and the distance l between extremum points. We find close agreement between the stationary homogeneous isotropic turbulence and the decay region of the fractal-generated turbulence as well as the production region of the fractal flow for small segments. The statistics of larger segments are very similar for the isotropic turbulence and the decay region, but differ for the production region. Specifically, we examine the first, second and third conditional mean u l n ⟨[ ] ∣ ⟩ D . Noticeably, non-vanishing u l n ⟨[ ] ∣ ⟩ D for n 1, 3 = are due to an asymmetry of positive and negative segments, i.e. those for which u 0 D > and u 0 D < , respectively. This asymmetry is not only kinematic, but is also due to dissipative effects and therefore u l n ⟨[ ] ∣ ⟩ D contains cascade information.