Line Dispersion in Homogeneous Turbulence: Stretching, Fractal Dimensions, and Micromixing

Motivated by the understanding of the turbulent mixing mechanisms at small scale, the time evolution of an initially regular passive scalar pattern in three-dimensional homogeneous turbulence is investigated in a line-dispresion experiment. The major observation is the increasing space-fillingness of the line as time elapses. It is shown that the evolution of the fractal dimension $d_f\mathrm{}\left(t\right)\mathrm{}$ of the support of the line can be related to the mean-field Kolmogorov scaling of velocity differences incorporating dissipative corrections and an expression for $d_f\mathrm{}\left(t\right)\mathrm{}$ is derived that compares very well with the experiments for several distinct Reynolds numbers. Following, a criterion of micromixing is discussed.