Turbulence statistics along gradient trajectories

By calculating gradient trajectories in direction of ascending and descending scalar gradients a local maximum and a local minimum point is reached. Dissipation elements may then be defined as the spatial region from which the same pair of maximum and minimum points in a scalar field is reached. By exploring the two-point correlation of the scalar gradient along such trajectories it was found that for large elements the mean velocity increment scales linearly with the arclength distance along the trajectory. This is different from the classical Kolmogorov scaling and has consequences for the modeling of the length distribution of dissipation elements.