Characterization of tracer cascade in physical space

Geophysical turbulent fluids are characterized by the presence of organized energetic structures which control tracer transport and stirring, while enabling a tracer cascade down to the smallest scales. In order to understand the physical mechanisms involved in this turbulent tracer cascade, we focus on the dynamics underlying the formation of tracer gradients which are necessarily associated to this cascade. We show that the dynamics of tracer gradients in physical space is mainly governed by their orientation with respect to the compressional eigenvector of the strain tensor. This relative angle results from the competition between strain and the ”effective rotation” (due to both vorticity and rotation of strain axes). The implication is that tracer gradients (be they passive or active) should align with specific directions of the flow field, which depends only on the local velocity and acceleration gradient tensors in physical space. Most of the tracer stirring is thus occurring at specific locations that can be identified analytically. These results have been confirmed by direct numerical simulations and enable a better characterization of the cascade in physical space.