Relationship between the power spectral density of the Lagrangian velocity and the hierarchy of coherent vortices in turbulence

We propose a scale-decomposition method for the Lagrangian velocity that relates the hierarchy of coherent vortices to the Lagrangian properties of turbulence. Our scale-decomposition analysis reveals how vortices at different scales form the power spectral density of the Lagrangian velocity: small-scale vortices in the inertial range contribute to the spectra in a self-similar manner, whereas the contribution from the largest-scale flows exhibits non-universal behavior and can contaminate the Kolmogorov scaling.