PhD Seminar Series: “How universal are Lagrangian statistics of turbulence? Insights from the hierarchy of coherent vortices” & “Forgetful turbulent energy cascade”

How universal are the Lagrangian properties of turbulence? From the Eulerian viewpoint, the energy spectrum, once normalized by the kinematic viscosity and the energy dissipation rate, collapses onto a single curve regardless of the method used to drive turbulence. The power spectral density of the Lagrangian velocity has also been reported to follow the Kolmogorov scaling within the Lagrangian inertial range. However, its universality and formation mechanism remain unclear.

To answer this question, we investigate the Lagrangian spectrum for turbulent flows with different Reynolds numbers and forcing methods using direct numerical simulations. This systematic comparison demonstrates that universal behavior is confined to a narrow high-frequency regime, whereas nonuniversality depending on the forcing method appears broadly in a low-frequency regime.

To identify the physical origin of these features, 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 spectrum in a self-similar manner, whereas the contribution from the largest-scale flows exhibits nonuniversal behavior and can contaminate the Kolmogorov scaling. These findings provide a perspective for interpreting experimental and numerical data on Lagrangian statistics based on the hierarchy of coherent vortices with different length scales.