Lagrangian Cascade in Three-Dimensional Homogeneous and Isotropic Turbulence

In this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high resolution direct numerical simulation with $Re_{lambda}=400$. Both the energy dissipation rate $epsilon$ and the local time averaged $epsilon_{tau}$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $rho(tau)$ of $ln(epsilon(t))$ and variance $sigma^2(tau)$ of $ln(epsilon_{tau}(t))$ obey a log-law with scaling exponent $beta=beta=0.30$ compatible with the intermittency parameter $mu=0.30$. The $q$th-order moment of $epsilon_{tau}$ has a clear power-law on the inertial range $10<tau/tau_{eta}<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-zeta_L(2q)$ where $zeta_L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.