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 $Re_λ=400$. Both the energy dissipation rate $ε$ and the local time averaged $ε_τ$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $ρ(τ)$ of $\ln(ε(t))$ and variance $σ^2(τ)$ of $\ln(ε_τ(t))$ obey a log-law with scaling exponent $β'=β=0.30$ compatible with the intermittency parameter $μ=0.30$. The $q$th-order moment of $ε_τ$ has a clear power-law on the inertial range $10<τ/τ_η<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-ζ_L(2q)$ where $ζ_L(2q)$ 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.

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