Lagrangian Cascade in Three-Dimensional Homogeneous and Isotropic Turbulence

Abstract

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 $R{e}_{\lambda }=400$. 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 ${\beta }^{\prime }=\beta =0.30$ 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.

10 pages with 7 figures accepted for Journal of Fluid Mechanics as Rapids

References in corpus (5)

• Multifractal statistics of Lagrangian velocity and acceleration in turbulence
• Lagrangian dynamics and statistical geometric structure of turbulence
• Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
• Second order structure function in fully developed turbulence
• A causal multifractal stochastic equation and its statistical properties

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