Acceleration of Lagrangian Particles in Shell Models of Turbulence

TL;DR

This paper demonstrates that the multifractal model can accurately predict extreme acceleration fluctuations in turbulence, even without vortex structures, across various Reynolds numbers.

Contribution

It extends the multifractal framework to shell models of turbulence, showing its effectiveness without the presence of vortical structures.

Findings

Multifractal model predicts acceleration fluctuations accurately.

Shell models without vortical structures still show intermittent acceleration.

Model remains robust across different Reynolds numbers.

Abstract

Lagrangian acceleration has been investigated both experimentally and numerically in the past, and it has been shown to exhibit extreme fluctuations, which have been rationalized as events in which tracer particles get trapped into vortical structures such as vortex tubes or filaments. Here, we consider the statistics of acceleration within the multifractal framework, as in Biferale et al. Phys. Rev. Lett. 93 064502 (2004), and investigate the statistics of Lagrangian acceleration using shell models of turbulence, as in G. Boffetta et al. Phys. Rev. E 66, 066307 (2002), that -- by construction -- do not contain vortical structures. Our analysis shows that, even in the absence of coherent vortex structures, the multifractal model accurately captures the extreme intermittent fluctuations observed in the acceleration, with predictions that remain robust across a wide range of Reynolds numbers.