Scale- and Structure-Dependent Fractal Dimensions in a Two-Dimensional Atomizing Liquid Jet

Fuente: arXiv
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Main Authors: Ji, Guangnian, Kulkarni, Yash, Zaleski, Stéphane
Format: Preprint
Published: 2026
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_version_ 1866915965665542144
author Ji, Guangnian
Kulkarni, Yash
Zaleski, Stéphane
author_facet Ji, Guangnian
Kulkarni, Yash
Zaleski, Stéphane
contents Atomization stretches and folds the liquid-gas interface before fragmenting it into ligaments and droplets, making fractal measures a natural descriptor of the breakup state. We examine this idea in two-dimensional volume-of-fluid direct numerical simulations, VOF-DNS, of a liquid jet with adaptive mesh refinement in Basilisk. Box counting of the full resolved interface does not yield a single scale-independent exponent. Instead, two scaling ranges appear, separated by a crossover near box-counting level Lbox about 7: coarser boxes measure the folded connected jet envelope, whereas finer boxes increasingly sample ligaments, droplets, and nearly smooth local interface segments. Decomposing the interface into detached droplets, ligaments, and the connected main body shows that the relevant effective dimension is structure dependent. Droplets remain near Euclidean at fine scales, ligaments occupy an intermediate level, and the main body carries the largest coarse-scale dimension. This hierarchy persists for liquid Reynolds numbers from 100 to 10000 at fixed gas Weber number 200. Thus, in this two-dimensional VOF-DNS setting, fractal dimension is best interpreted not as a single global exponent, but as a scale- and structure-resolved state variable for interfacial folding and breakup.
format Preprint
id arxiv_https___arxiv_org_abs_2604_26107
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Scale- and Structure-Dependent Fractal Dimensions in a Two-Dimensional Atomizing Liquid Jet
Ji, Guangnian
Kulkarni, Yash
Zaleski, Stéphane
Fluid Dynamics
76T99
J.2
Atomization stretches and folds the liquid-gas interface before fragmenting it into ligaments and droplets, making fractal measures a natural descriptor of the breakup state. We examine this idea in two-dimensional volume-of-fluid direct numerical simulations, VOF-DNS, of a liquid jet with adaptive mesh refinement in Basilisk. Box counting of the full resolved interface does not yield a single scale-independent exponent. Instead, two scaling ranges appear, separated by a crossover near box-counting level Lbox about 7: coarser boxes measure the folded connected jet envelope, whereas finer boxes increasingly sample ligaments, droplets, and nearly smooth local interface segments. Decomposing the interface into detached droplets, ligaments, and the connected main body shows that the relevant effective dimension is structure dependent. Droplets remain near Euclidean at fine scales, ligaments occupy an intermediate level, and the main body carries the largest coarse-scale dimension. This hierarchy persists for liquid Reynolds numbers from 100 to 10000 at fixed gas Weber number 200. Thus, in this two-dimensional VOF-DNS setting, fractal dimension is best interpreted not as a single global exponent, but as a scale- and structure-resolved state variable for interfacial folding and breakup.
title Scale- and Structure-Dependent Fractal Dimensions in a Two-Dimensional Atomizing Liquid Jet
topic Fluid Dynamics
76T99
J.2
url https://arxiv.org/abs/2604.26107