Growth of small localized perturbations in Surface Quasi-Geostrophic turbulence
Abstract
The butterfly effect, namely the amplification of an initially localized infinitesimal perturbation, is a fundamental hallmark of chaotic systems. While this phenomenon is well understood in low-dimensional chaotic systems, its implications become more complex in spatially extended systems characterized by multiple temporal and spatial scales, such as geophysical flows. In this Letter, we investigate the butterfly effect by examining the evolution of infinitesimal localized perturbations in a minimal model of mesoscale geophysical turbulence. We find that localized perturbations exhibit highly variable dynamics, including an initial transient regime during which perturbation energy decreases while the error spectrum shifts from the injection scale toward the system's most unstable configuration. The duration of this transient regime spans a broad range and may persist for several characteristic small-scale times, depending on the perturbation's size, its initial location, and the Reynolds number.
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BibTeX
@misc{valadao2026growth,
title = {{Growth of small localized perturbations in Surface Quasi-Geostrophic turbulence}},
author = {V. J. Valadão and M. Cencini and F. De Lillo and S. Musacchio and G. Boffetta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.08244},
eprint = {2605.08244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.08244},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Growth of small localized perturbations in Surface Quasi-Geostrophic turbulence
AU - V. J. Valadão
AU - M. Cencini
AU - F. De Lillo
AU - S. Musacchio
AU - G. Boffetta
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2605.08244
UR - https://arxiv.org/abs/2605.08244
AB - The butterfly effect, namely the amplification of an initially localized infinitesimal perturbation, is a fundamental hallmark of chaotic systems. While this phenomenon is well understood in low-dimensional chaotic systems, its implications become more complex in spatially extended systems characterized by multiple temporal and spatial scales, such as geophysical flows. In this Letter, we investigate the butterfly effect by examining the evolution of infinitesimal localized perturbations in a minimal model of mesoscale geophysical turbulence. We find that localized perturbations exhibit highly variable dynamics, including an initial transient regime during which perturbation energy decreases while the error spectrum shifts from the injection scale toward the system's most unstable configuration. The duration of this transient regime spans a broad range and may persist for several characteristic small-scale times, depending on the perturbation's size, its initial location, and the Reynolds number.
ER -