Using analogues to investigate error growth and predictability in turbulence
Abstract
In this study, we revisit Lorenz’s pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, we successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. Our analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. We interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. These findings not only validate Lorenz’s qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events.
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BibTeX
@misc{granerobelinchon2026using,
title = {{Using analogues to investigate error growth and predictability in turbulence}},
author = {Carlos Granero-Belinchon and Mickaël Bourgoin and Bérengère Dubrulle},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11796},
eprint = {2610.11796},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05785573v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Using analogues to investigate error growth and predictability in turbulence
AU - Carlos Granero-Belinchon
AU - Mickaël Bourgoin
AU - Bérengère Dubrulle
PY - 2026
DA - 2026/10/08
PB - HAL
DO - 10.48550/arxiv.2610.11796
UR - https://hal.science/hal-05785573v1
AB - In this study, we revisit Lorenz’s pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, we successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. Our analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. We interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. These findings not only validate Lorenz’s qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events.
ER -