Multiple self-similar crossovers in a hydrodynamic interface
Abstract
Self-similar dynamics are often described in terms of a single asymptotic scaling regime. Here we experimentally investigate the post-breakup recovery of a hydrodynamic interface over substantially wider temporal and spatial ranges than previously accessible. Beyond the previously identified scaling behavior, we find four successive self-similar regimes characterized by the Rβ-scaling with β=1/6, 1/2, 1, and 2, connected by three distinct crossovers. All four regimes exhibit robust collapse near the interface tip, while geometrical dependence becomes detectable farther from the singular region. This systematic variation across space and scaling regimes is consistent with scale separation and enhanced universality closer to the breakup singularity. The characteristic scales associated with the different Rβ-scalings become comparable at the common geometric scale zm ≃ R. These findings demonstrate that self-similar dynamics can undergo multiple successive crossovers among distinct scaling regimes rather than directly approaching a single asymptotic self-similar state.
Related
- Critical collapse remains discretely self-similar at large D
- Self-similar imploding solutions of the 1D compressible Euler equations with a far field cutoff
- Self-similar Worthington jets
- Anomalous response, re-emerging localization-transition and robust corner sates in self-similar peano fractal
- Polyakov backreaction in large D discretely self-similar collapse
BibTeX
@misc{gu2026multiple,
title = {{Multiple self-similar crossovers in a hydrodynamic interface}},
author = {Wanjing Gu and Ko Okumura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28849},
eprint = {2609.28849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28849},
}
RIS
TY - UNPB
TI - Multiple self-similar crossovers in a hydrodynamic interface
AU - Wanjing Gu
AU - Ko Okumura
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28849
UR - https://arxiv.org/abs/2609.28849
AB - Self-similar dynamics are often described in terms of a single asymptotic scaling regime. Here we experimentally investigate the post-breakup recovery of a hydrodynamic interface over substantially wider temporal and spatial ranges than previously accessible. Beyond the previously identified scaling behavior, we find four successive self-similar regimes characterized by the R_β-scaling with β=1/6, 1/2, 1, and 2, connected by three distinct crossovers. All four regimes exhibit robust collapse near the interface tip, while geometrical dependence becomes detectable farther from the singular region. This systematic variation across space and scaling regimes is consistent with scale separation and enhanced universality closer to the breakup singularity. The characteristic scales associated with the different R_β-scalings become comparable at the common geometric scale z_m ≃ R. These findings demonstrate that self-similar dynamics can undergo multiple successive crossovers among distinct scaling regimes rather than directly approaching a single asymptotic self-similar state.
ER -