Mode-2 solitary waves in continuous stratifications
Abstract
Computed herein are examples of mode-2 internal solitary waves to the Dubreil-Jacotin-Long (DJL) equation. These are localised, fully nonlinear waves in a continuously stratified, inviscid fluid under the Boussinesq and rigid-lid approximations. The equation is solved directly using finite differences on a periodic domain, enabling the computation of both generalised solitary waves, which possess oscillatory mode-1 tails, and embedded solitary waves, whose tails vanish. Two stratifications are considered. The first is a double pycnocline, generalising the three-layer system considered by Doak et al. (2022) by replacing each infinitesimal interface with a pycnocline of finite thickness. The second stratification, a surface mixed layer above an exponentially stratified layer, shows that embedded mode-2 solitary waves are not restricted to double-pycnocline stratifications. These are the first mode-2 solitary waves of the DJL equation computed for stratifications that are asymmetric about mid-depth.
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BibTeX
@misc{doak2026mode2,
title = {{Mode-2 solitary waves in continuous stratifications}},
author = {Alex Doak and Ricardo Barros and Paul l A. Milewski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37289},
eprint = {2610.37289},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37289},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mode-2 solitary waves in continuous stratifications
AU - Alex Doak
AU - Ricardo Barros
AU - Paul l A. Milewski
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37289
UR - https://arxiv.org/abs/2610.37289
AB - Computed herein are examples of mode-2 internal solitary waves to the Dubreil-Jacotin-Long (DJL) equation. These are localised, fully nonlinear waves in a continuously stratified, inviscid fluid under the Boussinesq and rigid-lid approximations. The equation is solved directly using finite differences on a periodic domain, enabling the computation of both generalised solitary waves, which possess oscillatory mode-1 tails, and embedded solitary waves, whose tails vanish. Two stratifications are considered. The first is a double pycnocline, generalising the three-layer system considered by Doak et al. (2022) by replacing each infinitesimal interface with a pycnocline of finite thickness. The second stratification, a surface mixed layer above an exponentially stratified layer, shows that embedded mode-2 solitary waves are not restricted to double-pycnocline stratifications. These are the first mode-2 solitary waves of the DJL equation computed for stratifications that are asymmetric about mid-depth.
ER -