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Hydroelastic waves near shear flows
Abstract
In this paper, we prove that symmetric, doubly-periodic, three-dimensional hydroelastic waves of small amplitude, bifurcating from a non-uniform shear flow, are necessarily two-dimensional to leading order. A detailed analysis of the solvability condition at quadratic order reveals that all Fourier coefficients with transverse dependence vanish identically. The dimensional reduction is controlled entirely by the vertical structure of the shear flow and is robust under changes to the dynamic boundary condition.
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BibTeX
@misc{li2026hydroelastic,
title = {{Hydroelastic waves near shear flows}},
author = {Jian Li and Shaojie Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21778},
eprint = {2609.21778},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21778},
}
RIS
TY - UNPB
TI - Hydroelastic waves near shear flows
AU - Jian Li
AU - Shaojie Yang
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21778
UR - https://arxiv.org/abs/2609.21778
AB - In this paper, we prove that symmetric, doubly-periodic, three-dimensional hydroelastic waves of small amplitude, bifurcating from a non-uniform shear flow, are necessarily two-dimensional to leading order. A detailed analysis of the solvability condition at quadratic order reveals that all Fourier coefficients with transverse dependence vanish identically. The dimensional reduction is controlled entirely by the vertical structure of the shear flow and is robust under changes to the dynamic boundary condition.
ER -