{"paper":{"title":"Stability of Fully Nonlinear Stokes Waves on Deep Water: Part 1. Perturbation Theory","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"David L. Ross, Shahrdad G. Sajjadi","submitted_at":"2017-04-22T22:38:41Z","abstract_excerpt":"We consider a full set of harmonics for the Stokes wave in deep water in the absence of viscosity, and examine the role that higher harmonics play in modifying the classical Benjamin-Feir instability. Using a representation of the wave coefficients due to Wilton, a perturbation analysis shows that the Stokes wave may become unbounded due to interactions between the $N^{th}$ harmonic of the primary wave train and a set of harmonics of a disturbance. If the frequency of the $n^{th}$ harmonic is denoted $ \\omega _{n} =\\omega \\left( {1 \\pm \\delta } \\right)$ then instability will occur if $$ 0<\\del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07778","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}