{"paper":{"title":"On the kurtosis of deep-water gravity waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Francesco Fedele","submitted_at":"2014-12-28T23:44:25Z","abstract_excerpt":"In this paper, we revisit Janssen's (2003) formulation for the dynamic excess kurtosis of weakly nonlinear gravity waves at deep water. For narrowband directional spectra, the formulation is given by a sixfold integral that depends upon the Benjamin-Feir index and the parameter $R=\\sigma_{\\theta}^{2}/2\\nu^{2}$, a measure of short-crestedness for the dominant waves with $\\nu$ and $\\sigma_{\\theta}$} denoting spectral bandwidth and angular spreading. Our refinement leads to a new analytical solution for the dynamic kurtosis of narrowband directional waves described with a Gaussian type spectrum. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8231","kind":"arxiv","version":3},"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"}