{"paper":{"title":"Note on the stability of viscous roll-waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"physics.flu-dyn","authors_text":"Blake Barker, Kevin Zumbrun, L. Miguel Rodrigues, Mathew A. Johnson, Pascal Noble","submitted_at":"2015-10-05T14:37:10Z","abstract_excerpt":"In this note, we announce a complete classification of stability of periodic roll-wave solutions of the viscous shallow-water equations, from their onset at Froude number $F\\approx 2$ up to the infinite-Froude limit. For intermediate Froude numbers, we obtain numerically a particularly simple power-law relation between $F$ and the boundaries of the region of stable periods, that appears potentially useful in hydraulic engineering applications. In the asymptotic regime $F\\to 2$ (onset), we provide an analytic expression of the stability boundaries whereas in the limit $F\\to\\infty$, we show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01168","kind":"arxiv","version":2},"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"}