On the vorticity threshold for steady water waves

[2404.04523] On the vorticity threshold for steady water waves Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2404.04523 (math) [Submitted on 6 Apr 2024 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: On the vorticity threshold for steady water waves Authors: Evgeniy Lokharu , Miles H. Wheeler View a PDF of the paper titled On the vorticity threshold for steady water waves, by Evgeniy Lokharu and Miles H. Wheeler View PDF HTML (experimental) Abstract: One of the most striking features of two-dimensional steady water waves with adverse vorticity is the emergence of stagnation points in the flow, even along branches of solutions that are initially unidirectional. In this paper we show that, for constant adverse vorticity above a certain explicit threshold, the first stagnation point must appear on the bed directly below the crest. This is in contrast to waves with favourable or even small adverse vorticity, where it is known that bottom stagnation cannot occur, leading to extreme waves exhibiting surface singularities. We also establish several related inequalities for unidirectional waves with strong adverse vorticity, including a new upper bound on the amplitude. Subjects: Analysis of PDEs (math.AP) ; Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2404.04523 [math.AP] (or arXiv:2404.04523v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2404.04523 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Evgeniy Lokharu [ view email ] [v1] Sat, 6 Apr 2024 06:46:19 UTC (12 KB) [v2] Sat, 15 Aug 2026 11:08:30 UTC (119 KB) Full-text links: Access Paper: View a PDF of the paper titled On the vorticity threshold for steady water waves, by Evgeniy Lokharu and Miles H. Wheeler View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2024-04 Change to browse by: math physics physics.flu-dyn References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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