{"title":"Gravity Water Waves over Constant Vorticity Flows: From Laminar Flows to Touching Waves.","authors":"Francisco Gonçalves","doi":"10.1007/s42286-025-00127-4","DOIUrl":"https://doi.org/10.1007/s42286-025-00127-4","url":null,"abstract":"<p><p>In a recent paper, Hur and Wheeler (J Fluid Mech 896:1, 2020) proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow under the influence of gravity. These solutions include overhanging wave profiles, some of which exhibit surfaces that touch at a point and thereby enclose a bubble of air. We extend these results by formulating a problem that encompasses both infinitely deep and finitely deep flows, and by proving the existence of a continuous curve of water waves that connects a laminar flow to a touching wave for fixed, nonzero gravity. This implies the existence of a wave profile featuring a vertical tangent at a point, which is not overhanging, and is referred to as a breaking wave. We also study the behavior of critical layers, which are points where the horizontal velocity vanishes, near the surface. In particular, this result holds for arbitrary vorticity.</p>","PeriodicalId":520532,"journal":{"name":"Water waves (Cham, Switzerland)","volume":"8 1","pages":"1-19"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13135555/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147848880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Steady Periodic Hydroelastic Waves in Polar Regions.","authors":"Bogdan-Vasile Matioc, Emilian I Părău","doi":"10.1007/s42286-024-00095-1","DOIUrl":"10.1007/s42286-024-00095-1","url":null,"abstract":"<p><p>We construct two-dimensional steady periodic hydroelastic waves with vorticity that propagate on water of finite depth under a deformable floating elastic plate which is modeled by using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis. This is achieved by providing a necessary and sufficient condition for local bifurcation from the trivial branch of laminar flow solutions.</p>","PeriodicalId":520532,"journal":{"name":"Water waves (Cham, Switzerland)","volume":"7 2","pages":"363-387"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12174212/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144334778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effect of Real-World Perturbations on Wave Breaking due to a Sharp-Crested Superharmonic Instability.","authors":"A Mansar, M R Turner, T J Bridges, F Dias","doi":"10.1007/s42286-025-00116-7","DOIUrl":"https://doi.org/10.1007/s42286-025-00116-7","url":null,"abstract":"<p><p>The mechanism for the emergence of breaking water waves in deep water, based on the superharmonic instability of periodic Stokes waves, is tested for the effect of real-world perturbations (dissipation, approximation error, changes in depth, non-zero air density, fluctuations in wave and frame speed). An implicit perturbation is added to a large-amplitude unstable Stokes wave, which is then taken as initial data in a direct numerical solution of the Navier-Stokes equations, using the Basilisk numerical software package. An SVD-based filtering algorithm is used to extract the shape of the unstable wave that grows on the background Stokes wave. We find a dipole shape in the filtered wave that correlates with the superharmonic unstable mode. Our findings show that the inclusion of real-world effects has little qualitative effect, when they are kept small, on the emergence of breaking. We conclude that the mechanism of crest instability of Stokes waves leading to wave breaking is a robust mechanism that is likely to occur in nature.</p>","PeriodicalId":520532,"journal":{"name":"Water waves (Cham, Switzerland)","volume":"7 1","pages":"159-198"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11980429/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144032656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}