南京大学学报（自然科学版）2025，Vol.61Issue(5)：816-828,13.DOI:10.13232/j.cnki.jnju.2025.05.010
圆锥底容器中多边形法拉第水波模式及其特性
Polygonal patterns and their characteristics in vertically vibrating vessels of water with conical bottoms
摘要
Abstract
In the recent research at our laboratory,Faraday waves on liquid layers of concave bottoms were observed to manifest themselves as some polygonal patterns.More importantly,these shallow-water gravity waves were found to be analogous to the collective excitations in Bose-Einstein condensates.In that research,the water containers employed had the geometries of smooth bottom profiles,typically of the paraboloidal ones.The present work extends the investigation to the geometries of conical bottom shapes,specifically examining how the non-smoothness at the cone apex impacts the polygonal patterns and associated wave characteristics.It is observed that accompanying a pure angular-mode excitation is a"central breathing",a radially symmetric vertical oscillation with a period exactly half that of the angular mode.This phenomenon is caused by the effect of the non-smooth conical apex on the polygonal patterns,further indicating the importance of the geometric constraint on the pattern formation.Also observed are other interesting phenomena including the polygonal patterns of even higher orders,mode competition,and radial-angular hybrid modes.By combining the numerical solutions to the mild-slope equation with numerical simulations and experimental observations,this study then elucidates the regulatory mechanisms of cone angle and water depth on modal eigenfrequencies,damping coefficients,and stability.These findings have deepened our understanding of the impacts of bottom topography on nonlinear shallow-water gravity waves.关键词
多边形模式/本征频率/浅水重力波/法拉第共振/非线性波Key words
polygonal patterns/eigenfrequency/shallow-water gravity waves/Faraday resonance/nonlinear waves分类
数理科学引用本文复制引用
陈心雨,沈宇飞,王新龙..圆锥底容器中多边形法拉第水波模式及其特性[J].南京大学学报（自然科学版）,2025,61(5):816-828,13.基金项目
国家自然科学基金(12174191) （12174191）
