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2006 中国数学科学与教育发展论坛 如 此 饶 趣 神 奇 的 水 波 Such interesting and marvelous water waves 吴耀祖 美国加州理工学院 浙江大学数学科学研究中心2006 年 7 月 1 日 Capillary waves Gravity waves Water waves of depth h Key parameters of water waves Dispersion relations on linear theory Water particle pathlines in waters Wave packet dispersion Wave packet group dispersion Generation of ship waves Ship wave in shallower waters Ship wave pattern John Scott Russell’s 1834 chance discovery Significances of the KdV evolution equation Grand discovery of the remarkable soliton Remarkable properties of solitons Forced forward-radiation of solitons Exciting discovery of forward-radiating solitons at Wu’s Laboratory - 1982 Agreement between theory and experiment Comparison between experiment and theory Experimental and computational views of forced radiation of solitary waves Hydrodynamic instabilities of resonantly forced solitons Camassa, R. and Wu, T. Y. (1991a) Phil. Trans. R. Soc. Lond. A337, 429-466 --- (1991b) Physica D 51, 295-307 Having profound discussions with Cambridge Univerisity Lucasian Professor Sir James Lighthill Part IReflection for Insight on Solitary Waves of Arbitrary Height Wu, T. Y., Kao, J. Zhang, J. V. Acta Mech. Sinica 21 (1), 1-15, 2005 Sir G.G.Stokes (1880) on the solitary wave outskirts Stokes: This relation is exact! Reflective Queries 1. What else? 2. Can linear theory hold for low waves of diminishing amplitude? Reflections on Boussinesq-Rayleigh: Asymptotic representation: Sir G. G. Stokes (1880):  Corner wedge flow under gravity Formulation and analysis Unified intrinsic functional expansion (UIFE) theory (i) First establish a UIFE expansion for ?(?) in terms of a set of intrinsic component functions (ICF), analytic in ?, to represent all the intrinsic wave properties in the entire flow field. (ii) The unknown coefficients in the UIFE expansion are determined under the given conditions by minimizing G and B: (iii) The minimization of E2 is i