The Patterns of Surface Capillary-gravity Short-crested Waves with Uniform Current Fields in Coastal Waters

A fully three-dimensional surface gravity-capillary short-crested wave system is studied as two progressive wave-trains of equal amplitude and frequency, which are collinear with uniform currents and doubly-periodic in the horizontal plane, are propagating at an angle to each other. The first- and second-order asymptotic analytical solutions of the short-crested wave system are obtained via a perturbation expansion in a small parameter associated with the wave steepness, therefore depicting a series of typical three-dimensional wave patterns involving currents, shallow and deep water, and surface capillary waves, and comparing them with each other.The project supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (200428), the National Natural Science Foundation of China (10272072 and 50424913), the Shanghai Natural Science Foundation (05ZR14048), and the Shanghai Leading Academic Discipline Project (Y0103). The English text was polished by Yunming Chen.