Particle trajectories in nonlinear water wave on uniform current

Hung Chu Hsu, Yang Yih Chen, Chia Yan Cheng, Wen Jer Tseng

Research output: Contribution to journalArticlepeer-review


The study in this paper is focusing on trajectories of particles in the irrotational progressive water waves coexisting with uniform current. The parametric equations of particle trajectories over a range of levels in a Lagrangian type of description are developed analytically via the Euler-Lagrange transformation. The Lagrangian wave period of particle motion differing from the Eulerian wave period and the mass transport can also be obtained directly. The third-order solution of particle trajectory exhibits that they do not move in closed orbital motion but represent a net movement that decreases exponentially with the water depth. Uniform current is found to have significant effect on the trajectories and drift velocity of gravity waves. Overall, the influence of increased uniform current is to increase the relative horizontal distance traveled by a particle, as well as the magnitude of the time-averaged drift velocity on the free surface. For adverse current cases, a reverse behavior is found. The obtained third-order solutions satisfy the irrotational condition contrasted to the Gerstner waves and are verified by reducing to those of two-dimensional gravity waves in Lagrangian coordinates.

Original languageEnglish
Pages (from-to)611-621
Number of pages11
JournalChina Ocean Engineering
Issue number4
Publication statusPublished - 2008 Dec

All Science Journal Classification (ASJC) codes

  • Oceanography
  • Renewable Energy, Sustainability and the Environment
  • Ocean Engineering
  • Mechanical Engineering


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