Lagrangian motion of fluid particles in gravity–capillary standing waves

Hung Chu Hsu, Meng Syue Li

Research output: Contribution to journalArticlepeer-review


A third-order analytical solution for the gravity–capillary standing wave is derived in Lagrangian coordinates through the Lindstedt–Poincare perturbation method. By numerical computation, the dynamical properties of nonlinear standing waves with surface tension in finite water depth, including particle trajectory and surface profile are investigated. We find that the presence of surface tension leads to a change of the crest form. Moreover, we also find that the particle trajectories near the surface oscillate back and forth along the arcs which will change from concave to convex as the inverse Bond number increases. There is no mass transport of the particles in a wave period.

Original languageEnglish
Article number103186
JournalNonlinear Analysis: Real World Applications
Publication statusPublished - 2021 Feb

All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics


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