Partially reflected waves in water of finite depth

Meng-Syue Li, Hung-Chu Hsu, Yang-Yih Chen, Qingping Zou

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
24 Downloads (Pure)


This paper presents a second-order asymptotic solution in the Lagrangian description for nonlinear partial standing wave in the finite water depth. The asymptotic solution that is uniformly valid satisfies the irrotationality condition and zero pressure at the free surface. In the Lagrangian approximation, the explicit nonlinear parametric equations for the particle trajectories are obtained. In particular, the Lagrangian mean level of a particle motion for the partial standing wave is found as a part of the solution which is different from that in an Eulerian system. This solution enables the description of wave profile and particle trajectory, which can be progressive, standing or partial standing waves. The dynamic properties of nonlinear partial standing waves, including mass transport velocity, radiation stress, wave setup and pressure due to reflection are also investigated.
Original languageEnglish
Article number103272
JournalNonlinear Analysis: Real World Applications
Early online date5 Dec 2020
Publication statusPublished - Jun 2021


  • Lagrangian
  • Nonlinear waves
  • Partial standing wave
  • Particle trajectory

ASJC Scopus subject areas

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


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