Parasitic capillary waves on small-amplitude gravity waves with a linear shear current

Sunao Murashige, Wooyoung Choi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

Original languageEnglish (US)
Article number1217
JournalJournal of Marine Science and Engineering
Issue number11
StatePublished - Nov 2021

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Water Science and Technology
  • Ocean Engineering


  • Conformal mapping
  • Fully nonlinear computation
  • Gravity-capillary waves
  • Shear current
  • Water waves


Dive into the research topics of 'Parasitic capillary waves on small-amplitude gravity waves with a linear shear current'. Together they form a unique fingerprint.

Cite this