Nonlinear concentric water waves of moderate amplitude

Nerijus Sidorovas, Dmitri Tseluiko, Wooyoung Choi, Karima Khusnutdinova

Research output: Contribution to journalArticlepeer-review


We consider the outward-propagating nonlinear concentric water waves within the scope of the 2D Boussinesq system. The problem is axisymmetric, and we derive the slow radius versions of the cylindrical Korteweg - de Vries (cKdV) and extended cKdV (ecKdV) models. Numerical runs are initially performed using the full axisymmetric Boussinesq system. At some distance away from the origin, we use the numerical solution of the Boussinesq system as the “initial condition” for the derived cKdV and ecKdV models. We then compare the evolution of the waves as described by both reduced models and the direct numerical simulations of the axisymmetric Boussinesq system. The main conclusion of the paper is that the extended cKdV model provides a much more accurate description of the waves and extends the range of validity of the weakly-nonlinear modelling to the waves of moderate amplitude.

Original languageEnglish (US)
Article number103295
JournalWave Motion
StatePublished - Jul 2024

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Physics and Astronomy
  • Computational Mathematics
  • Applied Mathematics


  • 2D Boussinesq system
  • Concentric waves
  • Extended cKdV equation


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