Complementary mild-slope equations in a two-layer fluid

Srinivasa R. Manam, Yaron Toledo*, Yehuda Agnon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Mild-slope (MS) type equations are depth-integrated models, which predict under appropriate conditions refraction and diffraction of linear time-harmonic water waves. By using a streamfunction formulation instead of a velocity potential one, the complementary mild-slope equation (CMSE) was shown to give better agreement with exact linear theory compared to other MS-type equations. The main goal of this work is to extend the CMSE model for solving two-layer flow with a free-surface. In order to allow for an exact reference, an analytical solution for a two-layer fluid over a sloping plane beach is derived. This analytical solution is used for validating the results of the approximated MS-type models. It is found that the two-layer CMSE model performs better than the potential based one. In addition, the new model is used for investigating the scattering of linear surface water waves and interfacial ones over variable bathymetry.

Original languageEnglish
Pages (from-to)223-234
Number of pages12
JournalWave Motion
Issue number3
StatePublished - Apr 2011
Externally publishedYes


  • Free-surface waves
  • Internal interfacial waves
  • Mild-slope equation
  • Streamfunction
  • Two-layer model


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