A higher-order Boussinesq-type model with moving bottom boundary: Applications to submarine landslide tsunami waves

B. Ataie-Ashtiani, A. Najafi Jilani

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)

Abstract

A two-dimensional depth-integrated numerical model is developed using a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundary and is applied for submarine-landslide-generated waves. The mathematical formulation of model is an extension of (4,4) Padé approximant for moving bottom boundary. The mathematical formulations are derived based on a higher-order perturbation analysis using the expanded form of velocity components. A sixth-order multi-step finite difference method is applied for spatial discretization and a sixth-order Runge-Kutta method is applied for temporal discretization of the higher-order depth-integrated governing equations and boundary conditions. The present model is validated using available three-dimensional experimental data and a good agreement is obtained. Moreover, the present higher-order model is compared with fully potential three-dimensional models as well as Boussinesq-type multi-layer models in several cases and the differences are discussed. The high accuracy of the present numerical model in considering the nonlinearity effects and frequency dispersion of waves is proven particularly for waves generated in intermediate and deeper water area.

Original languageEnglish
Pages (from-to)1019-1048
Number of pages30
JournalInternational Journal for Numerical Methods in Fluids
Volume53
Issue number6
DOIs
Publication statusPublished - 28 Feb 2007
Externally publishedYes

Keywords

  • Boussinesq model
  • Impulsive waves
  • Numerical model
  • Submarine landslide
  • Tsunami waves

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