4.7 Article

ISWFoam: a numerical model for internal solitary wave simulation in continuously stratified fluids

Journal

GEOSCIENTIFIC MODEL DEVELOPMENT
Volume 15, Issue 1, Pages 105-127

Publisher

COPERNICUS GESELLSCHAFT MBH
DOI: 10.5194/gmd-15-105-2022

Keywords

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Funding

  1. National Key Research and Development Program of China [2021YFB2601100]
  2. National Natural Science Foundation of China [51509183]

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This study develops a numerical model, ISWFoam, for simulating internal solitary waves in continuously stratified fluids. ISWFoam is able to accurately reproduce the characteristics and interactions of internal solitary waves through verification with experimental data.
A numerical model, ISWFoam, for simulating internal solitary waves (ISWs) in continuously stratified, incompressible, viscous fluids is developed based on a fully three-dimensional (3D) Navier-Stokes equation using the open-source code OpenFOAM(R). This model combines the density transport equation with the Reynolds-averaged Navier-Stokes equation with the Coriolis force, and the model discrete equation adopts the finite-volume method. The k-omega SST turbulence model has also been modified according to the variable density field. ISWFoam provides two initial wave generation methods to generate an ISW in continuously stratified fluids, including solving the weakly nonlinear models of the extended Korteweg-de Vries (eKdV) equation and the fully nonlinear models of the Dubreil-Jacotin-Long (DJL) equation. Grid independence tests for ISWFoam are performed, and considering the accuracy and computing efficiency, the appropriate grid size of the ISW simulation is recommended to be 1/150th of the characteristic length and 1/25th of the ISW amplitude. Model verifications are conducted through comparisons between the simulated and experimental data for ISW propagation examples over a flat bottom section, including laboratory scale and actual ocean scale, a submerged triangular ridge, a Gaussian ridge, and slope. The laboratory test results, including the ISW profile, wave breaking location, ISW arrival time, and the spatial and temporal changes in the mixture region, are well reproduced by ISWFoam. The ISWFoam model with unstructured grids and local mesh refinement can effectively simulate the evolution of ISWs, the ISW breaking phenomenon, waveform inversion of ISWs, and the interaction between ISWs and complex topography.

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