Experimental and numerical studies on internal solitary waves with a free surface

B. B. Zhao, Z. Wang (Lead / Corresponding author), W. Y. Duan, R. Cengiz Ertekin, M. Hayatdavoodi, T. Y . Zhang

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Abstract

Large-amplitude internal solitary waves in a two-layer fluid system with a free surface are investigated in this paper. Laboratory experiments on strongly nonlinear internal solitary waves with a free surface for a deep configuration are conducted. After comparing the experimental data with the results of the Miyata–Choi–Camassa model that includes the free-surface effects (MCC-FS), we find that the MCC-FS model does not calculate accurately the internal solitary waves with a free surface. Thus, we develop a strongly nonlinear model for a deep configuration, namely the two-layer high-level Green–Naghdi (HLGN-FS) model that includes the free-surface effects. Numerical results of the HLGN-FS model, including the wave profile, velocity field and wave speed, are presented for three cases. The first case is a shallow configuration with ρ2/ρ1 = 0.977 and h2/h1 = 1/4.13, where ρ2 and ρ1 are the densities of the upper-fluid layer and the lower-fluid layer, respectively, and h2 and h1 are the depths of the upper-fluid layer and the lower-fluid layer, respectively. The second case is also a shallow configuration, where h2/h1 = 1/5 while ρ2/ρ1 = 0.859. The third case is related to the present physical experiments, where ρ2/ρ1 = 0.869 and h2/h1 = 1/15. It is shown that the MCC-FS model can provide accurate results for the shallow configurations. Meanwhile, the HLGN-FS model is shown to be accurate for describing the internal solitary waves for both shallow and deep configurations.
Original languageEnglish
Article numberA17
Number of pages28
JournalJournal of Fluid Mechanics
Volume899
Early online date21 Jul 2020
DOIs
Publication statusPublished - 25 Sep 2020

Keywords

  • general fluid mechanics
  • internal waves
  • solitary waves

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