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

Published online by Cambridge University Press:  21 July 2020

Binbin Zhao ,
Zhan Wang Open the ORCID record for Zhan Wang [Opens in a new window] ,
Wenyang Duan ,
R. Cengiz Ertekin Open the ORCID record for R. Cengiz Ertekin [Opens in a new window] ,
Masoud Hayatdavoodi Open the ORCID record for Masoud Hayatdavoodi [Opens in a new window]  and
Tianyu Zhang
Binbin Zhao
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001Harbin, PR China
Zhan Wang*
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001Harbin, PR China
Wenyang Duan
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001Harbin, PR China
R. Cengiz Ertekin
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001Harbin, PR China Department of Ocean and Resources Engineering, University of Hawai'i, Honolulu, HI96822, USA
Masoud Hayatdavoodi
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001Harbin, PR China Civil Engineering Department, School of Science and Engineering, University of Dundee, DundeeDD1 4HN, UK
Tianyu Zhang
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, 150001Harbin, PR China
*
†Email address for correspondence: zhan.wang@hrbeu.edu.cn
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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 $\rho _{2}/\rho _{1}=0.977$ and $h_{2}/h_{1}=1/4.13$, where $\rho _{2}$ and $\rho _{1}$ are the densities of the upper-fluid layer and the lower-fluid layer, respectively, and $h_{2}$ and $h_{1}$ are the depths of the upper-fluid layer and the lower-fluid layer, respectively. The second case is also a shallow configuration, where $h_{2}/h_{1}=1/5$ while $\rho _{2}/\rho _{1}=0.859$. The third case is related to the present physical experiments, where $\rho _{2}/\rho _{1}=0.869$ and $h_{2}/h_{1}=1/15$. 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.

JFM classification

Waves/Free-surface Flows: Solitary waves Geophysical and Geological Flows: Internal waves Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A17
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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