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Oceanic internal solitary waves in three-layer fluids of great depth

大深度三层流体中的海洋内孤立波

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Abstract

This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth. The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration. Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows, strongly nonlinear and weakly nonlinear models are developed for the “shallow-shallow-deep” and “deep-shallow-deep” scenarios. Internal solitary waves are computed using numerical iteration schemes, and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models. For the “shallow-shallow-deep” case, both mode-1 and mode-2 internal solitary waves can be found, and a pulse broadening phenomenon resulting in conjugate flows is observed in the mode-2 branch. While in the “deep-shallow-deep” situation, only mode-2 solitary waves can be obtained. The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.

摘要

本文致力于研究深海非线性内波. 将海洋抽象为由三种流体构成的具有稳定密度层结的系统. 基于无旋流动的Ablowitz-Fokas-Musslimani公式, 我们对“浅水-浅水-深水”和“深水-浅水-深水”两种情形建立新的强非线性和弱非线性模型, 并详细比较了不同模型中内孤立波波形及“速度-振幅”的全局分叉图. 对于“浅水-浅水-深水”情形, 可以获得一模态和二模态两种类型的内孤立波, 并且在二模态内波中观察到脉冲展宽现象及其极限形态—共轭流. 然而对于“深水-浅水-深水” 情形, 只能得到二模态内孤立波.基于MITgcm求解原始方程, 我们证实了深海中二模态内波的存在性和稳定性.

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Authors and Affiliations

  1. Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Zi’an Wang  (王梓安) & Zhan Wang  (王展)

  2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Zi’an Wang  (王梓安) & Zhan Wang  (王展)

  3. School of Future Technology, University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhan Wang  (王展)

  4. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Chunxin Yuan  (袁春鑫)

Authors
  1. Zi’an Wang  (王梓安)
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  2. Zhan Wang  (王展)
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  3. Chunxin Yuan  (袁春鑫)
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Corresponding author

Correspondence to Zhan Wang  (王展).

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11911530171, 11772341, and 42006016), the Key Program of National Natural Science Foundation of China (Grant Nos. 12132018, and 91958206), and the Natural Science Foundation of Shandong Province (Grant No. ZR2020QD063).

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Wang, Z., Wang, Z. & Yuan, C. Oceanic internal solitary waves in three-layer fluids of great depth. Acta Mech. Sin. 38, 321473 (2022). https://doi.org/10.1007/s10409-021-09012-x

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  • DOI: https://doi.org/10.1007/s10409-021-09012-x

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