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Dynamical properties of ocean internal solitary waves: a study based on the modified intermediate long wave equation

Published online by Cambridge University Press:  20 October 2025

Di Yu Open the ORCID record for Di Yu [Opens in a new window]  and
Jinbao Song
Di Yu
Affiliation:
State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University , Zhoushan 316021, PR China
Jinbao Song*
Affiliation:
State Key Laboratory of Ocean Sensing & Ocean College, Zhejiang University , Zhoushan 316021, PR China
*
Corresponding author: Jinbao Song, songjb@zju.edu.cn
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Abstract

This study presents a modified intermediate long wave (mILW) equation derived from the Navier–Stokes equations via multi-scale analysis and perturbation expansion, aimed at describing internal solitary waves (ISWs) in finite-depth, stratified oceans. Compared to the classical ILW model, the proposed mILW equation incorporates cubic nonlinearities and captures the dynamical behaviour of large-amplitude ISWs more accurately. The equation reduces to the modified Korteweg–de Vries equation and modified Benjamin–Ono equations in the shallow- and deep-water limits, respectively, thus providing a unified framework across varying depth regimes. Soliton solutions are constructed analytically using Hirota’s bilinear method, and numerical simulations investigate wave–wave interactions, including rogue waves and Mach reflection. Furthermore, a smooth tanh-type density profile is adopted to reflect realistic stratification. Associated vertical modal structures and vertical velocity fields are analysed, and higher-order statistics (skewness and kurtosis) are introduced to reveal the density dependence of wave asymmetry. The results offer new insights into the nonlinear dynamics of ISWs, with implications for ocean mixing, energy transport and submarine acoustics.

JFM classification

Geophysical and Geological Flows: Internal waves Mathematical Foundations: Navier-Stokes equations Waves/Free-surface Flows: Solitary waves

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1021 , 25 October 2025 , A32
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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