Internal solitary waves in the presence of linear and nonlinear shear currents

Binbin Zhao, Tianyu Zhang, Wenyang Duan, Zhan Wang (Lead / Corresponding author), Masoud Hayatdavoodi, R. Cengiz Ertekin

Research output: Contribution to journalArticlepeer-review


In this paper, the effects of background linear and nonlinear shear currents on internal solitary waves in a two-layer fluid system are studied. In the linear shear-current case, the strongly nonlinear internal-wave equations (SNIWE) and the high-level Green-Naghdi (HLGN) equations are used to study the effect of the current on the wave speed, wave profile and velocity distribution. A comparative study between the results of these two models is presented. The SNIWE, commonly used in the literature, however, is confined to a condition where the horizontal velocity is invariant in the vertical direction in the absence of current, and it varies linearly in the presence of a shear current. It is shown in this study that this assumption is not valid under nonlinear shear current conditions, or when current is in the opposite direction to wave, resulting in large errors. In such cases, the use of a nonlinear theory which relaxes this assumption, e.g. the HLGN equations, is necessary. The effects of background nonlinear shear currents on the speed, profile and velocity field of internal solitary waves are investigated here by use of the HLGN equations. It is found that the nonlinear shear currents affect the velocity field of the internal solitary wave significantly more than the linear shear currents.
Original languageEnglish
Article number103217
Number of pages18
JournalWave Motion
Early online date16 Sept 2023
Publication statusE-pub ahead of print - 16 Sept 2023


  • HLGN theory
  • internal solitary wave
  • shear current


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