TY - JOUR

T1 - Internal solitary waves in the presence of linear and nonlinear shear currents

AU - Zhao, Binbin

AU - Zhang, Tianyu

AU - Duan, Wenyang

AU - Wang, Zhan

AU - Hayatdavoodi, Masoud

AU - Ertekin, R. Cengiz

N1 - Funding Information:
The first, third and fourth authors’ (B.B.Z, W.Y.D and Z.W) work are supported by the National Natural Science Foundation of China (Nos. 12202114, 52261135547), the China Postdoctoral Science Foundation (No. 2022M710932), the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology (No. LP2202), the Fundamental Research Funds for the Central Universities (No. 3072022FSC0101), the Qingdao Postdoctoral Application Project and the Heilongjiang Touyan Innovation Team Program

PY - 2023/9/16

Y1 - 2023/9/16

N2 - 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.

AB - 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.

KW - HLGN theory

KW - internal solitary wave

KW - shear current

M3 - Article

SN - 0165-2125

JO - Wave Motion

JF - Wave Motion

M1 - 103217

ER -