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

Abstract

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 of the 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 do.