Lagrangian drift modulated by nonlinear interaction between surface gravity waves and internal solitary waves

Nonlinear interactions between internal solitary waves (ISWs) and surface gravity waves (SGWs) modulate SGW amplitudes and wave steepness. These modulations must also affect SGW Lagrangian drift and, therefore, the transport of particles such as microplastics and other pollutants in the marine environment. This simulation-based study primarily focuses on the Lagrangian motions of tracer particles at the free surface, particularly when an ISW modifies the Stokes drift caused by SGWs. In our simulation, the ISW is modelled as a spatially varying surface current that propagates at the phase speed of the ISW. Its impact on SGWs is captured through the nonlinear wave-current interaction. A high-order spectral method is used to solve the Zakharov equation governing the wave dynamics. We have performed parametric studies by varying the current strength, controlled by the ISW amplitude, and the background surface wave statistics to quantify their contributions to the particle motions. We show that these nonlinear interactions between SGW and ISW result in a correction to the linearly combined Stokes drifts generated by SGWs and the displacement caused by ISWs. Notably, the combination of drifts from co-propagating SGWs and ISWs often results in an overestimation of the actual drift values.