International Journal of Marine Science, 2024, Vol.14, No.4, 266-274 http://www.aquapublisher.com/index.php/ijms 267 be categorized into weakly and strongly nonlinear processes. Weakly nonlinear interactions, such as those described by resonant and near-resonant internal wave triads, are essential for understanding energy transfer in non-uniform stratifications and varying bathymetry (Gururaj and Guha, 2021). These interactions are governed by wave amplitude equations that account for the spatial and temporal variations in wave properties. In the context of internal gravity waves, nonlinear interactions are a principal part of the dynamics, contributing to the overall energy cascade. Various approaches, including the evaluation of transfer integrals, turbulence theories, and numerical simulations, have been employed to study these interactions. However, each method has its limitations, particularly in handling high-wave number, high-frequency waves and interactions with vortical modes (Whalen et al., 2020). Nonlinear wave interactions also play a significant role in equatorial wave-current dynamics, where the Hamiltonian formulation of the governing equations reveals differences between short- and long-wave regimes. In particular, weakly nonlinear long-wave regimes can capture wave-breaking phenomena, which are crucial for understanding the energy distribution in the ocean (Constantin and Ivanov, 2019). 2.2 Basics of oceanic mixing mechanisms Oceanic mixing mechanisms are fundamental to the transport of heat, momentum, and other climatically important tracers within the ocean. Turbulent mixing driven by breaking internal waves is a key process that influences vertical transport and shapes the circulation and distribution of heat and carbon in the climate system (Whalen et al., 2020). The life cycle of internal waves, including their generation, propagation, and breaking into turbulence, is complex and varies spatially and temporally. Nonlinear vertical mixing processes are particularly important in the surface mixed layer and during deep convection. Large-eddy simulation (LES) models have been used to study these processes, revealing the roles of Langmuir circulation, organized circulations, and shear instability in the mixed layer. These studies help develop more effective parameterizations for ocean general circulation models. Additionally, the effects of vertical mixing on nonlinear Kelvin waves highlight the importance of submesoscale processes along coastal boundaries. These processes, characterized by strong turbulent mixing and nonlinearity, significantly modify the flow and contribute to the dissipation of mesoscale kinetic energy (Crowe and Johnson, 2020). Observations of sediment transport by nonlinear internal waves further emphasize the role of bed-stress intensification, turbulent transport, and vertical pumping mechanisms in boundary-layer dynamics (Polzin and Lvov, 2017). 3 Nonlinear wave-current interactions 3.1 Impact of currents on wave propagation Currents significantly influence the propagation of oceanic waves, including internal waves and surface waves. The interaction between currents and waves can modify wave characteristics such as amplitude, wavelength, and direction. For instance, internal waves generated by tides, winds, and geostrophic currents can be altered by background currents, which affect their propagation and energy distribution (Whalen et al., 2020). Additionally, submesoscale currents, which are intermediate-scale flow structures, play a crucial role in the energy transfer towards microscale dissipation and diapycnal mixing, thereby impacting wave propagation (McWilliams, 2016). 3.2 Energy transfer mechanisms 3.2.1 Wave breaking and dissipation Wave breaking is a critical mechanism for energy dissipation in oceanic waves. It occurs when waves become unstable and break, leading to turbulent mixing and energy loss. This process is particularly important for internal solitary waves (ISWs) breaking over slope-shelf topography, where shear and convective instabilities trigger wave breaking, resulting in significant energy dissipation (He et al., 2023). Moreover, wave breaking is essential for the dissipation of energy input into ocean waves by wind and transferred across the spectrum by nonlinearity (Eeltink et al., 2022). The dissipation of internal waves, especially above rough topography, also contributes to energy loss and mixing in the ocean (Zemskova and Grisouard, 2021).
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