International Journal of Marine Science, 2024, Vol.14, No.4, 266-274 http://www.aquapublisher.com/index.php/ijms 268 3.2.2 Resonant interactions and energy cascades Resonant interactions among oceanic internal waves are a key mechanism for energy transfer within the wave field. These interactions involve the transfer of energy between different wave components, leading to energy cascades across various scales. Analytical evaluations of nonlinear resonant interactions, such as elastic scattering, induced diffusion, and parametric subharmonic-instability mechanisms, reveal their significant role in the energy transfer processes within the internal wave field (Gula et al., 2016). Additionally, nonlinear energy transfers involving infragravity frequencies contribute to the redistribution of energy within the wave spectrum, with energy cascading to higher frequencies where it is eventually dissipated (Bakker et al., 2015). 3.2.3 Wave-current instabilities Wave-current instabilities arise from the interaction between waves and currents, leading to enhanced mixing and energy dissipation. For example, submesoscale processes along coastal boundaries, characterized by strong turbulent mixing and nonlinearity, can cause wave breaking and modify the flow of baroclinic Kelvin waves (Crowe and Johnson, 2020). Furthermore, the generation of submesoscale flows through topographic interactions with geostrophic currents provides a significant route for energy dissipation, as seen in the context of the Gulf Stream (Gula et al., 2016). These instabilities play a crucial role in the overall energy budget and mixing processes in the ocean. In summary, the nonlinear interactions between waves and currents, including wave breaking, resonant interactions, and wave-current instabilities, are fundamental mechanisms driving energy transfer and mixing in the ocean. These processes significantly impact the propagation and dissipation of oceanic waves, contributing to the dynamic and complex nature of oceanic wave and mixing processes (Wang, 2024). 4 Nonlinear Internal Waves and Mixing Processes 4.1 Generation and propagation of internal waves 4.1.1 Internal solitary waves Internal solitary waves (ISWs) are large-amplitude, horizontally propagating waves that play a significant role in ocean dynamics. These waves are often generated by the interaction of barotropic tidal currents with topographic features such as continental shelves, sills, and bottom ridges (Grimshaw, 2016). The generation of ISWs can be modeled using nonlinear evolution equations of the Korteweg-de Vries (KdV) type, which account for the variable coefficients due to changing bottom topography (Grimshaw et al., 2007; Whalen et al., 2020). For instance, in a coastal plain estuary, ISWs evolve from internal lee waves generated at the channel-shoal interface, transforming through nonlinear steepening and dispersion effects (Li and Li, 2023). 4.1.2 Interaction with topography The interaction of internal waves with topography is a critical factor in their evolution and transformation. When ISWs encounter variable bottom topography, such as underwater obstacles or slopes, they can undergo significant changes. For example, in stratified lakes, the interaction with lake boundaries and bottom features can lead to the formation of secondary waves and wave trains, as well as wave breaking and turbulent mixing (Yi et al., 2021). Numerical simulations have shown that the response of ISWs to topographic features depends on the Froude number and the height of the topographic forcing term, which can result in the generation of undular bores and solitary waves (Grimshaw and Helfrich, 2017). 4.1.3 Nonlinear dispersion effects Nonlinear dispersion effects are crucial in the propagation and transformation of ISWs. These effects can lead to the splitting of a solitary wave into a sequence of secondary waves, as observed in various scenarios of wave evolution over variable bottom topography (Yuan et al., 2017). The balance between nonlinear steepening and frequency dispersion determines the formation and stability of solitary waves. For instance, the propagation of ISWs over a three-dimensional semicircular shoal can result in wave splitting and the formation of multiple waves of decreasing amplitudes (Zhong and Wang, 2019). Additionally, the vertical structure of ISWs is influenced by nonlinearity, which affects their energy distribution and interaction with background flows (Yi et al., 2021).
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