International Journal of Marine Science, 2024, Vol.14, No.4, 266-274 http://www.aquapublisher.com/index.php/ijms 269 4.2 Role in vertical mixing Internal waves, particularly ISWs, play a significant role in vertical mixing within the ocean. The breaking of internal waves leads to turbulent mixing, which drives the vertical transport of water, heat, and other climatically important tracers. This process is essential for shaping the circulation and distribution of heat and carbon within the climate system (Whalen et al., 2020). The energy pathways from tides, winds, and geostrophic currents to internal wave mixing are complex and involve interactions with topography and other internal waves. These interactions transfer energy to smaller scales, leading to turbulent dissipation and mixing across density classes. The cumulative effects of nonlinearity and dispersion in ISWs contribute to enhanced mixing in the turbulent benthic boundary layer, as observed in stratified lakes and coastal regions (Li and Li, 2023). 5 Turbulence and Nonlinear Mixing in the Ocean 5.1 Nonlinear instabilities leading to turbulence Nonlinear instabilities play a crucial role in the transition from wave motions to turbulence in the ocean. One significant mechanism is the parametric subharmonic instability, which can amplify disturbances in internal gravity waves, leading to secondary instabilities and eventually to turbulence. This process is characterized by the transfer of wave energy into turbulence energy, which is then dissipated (Onuki et al., 2020). Additionally, the Kelvin-Helmholtz instability, driven by stratified shear flows, is another key process. This instability grows to finite amplitude and transitions to turbulence, with the nature of secondary instabilities being influenced by the Prandtl number (Salehipour et al., 2015). The presence of pre-existing turbulence can also modify the evolution of stratified shear layers, suppressing classical billow structures and affecting the mixing efficiency (Kaminski and Smyth, 2019). 5.2 Turbulent mixing in stratified waters Turbulent mixing in stratified waters is a complex process influenced by various factors, including the nature of the stratification and the presence of internal waves. In stratified shear flows, the mixing efficiency is affected by the Prandtl number, with higher values leading to enhanced convective instabilities and reduced scale selectivity. The role of overturns is also critical, as the optimal mixing occurs when the Ozmidov length scale is comparable to the Thorpe overturning scale, indicating efficient stirring by large overturns (Mashayek et al., 2017). Experimental observations have shown that internal wave turbulence can transition through different regimes, with the buoyancy Reynolds number marking the transitions between weak wave turbulence and strongly stratified turbulence (Rodda et al., 2022). Furthermore, the interaction of nonlinear internal waves with the bottom boundary layer can lead to asymmetries in turbulence and sediment transport, with onshore pulses being more energetically turbulent and carrying more sediments than offshore pulses (Figure 1) (Becherer et al., 2020). The mixing across stable density interfaces is another important aspect, where significant mixing can occur in anisotropic statically stable regions, often associated with high vertical shear (Couchman et al., 2022). 6 Numerical and Experimental Studies 6.1 Modeling nonlinear oceanic processes Numerical modeling plays a crucial role in understanding and predicting nonlinear oceanic processes. Recent studies have utilized advanced simulation techniques to explore various aspects of these complex phenomena. For instance, large-eddy simulation (LES) models have been employed to investigate the role of wind and heat-flux forcing in the tropical western Pacific Ocean's surface mixed layer. These studies revealed that mixing is dominated by Langmuir circulation, organized circulations, and shear instability at the mixed-layer base (Dudley et al., 2019). Additionally, numerical experiments using nonhydrostatic and non-Boussinesq regional oceanic circulation models have been conducted to study the nonlinear processes generated by supercritical tidal flow in shallow straits . These simulations highlighted the importance of topography in the formation of internal solitary waves and local breaking events, both of which are significant turbulence-producing phenomena (Bordois et al., 2017). Furthermore, algorithms for reconstructing and predicting nonlinear ocean wave fields from remote measurements have been developed. These algorithms, which include linear, weakly nonlinear, and highly nonlinear prediction
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