**4. Discussion**

Internal waves in the South China Sea begin as sinusoidal disturbances in the Luzon Strait [15]. Zhao and Alford presented a simple prediction model that can estimate the arrival times of internal solitary waves in the northeastern South China Sea based on a phase-locked relationship within the tidal cycle between internal solitary waves on the South China Sea shelf and westward tidal currents in the Luzon Strait [9]. However, the amplitude of the internal solitary waves, which depends on the strength of tidal forcing, background flow, and stratification near the generation region, is unpredictable in the prediction model in the above work. There is a clear correlation between the magnitude of semidiurnal tidal current in the Luzon Strait and the corresponding height of the leading solitary wave in the basin of South China Sea [12], which suggests the importance of fortnightly variability in the prediction of internal waves. The intensity of the initial disturbances that can be represented by the baroclinic potential energy at the generation source depends on the local stratification and flow. The local stratification and flow can be modified by Kuroshio and mesoscale eddies in the Luzon Strait, thereby affecting the internal wave generation and evolution [18,45–47]. Except for these two factors, our model results demonstrate that the stratification can also be altered by rectified baroclinic flows, thereby resulting in a lead–lag phenomenon within the fortnightly cycle.

There are some factors that may alter the stratification in our simulation. The tworidge system in the Luzon Strait enhances the interaction between baroclinic tides from different sites, which may also affect the stratification variation in our model. This effect is considered to be responsible for the high local dissipation [11,24], which should weaken the stratification. Thermal wind balance driven flows caused by the horizontally non-homogeneous stratification may enhance mixing and ultimately weaken the stratification. Mean barotropic flows caused by tidal rectification can also suppress or uplift the stratification and thus modulate the stratification redistribution [36,37]. The strong mean barotropic flows exist only near the ridges, while the redistribution of stratification occurs over the whole Luzon Strait, therefore these mean barotropic flows play a secondary role for modulating the stratification over this research domain.

Although our model grid is too coarse to discuss the details of internal solitary wave generation and our diffusion and viscosity scheme cannot resolve wave-breaking, the energy calculation is still credible as background dissipation is included to parameterize this effect. Meanwhile, the interaction between the asymmetric tidal current and the topography generally exists in the Luzon Strait, and can uplift and suppress the isotherms [18]. Thus, the fortnightly variability of stratification revealed by our model results certainly affects the prediction of internal wave amplitude. Our model results suggest that due to this lead-lag relation, the maximum internal solitary wave under certain conditions may not be triggered by the maximum barotropic forcing.
