*3.2. Stratification Variability*

The variability of stratification in our investigation is an important part of baroclinic responses. Therefore, we investigate this feature in more detail. The depth and strength of the pycnocline are two parameters used to evaluate stratification, whereas buoyancy frequency *N* provides a more concise measure of ocean stratification. Given that barotropic tidal current in the Luzon Strait has a significant spring-neap tidal cycle, we calculate a time average over the spring-neap tidal cycle (model days 24 to 38) to determine the background field. For example, the background buoyancy frequency *N<sup>b</sup>* = h*N*i, where h·i <sup>=</sup> <sup>1</sup> *T* R *<sup>t</sup>*+*<sup>T</sup> t* (·)*dτ*, is the time average of a quantity over the time interval *T*, *T* is 15 days covering a spring-neap cycle in this case. Apparently, the model results show different background stratification at different locations (Figure 2). At L1, which is located on the eastern side of the ridge and has a sharp topography, the *N<sup>b</sup>* shows no prominent peaks, which means the water column here has experienced significant vertical mixing and diffusion since initialization. At B2, which is located in the sea basin with more than 3000 m depth, *N<sup>b</sup>* is similar to the initial state, which means that stratification here is only slightly changed and that the vertical structure of the water column can be well maintained. For a more integrated picture, we analyze the time series of the depth-averaged *N*<sup>2</sup> between the surface and a depth of 300 m instead of the profiles below (Figure 6a).

According to the time series of the depth-averaged *N*<sup>2</sup> , the stratification at L1 exhibits daily oscillations. After applying two times a moving average with a window size of 24 h, the time-smoothed result of stratification is marked by a bold line indicating the approximate fortnightly variability (Figure 6a). This variability shows a buoyancy increase and decrease cycle at L1 in the model, although no buoyancy input takes place during the model run, leading to the question as to which process is responsible for the enhancement of stratification. The low-pass decline of the depth-averaged *N*<sup>2</sup> is due to numerical diffusion and mixing. Finally, the stratification will almost disappear according to our model setting of no surface buoyancy forcing. The boundary tidal current signal plays an important role on the stratification variability, as it quickly traverses the model domain and dominates its variability. To investigate the reason for these results, we reviewed the local barotropic current field first (Figure 6b,c). The time series of zonal and meridional barotropic velocities suggest that the local barotropic flows are asymmetric, which means that these flows have different strengths in opposite directions, and the stratification shows a similar springneap cycle as the barotropic velocity, which means there is an impact from barotropic forcing on stratification. The asymmetry in the barotropic tidal flows is defined by the discrepancies in the duration of the eastward (northward) and westward (southward) tidal currents [18]. The interactions and phase difference between tidal constituents are the major source behind the barotropic tidal asymmetry [34,35]. Besides, there are some barotropic mean flows on the order of 0.1 m/s near the west ridge (not shown), which are considered to be caused by topographic rectification [36–38], also contribute to the asymmetric barotropic flows.

**Figure 6.** (**a**) The time series of 0–300-meter depth-averaged *N*<sup>2</sup> and corresponding time-smoothed result (bold line) at L1. The shaded bar represents a three-day period. (**b**) The zonal barotropic *U* and (**c**) *V* at L1.

In the following, we introduce the potential energy anomaly *ϕ* = *g H* (*ρ*ˆ − *ρ*)*z* [39,40] to explain what happens during stratification changes, where *g* is the gravity acceleration and *ρ*ˆ is the depth-averaged density. *ϕ* is a depth-integrated value that represents changes in potential energy relative to the vertically homogeneous conditions. For a given density profile, *ϕ* is the amount of work per unit volume required to completely homogenize the water column [40]. Thus, we define ∆*ϕ* = *ϕ* − *ϕ*<sup>0</sup> as the potential energy anomaly change, where *ϕ*<sup>0</sup> is calculated from the initial field.

The interaction between barotropic flows and ridges causes vertical movements (Figure 7a) and thus can uplift or depress the isopycnals. Through this physical process, *ϕ* can decrease or increase (Figure 7b). Considering the generation of internal waves here and the accompanying intense baroclinic currents, the baroclinic component is expected to dominate the vertical velocity. These baroclinic flows are associated with the asymmetric barotropic forcing and exhibit a fortnightly cycle. Thus it is evident that the accumulated enhancing of stratification is unequal to the weakening (Figure 7b), and finally overwhelms the *ϕ*, thereby contributing to the fortnightly stratification variability (Figure 6a).

**Figure 7.** (**a**) The vertical velocity *w* (positive upward) and (**b**) the potential energy anomaly *ϕ* and the corresponding time-smoothed result at L1 over three days (shaded in Figure 6a).

Figure 8 shows the position of the isopycnals in relation to the baroclinic flow in the zonal L1-section during a tidal cycle. The interaction between barotropic forcing and topography in the stratified ocean can produce intense baroclinic currents. The simulated baroclinic currents show a structure of wave beams and their speed can reach to about 0.5 m/s, which are in agreement with the in situ observations [38]. Therefore, it can be concluded that our model performance is acceptable. According to our simulation, the horizontal baroclinic currents change directions with the tidal phase. The isopycnals also vary during a tidal cycle. In addition, the horizontal baroclinic velocity at L1 beats at a fortnightly cycle (not shown), which implies the impact of horizontal bariclinic currents on fortnightly stratification variability.

**Figure 8.** (**a**) The daily cycle of barotropic U-velocity in the zonal L1-section of day 25. The corresponding baroclinic U-velocity (shaded) and the isopycnals (contours) at (**b**) 4:00, (**c**) 10:00, and (**d**) 16:00.

Figure 9 shows daily averages of temperature and salinity when the time-smoothed depth-averaged *N*<sup>2</sup> is ascending or descending. Daily averages of the baroclinic U-velocity and V-velocity as well as the full W-velocity are shown in Figure 10. As can be seen, the magnitude of these mean currents and their temporal variability are in a reasonable range, indicating that the model is able to reasonably reproduce the underlying processes. The baroclinic velocity fields are associated with the asymmetric barotropic forcing in our simulation, and thus these rectified baroclinic flows also exhibit a fortnightly variability. As shown in Figure 9, the halocline at L1 is depressed at day 25 and it is uplifted at day 32 above the ridge. Considering the vertical rectified flow exists in this area (Figure 10), the vertical movement of the halocline demonstrates that the vertical advection of buoyancy by the rectified flow near the ridge contributes to the fortnightly stratification variability. Due to the effect of internal wave generation, the stratification at L1 is relatively weak compared to its surroundings. Considering the horizontal difference of stratification and the existence of the horizontal mean baroclinic flow in this area (Figure 10), the horizontal advection by the baroclinic flow also contributes to the fortnightly stratification variability.

**Figure 9.** Daily averages of salinity and temperature in the zonal L1-section over (**a**) the ascending part day 25 and (**b**) the descending part day 32 shown in Figure 6.

**Figure 10.** Daily averages of (**a**,**b**) baroclinic U-velocity, (**c**,**d**) baroclinic V-velocity, and (**e**,**f**) W-velocity in the zonal L1-section over the ascending part day 25 and the descending part day 32.

These dynamics can explain how the stratification process varies at L1. Subject to our model configuration, the energy that enhances the stratification must originally come from boundary forcing. Given that there are two ridges in the Luzon Strait, when the stratification at L1 is enhanced, the stratification at other places within the Luzon Strait should be weakened. Figure 11a,b shows ∆*ϕ* and the corresponding time-smoothed result at L1 and L2, respectively, where L1 is on the east side of the ridge and L2 is on the west side of the ridge. The time-smoothed result at L2 shows an almost inverse phase compared to that at L1, which proves our speculation. In order to determine the spatial distribution, we calculated three daily averages h∆*ϕ*i that are separated by 6 days, *d*1,*d*2 and *d*3 (Figure 11a).

**Figure 11.** (**a**) The time series of potential energy anomaly change ∆*ϕ* and corresponding timesmoothed result at L1 and (**b**) L2. The shaded bars *d*1, *d*2, and *d*3 represent one-day periods on different dates. (**c**) The distribution of the differences of ∆*ϕ* between *d*2 and *d*1, and (**d**) between *d*3 and *d*2.

Figure 11c,d shows the differences in ∆*ϕ* between different intervals. For different intervals, these differences are almost in anti-phase, suggesting that the stratification in the Luzon Strait is always being redistributed within a spring-neap cycle. Regarding stratification, this result means that the baroclinic field in the Luzon Strait can be disturbed and redistributed by the interaction between asymmetric barotropic forcing and topography. Due to this redistribution, the energy transfer and the internal wave generation, which strongly depend on stratification, will be affected.
