*3.4. Relationship between Barotropic Tides at Source and ISWs*

It is generally believed that ISWs in the LS are generated by the interaction between tidal current and the Nusa Penida sill [17,23,31]. Understanding the relationship between the ISW generation and barotropic tides is of great significance for estimating the occurrence time of ISWs in the BS around the time of submarine wreck.

In the MODIS image taken at 9:45 on 14 April, it can be seen that the crest of S3-a was only about 10 km to the north of the source site (Figure 6a). Moreover, we calculated the internal Froude number (Fr) to examine the criticality of the tidal flow over the Nusa Penida sill. The Froude number (Fr = u/c) is a dimensionless quantity that expresses the ratio of barotropic flow speed (u) to the phase speed (c) of long internal wave [32]. At the above tidal peak, the Fr over the sill is 1.25 greater than 1, from which we can infer

that S3 was likely released within the southward tidal. Backtracking at an average *C*<sup>0</sup> of 1.8 m/s, calculated from Equation (2), the generation time of S3 at the source site was about 08:12 (dashed red line in Figure 6b), adjacent to a TPXO southward tidal current peak. Purwandana et al. proposed that the generation of ISWs in the LS was related to the lee-wave mechanism [19], consistent with the near-source emergence of ISWs in the MODIS image in Figure 6a and the estimated release time of ISWs around the southward tidal current peak in Figure 6b.

**Figure 5.** Underwater structure of the ISW. (**a**) Horizontal current along the wave propagation direction. The gray lines are isopycnal. (**b**) Vertical current. The white lines represent 6 cm/s isoline.

As previous measurements have revealed [19], the barotropic tidal current at the Nusa Penida sill was dominated by semi-diurnal component, and every day there were two southward barotropic tidal current peaks, occurring about 20–30 min later than the barotropic tides each day (Figure 6c). This indicates that two ISWs were generated in one day over the April tidal period. We traceback each ISW along the propagation path using the speed obtained from the satellite images and the calculated theoretical speed, and connect these ISWs, in Figure 6c and Table 1, with the suspected tidal peaks that generated them. From 11–20 April, the interval between the generation of two ISWs every day was reduced from 12.3 h to 11.7 h, slightly less than the 12.4 and the 12.42 h intervals defined by Matthews et al. and Karang et al. [21,29]. In addition, by comparing the distance between adjacent ISW crests and the time interval between their formation, we obtain a mean speed range of 1.35 (S1-a, S2) to 2.77 (S7, S8) m/s for the ISWs propagating in the BS.

**Figure 6.** (**a**) Remote sensing images of S3 in the LS taken at 9:45 on 14 April local time. (**b**,**c**) Barotropic tide variation at the Nusa Penida sill from TPXO. The colored triangles represent the time when the ISWs were observed, and the dotted lines of the same color indicate the tidal current peaks associated with the generation of those ISWs.

**Table 1.** The observed time of ISWs in satellite images from 12 to 21 April 2021 and the occurrence time of southward tidal current peaks (STCP) associated with their generation.

