Figure 8.3 is a compilation of sea surface signatures (sea surface zonal velocity gradient) of the leading ISWs at different stages. The corresponding time (in hours) is labeled along with each ISW. Three snapshots at t= 24, 34, and 48 h are the fragments from the model output, whereas the thick black lines show only the positions of the leading ISWs. The profile of the incoming ISW is not subjected to any substantial changes until it approaches the 1000 m isobath, where the topography starts to shoal drastically. As a consequence of the south-north asymmetry of the bathymetry, the southern periphery of the ISW travels faster due to larger water depth, hence the wavefront is deflected (compare profiles at t=20 and 24 h). At the same time, the northern part of the wave looks stronger than the southern counterpart due to the decreasing waveguide.
Three-dimensionality is getting much more remarkable as the wave propagates up onto the slope. Wave refraction is visible near the Dongsha Atoll, where ISW splits into two parts which, however, merge again later behind the atoll. Wave reflection in all directions occur around the atoll (not shown). The impact of the underwater banks (shown by the triangles in Figure 8.3) is pronounced, particularly at t=34 h, when the wavefront splits into several fragments. Wave fission starts to develop in the shallow water, as is clearly seen at t=34 h. As time progresses, the disintegrated ISWs are stretched due to nonlinear dispersion (compare wave fragments at t=34 and 48 h). Subsequent evolution of sea surface signals in the shallow water will be discussed later.
To inspect the corresponding underwater wave structures, two cross-sections in Figure 8.3 (21.5◦Nand 20.4◦N; see the two solid lines) were chosen. Four snapshots (t=16, 24, 34, and 48 h) for every cross-section shown in Figure 8.4 illustrate the evolution of the vertical density and
8.3. THREE-DIMENSIONAL SIMULATION OF INTERNAL SOLITARY WAVE SHOALING IN THE NORTHERN SOUTH CHINA SEA
Figure 8.3:Compilation of the modeled sea surface velocity gradient overlapped on bathymetry (water depth of 100, 500, 1000, 2000, and 3000 m is shown) at dif-ferent stages, with the time labeled accordingly. Three snapshots taken at t=24, 34, and 48 h are plotted straight from model results and the time labels are in the square brackets, whereas the bold solid lines are sketches of the leading waves at the other moments. Two bold dashed lines are sketches of the leading waves at t=58 h and t=72 h when rotation is switched off. The two thin lines along 21.5◦N and 20.4◦N (only the left parts are drawn to make the figure more readable) are chosen to illustrate the evolution of density and velocity fields in the vertical direc-tion, as will be shown in Figure 8.4. The two grey rectangles mark two averaged topography that will be used in section 8.5. The triangles in the figure mark the approximate location of the underwater banks, whilst ’D’ denotes the Dongsha Atoll.
8.3. THREE-DIMENSIONAL SIMULATION OF INTERNAL SOLITARY WAVE SHOALING IN THE NORTHERN SOUTH CHINA SEA
Figure 8.4:Vertical structures of density and velocity along the two cross-sections shown in Figure 8.3. Panels a and b correspond to cross-sections 21.5◦Nand 20.4◦N, respec-tively. Four instants at t=16, 24, 34, and 48 h are shown for both cross-sections, with the last three instants corresponding to the three realistic model outputs in Figure 8.3. The plotted isopycnals are, from top to bottom, 1023, 1025, 1026, 1027, and 1027.5 kg/m3, respectively.
velocity fields. The northern cross-section (panel a), which features steep yet smooth change of topography, is more effective in scattering wave energy. Wave amplitude at t=16 h (80 m) has decreased moderately from the initial 100 m along this cross-section, whereas it drops more quickly to 60 m after traveling onto the shelf (t=34 h) and to only 20 m further up (t=48 h).
Transformation on the slope is drastic, with the detailed process shown in Figure 8.5. In panel a (t=20 h), wave profile reveals asymmetry, with the frontal side steeper whilst the rear gentler.
A secondary wave, though still weak, is shed backwards and trails the main wave. This wave continuously grows, and at t=28 h, a clear wave of elevation is seen behind the leading ISW.
On the other hand, the amplitude of the leading ISW keeps decreasing during this process and the wave itself gradually transforms into two waves after going onto the shelf, as is shown in Figures 8.3 and 8.4a (t=48 h).
The southern cross-section in Figure 8.3, which features an underwater bank with the depth of about 300 m, exhibits different scenario in wave evolution, as is shown in Figure 8.4b. Wave profile transformation is not significant until it gets close to the bank, over which the incoming wave amplitude decreases from 60 m at t=24 h to 50 m at t=34 h. Despite the slight decrease of the wave amplitude after the collision with the bank, the transmitted wave, which is as yet non-stationary, is much narrower, implying the loss of wave energy and the occurrence of localized wave scattering and energy transfer at the bank. The detailed interaction process between these
8.3. THREE-DIMENSIONAL SIMULATION OF INTERNAL SOLITARY WAVE SHOALING IN THE NORTHERN SOUTH CHINA SEA
Figure 8.5:Evolution of vertical density and velocity fields near the shelf break along cross-section 21.5◦N(Figure 8.4a). Time instants of 20, 22, 26, and 28 h are shown. The plotted isopycnals are, from top to bottom, 1023, 1024.2, 1025, 1025.5, 1026, and 1027 kg/m3, respectively.
two moments is shown in Figure 8.6 with a time interval of two hours. Just as the scenario in the northern cross-section, the incoming wave also goes through an asymmetrical deformation but with a faster pace (panel a of Figure 8.6). A pronounced ray structure is formed as well near the bank top during the wave passage and it continuously evolves. After the detachment of the ISW from the bank, the beam structure starts to attenuate, gradually transforming into a series of high mode waves (panels c and d). After passing over the bank, the incident ISW exhibits a tendency to fission (Figure 8.6c). Overall, the southern portion of the wave is weaker and even indistinguishable in the sea surface signal field (see Figure 8.3), which is consistent with the SAR observations (Figure 1.3).