CHAPTER III: SEXUAL VIOLENCE DURING WAR AND POSTWAR: CONTEXT,
3.6. Action to Stop and Prevent Sexual Violence in Afghanistan
Figure 4.6:Zonal velocity field (m/s) along cross-section b (see Figure 4.1). Superimposed are several radiated tidal beams calculated from the background stratification. Dashed and solid lines correspond to the beams emitted from the western ridge and the eastern ridge, respectively.
see its qualitative feature at this initial stage, given that later wave evolution and the resulting turbulence and mixing will smear the general picture. It is seen that, for a cross-section with an underwater eastern ridge (not intersecting an island), an internal wave of depression is formed at the downstream side of the ridge. This wave is trapped there and grows in amplitude by draining energy from the background flow in the first quarter tidal cycle. However, when the eastward barotropic tide slackens and turns westward, the wave of depression is released and propagate westward. While these waves occur locally near the ridge peaks and much resemble the lee wave generation, meanwhile beyond the generation site, long waves of depression are radiated to both directions, clearly a sign of internal tide generation. The above discussion about the magnitude of ku0/ω and ε, and the vertical wave evolution and structure all demonstrate features of both internal tides and lee waves, thus it denotes an intermediate case: mixed lee wave regime.
4.4 The effects of the double-ridge topography
The influence of the western ridge on the generation of internal waves has been discussed by a number of papers (Chao et al. 2007, Du et al. 2008, Jan et al. 2008, Warn-Varnas et al. 2009, Buijsman, McWilliams & Jackson 2010, Echeverri & Peacock 2010, Li & Farmer 2011, Alford et al. 2011, Zhang et al. 2011, Buijsman et al. 2012). However, inconsistent conclusions are drawn in terms of if it actually enhances or damps wave generation.
To first understand the separate role played by each ridge in determining the internal wave field near LS, two extra numerical experiments were conducted, each with one ridge truncated.
The temperature cross-sections along 20◦460N(cross-section b in Figure 4.1) for the reference
4.4. THE EFFECTS OF THE DOUBLE-RIDGE TOPOGRAPHY
Figure 4.7:Temperature profiles along cross-section b (see Figure 4.1) after 5 tidal periods.
The top three panels show the cases of a) real topography; b) without the western ridge; c) without the eastern ridge. The corresponding bottom profiles are shown in panel d.
experiments and the ’truncated experiments’ are compared in Figure 4.7. It can be seen from the figure that without the western ridge (panel b), the first mode ISW packet with two waves is essentially unaffected except that it travels farther due to the removal of the blocking effect of the western ridge. Meanwhile, the second mode ISW, which is otherwise trailing the first mode packet in the reference experiment (A2 in panel a), could hardly be discerned without the western ridge, neither could the other second mode (B in panel a). In the near-field of the generation site, without the western ridge the undulation of the isotherms shows a less high-modal structure and is more smooth.
On the other hand, when the eastern ridge is truncated, a rather different scenario is seen (panel c in Figure 4.7). The large first mode packet in the reference experiment vanishes in this case.
Some weak oscillations are barely noticed in the far-field. However, localized above the western ridge, tidal beams emitting from the ridge peaks are obvious, despite that no efficient disinte-gration of first or second mode ISWs emerges.
Clearly, the total wave field is not merely a linear superposition of the signal generated by each
4.4. THE EFFECTS OF THE DOUBLE-RIDGE TOPOGRAPHY
Figure 4.8:Zonal bottom profiles of the LS taken between 20.25◦Nand 20.75◦N. The thick solid line denotes the average bottom profile, with the thick dashed and dotted lines showing the divergence.
ridge. Rather, nonlinear interference and superposition is likely to play a significant role. This is especially apparent for the second mode generation when one of the two ridges is truncated:
their linear superposition amounts to a wave signal much weaker than that when both ridges are present. Nevertheless, for the first mode ISW, it is robust from Figure 4.7 that the wave packet is correlated with the eastern ridge and the western ridge plays little role.
The generation of first and second mode ISWs over the two ridges can be explained in terms of a resonant excitement of waves in a double-ridge system and their further nonlinear interference and amplification. A linear analytical model derived by Vlasenko et al. (2005) indicates that, beyond the topography the solution is a superposition of multiple propagating baroclinic modes, which, in terms of vertical displacement ζ (x, z,t), has the form:
ζ (x, z, t) = ε0 mode; gj(z) and kj are the corresponding vertical profile and wavenumber, defined from a standard eigen-value problem. The small parameter ε0 is an ’efficient’ height of the bottom topography defined as:
where H and Hmare the total water depth and ridge height, respectively; N(z) is the buoyancy frequency. Detailed formulation and solution of the model are described in detail by Vlasenko et al. (2005).
For the case at LS, due to the remarkable three-dimensionality, a mean bottom profile was obtained by averaging 13 zonal cross-sections across the strait between 20.25◦Nand 20.75◦N with a distance of 2.50 (Figure 4.8). The dependence of the generated wave amplitude for the eastern ridge (aej) and western ridge (awj) on the ridge width (l) was calculated and the first
4.4. THE EFFECTS OF THE DOUBLE-RIDGE TOPOGRAPHY
Figure 4.9:Predicted wave amplitudes of the first (solid line) and the second (dashed line) baroclinic modes generated by the a) eastern ridge and b) western ridge, respec-tively. The gray boxes indicate the likely variation of the ridge widths.
two modes are shown in Figure 4.9. For the eastern ridge and western ridge, l is estimated as 120 ± 5 km and 90 ± 15 km, respectively. Note that the position of the western ridge varies more significantly than the eastern one and hence exhibits more divergence.
It is evident from Figure 4.9 that wave amplitude aj(l) reveals clear resonant properties with the varying ridge width. For the eastern ridge with a width of 120 ± 5 km, the predicted first mode wave amplitude ae1(l) is nearly at the maximum value (71 ± 1 m), whereas the second mode wave amplitude ae2(l) is close to zero (only 8 ± 4 m). This is confirmed by Figure 4.7b in which the second mode is negligibly weak but the first mode is still very pronounced.
In a similar manner, for the western ridge with a width of 90 ± 15 km, the analytical prediction reveals weak yet comparable amplitudes of the first mode (14 ± 2 m) and second mode (7 ± 3 m), which explains the non-existent solitary wave and the clear beams in Figure 4.7c.
For the linear analytical model used here, the resulting total wave field is a linear superposition of the waves generated by the two ridges separately, which can enhance or suppress the total wave field depending on the phase shift ϕej− ϕwj. As is shown in Figure 4.10, the final second mode wave amplitude varies substantially when the waves are in phase (ϕ2e = ϕ2w+ 2πn, n =