## 4 Discussion
Note that each sloshing mode depends on the tank geometry and filling level, and the mode shape (\(m\),\(n\)) is characterised by \(m\) nodes in the spanwise direction and \(n\) nodes in the chordwise direction [28]. The vertical acceleration gradient increases further towards the tip-end of the tank (left-hand side in Figure 16), where the maximum \(A1\) accelerations of 5.5 g are reached. This gradient causes the liquid sloshing motion to be increasingly more violent as we move from cells 5 to 8. This violent vertical behaviour is observed up to \(t=9\)\(T\) in cell 8 followed by only occasional roof impacts afterwards. These motions are typical of the most dissipative region R1. Furthermore, since these violent sloshing patterns are localised predominantly outboard, the developed sloshing force has a larger moment arm relative to the root, maximising thus the dissipative influence of the sloshing liquid. The numerical results presented in Section 3 confirm the experimentally-observed damping trends, and the high amplitude behaviour was shown to be modelled well when a sloshing smoothing function is considered in the first part of the transient (see Section 3, Figure 15). Shifting focus on the lower acceleration amplitude range, past point  
Figure 16: Selection of video segments for one representative 50% filling level test. Local acceleration for the first vibration component shown (left: tank tip). **B** in Figures 12 and 13, it was mentioned in Section 2 that the choice of the surrogate model's frequency is not straightforward. The reason behind this is that different tank geometries at different scales can excite different sloshing patterns. Figure 17 shows the spanwise variation of the three sloshing mode frequencies (for modes (2,0), (2,1) and (1,2)) depending on tank cell geometry. For example, Figure 18 shows the high amplitude sloshing patterns developed from the first symmetric sloshing mode (2,0). Since the tank width (dimension in the chordwise direction) is variable, the sloshing frequencies were approximated considering an average tank width for each cell. The direction of excitation is significantly vertical, and the sloshing patterns will be excited when the frequency of excitation (F1 in this case) is double the sloshing modal frequency. This parametric excitation regime generates Faraday waves [28]. Such effects were extensively studied before in the controlled high-amplitude vertical sloshing experiments and were shown to be responsible for energy dissipation [5,7]. As seen in Figure 17, the sloshing mode (2,0) has its frequency in the vicinity of one-half of the first bending mode frequency of the MiniWot demonstrator for most of the tank cells. Furthermore, especially in the cells closer to the tip of the wing model (6,7,8), there are two additional modes (2,1) and (1,2) that may be excited. This suggests that in-plane sloshing influences can be expected at the tip of the wing. Referring to Figure 16, this behaviour can indeed be observed in the recorded footage. This discussion shows that the insights based on the linear modal analysis can still be used to support the analysis of these highly nonlinear and transient sloshing regimes. Figure 18 evidences a similarity between the sloshing patterns based on which the surrogate model was generated (Section 2) and those observed in the MiniWoT experiments. On the left-hand side, the averaged location of the sloshing surface under harmonic excitation can be seen for the 8.3 Hz frequency of excitation. This sloshing pattern involves energy-dissipative liquid impacts on the top of the tank, with substantial influences on the sloshing mode shape (2,0). On the right-hand side, similar patterns are observed in MiniWot tank cells where the local Froude number (\(Fr=\sqrt{A_{1}/g}\)) is similar at approximately 1.17.