## 4 Analysis of the Influence of Water Depth on Air Layer Drag Reduction
### Effect on the Drag Reduction  
The effects of channel depth variation on drag reduction for two distinct model speeds--\(F_{r}\) = 0.057 and \(F_{r}\) = 0.091--under saturated jetting circumstances are shown in Tables 7 and 8. In the Tables, \"No Groove\" denotes a model without a bottom groove, \"Groove No Jetting\" denotes a model with a bottom groove but no air injection, and \"Groove Saturated Jetting\" denotes a model with a bottom groove and jetting with the saturated airflow rate. In Tables 7 and 8, \"Relative Reduction\" indicates a reduction in resistance when comparing the resistance of \"Groove Saturated Jetting\" with \"Groove No Jetting\", whereas \"Absolute Reduction\" indicates a reduction in resistance when comparing the resistance of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{_h/T_} & \multicolumn{3}{c}{\(R_{t}\) (N)} & \multicolumn{3}{c}{**Resistance Reduction (N)**} & \multicolumn{3}{c}{**Reduction Rates (\%)**} \\ \cline{2-9}  & **No Groove** & **Groove No Jetting** & **Groove Saturated Jetting** & **Relative** & **Absolute** & **Relative** & **Absolute** \\ \hline
1.18 & 12.33 & 14.33 & 9.84 & 4.48 & 2.49 & 31.33\% & 20.19\% \\
1.35 & 10.34 & 11.30 & 7.63 & 3.67 & 2.71 & 32.48\% & 26.21\% \\
2.25 & 7.17 & 7.71 & 5.60 & 2.11 & 1.57 & 27.37\% & 21.90\% \\
4.0 & 5.90 & 6.47 & 5.01 & 1.45 & 0.88 & 22.57\% & 15.08\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Effect of water depth on total resistance reduction (\(F_{r}\) = 0.057). Figure 10: Wave motion and spillover of air layer in ultra-deep and ultra-shallow water. (**a**) deep water (\(h/T\) = 4); (**b**) extremely shallow water (\(h/T\) = 1.18). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{_h/T_} & \multicolumn{3}{c}{\(R_{t}\) (N)} & \multicolumn{3}{c}{**Resistance Reduction (N)**} & \multicolumn{3}{c}{**Reduction Rates (\%)**} \\ \cline{2-9}  & **No Groove** & **Groove No Jetting** & **Groove Saturated Jetting** & **Relative** & **Absolute** & **Relative** & **Absolute** \\ \hline
1.18 & 29.08 & 34.04 & 22.25 & 11.79 & 6.84 & 34.64\% & 23.52\% \\
1.35 & 24.28 & 26.30 & 17.41 & 8.88 & 6.86 & 33.76\% & 28.25\% \\
2.25 & 16.85 & 18.27 & 10.11 & 8.16 & 6.75 & 44.66\% & 40.06\% \\
4.0 & 13.89 & 15.37 & 10.08 & 5.28 & 3.81 & 34.35\% & 27.43\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Effect of water depth on total resistance reduction (\(F_{r}\) = 0.091). \"Groove Saturated Jetting\" with \"No Groove\". The appropriate ratios of the reduction in resistance are shown by the relative drag reduction rate and absolute drag reduction rate. As can be seen from Tables 7 and 8, the overall model resistance rises for all scenarios of \"No Groove\", \"Groove No Jetting\", and \"Groove Saturated Jetting\" as the water depth decreases. In comparison to the situation without jetting, the decrease in total resistance brought on by jetting rises initially and then falls as the water depth lowers. The absolute drag reduction rate and relative drag reduction rate both show this pattern. Depending on the model speed, different water depths correspond to the best drag reduction efficacy. If \(F_{r}\) is 0.057, the depth-to-draft ratio at which the drag reduction is most effective is 1.35; if \(F_{r}\) is 0.091, the ratio at which the drag reduction is most effective is 2.25. However, the absolute and relative drag reduction rates are greater than 30% and 20%, respectively, even in extremely shallow water circumstances. This suggests that even in shallow and extremely shallow water, the jetting drag reduction technique still has a noticeable drag reduction effect. The impacts of bottom groove jetting on frictional resistance under various water depths are provided in Tables 9 and 10, which help to further study the variation of various resistance components. The following observations can be drawn from the tables: (1) The model with a bottom groove but no jetting displays a decrease in frictional resistance in comparison to the \"No Groove\" example.