## 4 Complex Coupled Effect of Propeller-Induced Wave Impact on Vegetated Flow  
In this section, the coupled effect of vegetated flow with propeller-induced dynamics is investigated. To study the impact of propeller operation on vegetation-induced flow patterns, the afore-discussed three-layer vegetated flow model (i.e., with modified log law at the inner vegetation zone) was coupled with the propeller model in Equations (14) and (15) to perform various theoretical tests on submerged vegetated flow fields. For the tested vegetation channel, the water depth was set at 35 cm with a vegetation height of 20 cm. A total of four theoretical tests with different propellers were conducted, in which their test conditions are summarised in Table 2. Each propeller test was executed at a range of speeds, n: 500, 750, 1000, 1250, and 1500 RPM; and the propeller has been placed at three different vertical locations for testing: 26.0 cm above the bed (at free-water layer), 20.0 cm (at interface zone between vegetation and free-water layers), and 10.6 cm (at vegetation layer). In Figures 6-9, one can observe that all calculated coupled velocity profiles for different propellers have reasonable features, such as vegetated flow profile shape and propeller-driven flow turbulence. In terms of distribution across different RPMs of speed, the propeller with a higher n incited higher velocity (consistently featured for all tests), which is sensible. Detailed analysis revealed that there is a mix of flow characteristics when the propeller was placed at vegetated, interfacial, and free-water zones. When it is located at the free-water layer, one can observe that the flow propagation presents a balanced \"M\" shape. When free from the vegetated field, the free-water flow introduces no resistance to the original propeller-induced profile; hence, the 'M' shape remains almost undisturbed. Figure 5: Comparison of the calculated result with measured data of **(a)** Run F-3 by [PERSON] [8] and the **(b)** test with various n by [PERSON] and [PERSON] [9]. However, at the interface and vegetated zones, the 'M' shape was distorted due to vegetation's obstructive effect. For both of those zones, it was found that the profile was enhanced at the upper portion of the propeller's hub, expanding its profile as compared to the lower part. The upper part of the interface zone was located at an unobstructed zone and, hence, permitted less restriction to the propagation of flow and caused higher profiles. Moreover, the flow's momentum from the lower portion of the propeller was transferred to the upper half in order to cause shrinkage in the lower profile. In the vegetated layer, the velocity profile's calculation was heavily influenced by the coupled model's \(\mathrm{k_{s}}\) at the lower half from the propeller hub, and this caused low velocities. Figure 6: Propeller 1’s coupled model results for different n when the propeller is located at (**a**) free-water, (**b**) interface, and (**c**) vegetation zones. Figure 8: _Cont._  
Figure 7: Propeller 2’s coupled model results for different n when the propeller is located at (**a**) free-water, (**b**) interface, and (**c**) vegetation zones. Figure 8: Propeller 3’s coupled model results for different n when the propeller is located at (**a**) free-water, (**b**) interface, and (**c**) vegetation zones. \begin{table}
\begin{tabular}{l c c c c} \hline  & **D\({}_{\text{p}}\) (cm)** & **Blade Area Ratio, \(\beta\)** & **Number of Blades, N** & **x/D\({}_{\text{p}}\)** \\ \hline
**Propeller 1** & 7.6 & 0.4700 & 3 & 4.605 \\ \hline
**Propeller 2** & 9.2 & 0.4525 & 4 & 3.804 \\ \hline
**Propeller 3** & 10.3 & 0.6417 & 4 & 3.398 \\ \hline
**Propeller 4** & 13.1 & 0.9220 & 6 & 2.672 \\ \hline \end{tabular}
\end{table} 
Table 2: Input data from theoretical tests on vegetated flow. Figure 9: _Cont_. Due to the importance of this coupled flow phenomenon, it is crucial that further studies will be carried out after this research study.