**2. Experimental Setup and Methodology**

The experiments were conducted in a straight flume that is 11 m long, 0.6 m wide, and 0.7 m deep, in the Hydraulic Modeling Laboratory, Nanyang Technological University. The glass-sided flume walls enabled optical observations through the use of PIV techniques. The test section was located at a distance of 7 m downstream from the flume entrance. A five-bladed propeller with an overall diameter of *<sup>D</sup>*p = 7.5 cm and a hub diameter of *D*h = 1.0 cm was used in this study. The propeller rig was mounted on an appropriately designed movable carriage that spanned transversely across the flume and could be moved along the longitudinal rail installed on the sidewalls of the flume. In this way, the propeller was able to operate at different clearances from the model quay wall, namely the wall clearance *X*w, which is defined as the longitudinal distance between the propeller face and vertical wall. The quay model located downstream of the propeller was built using an acrylic plate with a dimension of 60 cm (height = water level) × 60 cm (width = flume width) × 2 cm (thickness). A 10 cm thick sand bed with uniform sediment of *d*50 (=0.45 mm) was placed on the bottom of the flume. The still water depth above the sand bed was 0.5 m, which is reasonably deep, such that the e ffect of the free surface is negligible. Before the commencement of each test, the sand bed was carefully prepared and leveled to minimize the compaction di fference among di fferent test runs. The experimental setup is shown in Figure 1, in which a right-handed coordinate system (*<sup>o</sup>*-*xyz*) is adopted, with the origin located at the undisturbed bed level and directly beneath the propeller face plane. The *x*-axis is streamwise-oriented along the bottom centerline, the *y*-axis spanwise-oriented toward the starboard, and the *z*-axis along the upward vertical. Accordingly, the mean velocity components in the direction of (*<sup>x</sup>*, *y*, *z*) are represented by (*<sup>u</sup>*, *v*, *w*). The PIV system comprised a 5-W air-cooling laser with a wavelength of 532 nm as the light source and a high-speed camera. The laser was placed on top of the flume and the beam emitted from the laser source passed through the optics, resulting in a laser light fan of 1.5 mm thickness being cast down into the water. The laser sheet was set to align with the propeller axis of rotation, which is in the vertical plane of symmetry of the flume (see Figure 1a). In this way, the streamwise flow data were collected from the sectional view of the jet central plane (see Figure 1b). Meanwhile, using GetData Graph Digitizer Software, the centerline scour profile was determined from the illuminated line where the laser sheet intersects the sand bed. The high-speed camera used (Phantom Miro 320 with Nikkor 50 mm f/1.4 lens) had a maximum resolution of 1920 × 1200 pixels, 12-bit depth, and more than 1200 frames per second (fps) sampling rate. A sampling rate of 300 fps was used in this study to ensure that the particle displacement was within 50% overlap between adjacent interrogation windows for cross-correlation analyses. Aluminium particles with *d*50 of 10 μm and specific density of 2.7 were used as seeding particles. The settling velocity of the aluminium particles was estimated to be 92.6 μm/s using Stoke's law, which is negligible compared with the propeller jet velocity. The same particle has been extensively used in previous studies (e.g., Lin et al. [12], Hsieh et al. [13] and Wei et al. [14]) and validated as a satisfactory seeding particle in PIV applications.

**Figure 1.** Experimental setup of PIV system, (**a**) top view; (**b**) side view; (**c**) end view, where FOV = field of view.

*Water* **2019**, *11*, 1538

For a three-dimensional scour hole induced by a propeller jet, one may find it di fficult to capture the flow field within the scour hole, since the lateral sediment deposition could block the optical access in a normal PIV operation where the camera is 90◦ to the laser sheet. For this reason, Wei and Chiew [10] adopted an oblique particle image velocimetry (OPIV) method, in which the camera was tilted with a depression angle, and thus could capture a complete view of the flow field inside the scour hole. By performing an image correction procedure, their error analysis confirmed a reasonable accuracy of the OPIV method in measuring the flow field within a developing three-dimensional scour hole. Guan et al. [15] have also successfully applied the same protocol for measuring the horseshoe vortex evolution of a pier-scour hole. By following a similar approach as in those studies, the camera in this study was set at a depression angle of 20◦ to cover a rectangular field of view (FOV) in front of the quay wall as shown in Figure 1b,c. To ensure that the entire FOV was in focus, the lens aperture was set to *f* = 5.6 to achieve a su fficient depth of field for the oblique viewing. Before capturing the particle seeded flow field, a calibration plate (with a regularly spaced grid of markers) was placed at the position of the laser sheet in still water, and a calibration image was obtained as shown in Figure 2a, which shows that the coordinates of the markers were distorted from their actual positions due to the oblique viewing. To correct this distortion, a third-order polynomial transformation function was employed, in which the calibration coe fficients were obtained by fitting the position of the distorted dots to the regular grid as shown in Figure 2b. Thereafter, the same calibration parameters were applied to correct all the raw PIV images during the postprocessing stage. A comparison of sample images before and after correction is exemplified in Figure 2c,d. In addition, a Butterworth high pass filter [16] was applied to filter out undesirable light reflections (low-frequency) and highlight the seeding particles (high-frequency), as illustrated in Figure 2c,d. The velocity vector fields were then calculated by using the Davis 8.4.0 software, in which a multi-pass iteration process was adopted with the interrogation windows starting from 64 × 64 pixels to 32 × 32 pixels.

**Figure 2.** Comparison of calibration and PIV images before and after correction.

To examine the influence of wall clearance on the final scour profile, the tests were conducted at four wall clearances, i.e., *X* w = <sup>1</sup>*D*p, 2 *<sup>D</sup>*p, 3 *<sup>D</sup>*p, and 4 *<sup>D</sup>*p, of which the asymptotic scour profiles and their associated flow fields were measured using OPIV. To further examine the temporal development of the flow and scour subject to the wall confinement, a small clearance of *X*w = <sup>2</sup>*D*p was selected as a typical case, for which PIV measurements were carried out during the entire scouring process from the initial instant to the asymptotic state at predetermined time intervals of *t* = 0, 0.5, 2, 12, 24 h. The other variables were kept as constant, including the clearance height *Z*b = *<sup>D</sup>*p, and propeller rotational speed *n* = 300 rpm (revolution per minute), where *Z*b is the vertical distance between the propeller axis and the undisturbed sand bed; and *n* is the propeller rotational speed. The specific test conditions are tabulated in Table 1, in which *U*o is the efflux velocity obtained as the maximum mean velocity along the initial efflux plane (i.e., the propeller disk) [5]; and *F*o is the densimetric Froude number calculated as *U*o/ %( ρ*s*<sup>−</sup>ρ ρ )*gd*50, with ρ*s* denoting the density of sediment grains, ρ the density of water, and *g* the gravitational acceleration. For each case, 3683 images were captured and then used for data analysis. According to a convergence analysis, the maximum residual within the FOV of the mean velocity fields was calculated as 0.00028 m/s. Furthermore, to assess the PIV measurement error, the uncertainty calculation was performed in DaVis software, which quantifies the differences between the two interrogation windows mapped onto each other by the computed displacement vector. In the case of the current study (*X*w = 2*D*p), the velocity vector uncertainty inside the scour hole ranges from 0.002 m/s to 0.023 m/s, which is far less than the target flow velocity. Moreover, a detailed error analysis associated with the OPIV method can be found in Wei and Chiew [10].



#### **3. E**ff**ects of Wall Clearance and Type of Quay**

Figure 3 depicts the comparison of the asymptotic scour profiles between the unconfined (*X*w = ∞) and confined cases at different wall clearances (*X*w = <sup>1</sup>*D*p, <sup>2</sup>*D*p, <sup>3</sup>*D*p, and 4*D*p). Also superimposed in the figure is the unconfined profile that was obtained under the same test conditions, but without any quay wall [10]. Hong et al. [17] observed that an unconfined propeller scour hole comprises a small scour hole directly beneath the propeller (due to the ground vortex), a primary scour hole (due to jet diffusion) and a deposition mound. In contrast, Figure 3 shows that the confined scour profiles around a vertical quay wall were significantly altered, as the primary scour hole was truncated in length but enlarged in depth. In general, with the increasing wall clearance, the development of the scour profile exhibits a trend approaching that of its unconfined counterpart. Specifically, Figure 3a–c show that the scour profiles are featured by a single primary scour hole when *X*w ≤ <sup>3</sup>*D*p. As the wall clearance further increases to *X*w = <sup>4</sup>*D*p, the wall effect is less pronounced, and the scour profile evolves into a combination of a primary scour hole and a small scour hole immediately in front of the wall (see Figure 3d). A similar behavior was also observed by Wei and Chiew [8], who experimentally investigated toe clearance effects on the propeller jet induced scour hole around a sloping quay and found that the asymptotic scour profiles could be classified into three types in terms of the toe clearance, namely, near field (featured by a single toe scour hole), intermediate field (featured by a primary and a toe scour holes), and far field (resembling the unconfined case). However, in terms of the development of the maximum scour depth, Figure 3 shows that its magnitude appears to decrease monotonically as the wall clearance increases, which agrees well with what was observed in Hamill et al. [4]. This further confirms the marked difference of the in scouring mechanisms associated with the closed and open quay, as was already pointed out in the introduction section.

**Figure 3.** Comparison of asymptotic scour profiles between unconfined and confined cases: (**a**) *X*w = <sup>1</sup>*D*p; (**b**) *X*w = <sup>2</sup>*D*p; (**c**) *X*w = <sup>3</sup>*D*p; (**d**) *X*w = <sup>4</sup>*D*p.

To examine the underlying mechanism associated with the observed scour characteristics at different wall clearances, it is useful at this stage to qualitatively discuss the features of the flow pattern within an asymptotic scour hole, which is most explicitly described in the streamline plots as shown in Figure 4. Corresponding to Figure 3, Figure 4a–d depict a comparison of the results obtained in the present study for the four wall clearances, *X*w = <sup>1</sup>*D*p, <sup>2</sup>*D*p, <sup>3</sup>*D*p, and <sup>4</sup>*D*p. Additionally, Figure 4e,f, which present the flow fields around two typical open quay cases with toe clearances of *X*t = <sup>2</sup>*D*p and <sup>4</sup>*D*p, are also included in the figure for illustrating the effect of the type of quay. Please note that the open quay cases were conducted by Wei and Chiew [10] under the same test conditions (e.g., propeller configurations, bed material, etc.) as those in the current study but with an inclining quay.

**Figure 4.** Comparison of streamline plots of the asymptotic state at different wall clearances (vertical quay wall) and toe clearances (slope quay wall): (**a**) *X*w = <sup>1</sup>*D*p; (**b**) *X*w = <sup>2</sup>*D*p; (**c**) *X*w = <sup>3</sup>*D*p; (**d**) *X*w = <sup>4</sup>*D*p; (**e**) *X*t = <sup>2</sup>*D*p; (**f**) *X*t = <sup>4</sup>*D*p. Note: (**e**) and (**f**) are reproduced from Wei and Chiew [10].

In general, Figure 4a,b reveal that the dimension of the asymptotic scour hole is closely related to the size of vortex that resides in it. Specifically, Figure 4a,b show that with small wall clearances, in other words, intense wall effects, there exists a complex vortex system comprising three vortices in front of the wall, in which the primary vortex completely fills the entire scour hole, signifying its dominating role in shaping the scour hole. As the wall effect decreases with the increase in wall clearance, only one vortex that is responsible for scouring persists at *X*w = <sup>3</sup>*D*p (see Figure 4c). When *X*w = <sup>4</sup>*D*p, Figure 4d reveals that only a feeble vortex remains, with the formation of a small scour hole at the base of the quay wall because the majority of jet energy has already been dissipated before the jet impinges onto the wall. Based on this observation, one can reasonably infer that in the case of the closed quay, the confinement effect of the wall plays a crucial role in generating and stabilizing the vortex, which in turn facilitates the scouring development. An implication of this phenomenon is that the formation of a well-established vortex, i.e., the driving force of the scouring action, is positively related to the wall effect, which provides an explanation for the observed inverse correlation between the maximum scour depth and wall clearance. On the other hand, in the case of the open quay, only one vortex can be observed around the slope toe, even with the small toe clearance of *X*t = <sup>2</sup>*D*p (see Figure 4e). This is because the sharp edge of the slope toe fixes the separation point at the toe, thus limiting the size of the vortex. Moreover, the open type quay, as its name implies, provides an open space above the slope for jet energy dissipation, which allows much of the jet energy to be deflected upwards along the slope upon the flow separation takes place at the toe. This is especially true for the cases with the small clearance, i.e., the near field scenario defined in Wei and Chiew [10], in which the maximum scour depth is positively correlated with the toe clearance, thus highlighting a significant difference between the scouring mechanism in open and closed quay.

For larger wall/toe clearances, Figure 4d,f show that for the upstream portion, where the jet essentially is unconfined, the primary scour hole is subject to the direct impact associated with the radial expansion of the jet, in which the underlying scouring mechanism resembles that of an unconfined propeller scour. Given the similarities of the scour profile and the associated flow structures shown in Figure 4d,f, one may conclude that as the wall/slope effect decreases with the increasing wall/toe clearance, the type of the quay, either closed (with vertical wall) or open (with slope wall) types, does not matter as much as in the small clearance cases.

#### **4. Temporal Development of Mean Flow Structure**
