*4.1. Evolution of Vortex System*

To further examine how the vortex system evolves during the scouring process, the temporal development of the flow field at a near wall clearance case of *X*t = <sup>2</sup>*D*p is exemplified in this section. Figure 5 compares the flow patterns at different scouring phases (*t* = 0, 0.5, 2, 12, and 24 h) in terms of the mean vorticity contour (left column) and the streamline plot (right column). The out-of-plane vorticity is calculated by using ω = ∂*w*∂*x* − ∂*u*∂*z* and normalized with the propeller diameter *<sup>D</sup>*p and efflux velocity *U*o. It should be noted that the mean velocity vectors are also superimposed in the vorticity contour, in which the magnitude and direction of the velocity vectors are calculated as (*u*<sup>2</sup> + *w*2)1/<sup>2</sup> and tan−1(*w*/*u*), respectively. For the convenience of discussion, the three vortices identified in the streamline plots are hereinafter referred to as V1, V2, and V3, whose center locations are denoted as VC1, VC2, and VC3, respectively.

Before a close examination of Figure 5, it would be helpful to revisit the flow structures associated with the free expanding jet and the confined jet in the presence of a quay wall alone. Several previous studies have shown that a free expanding propeller jet features an iconic double-stream flow structure due to the presence of the hub at the center of the propeller disk [14,18,19]. Wei and Chiew [11] reported that when the propeller jet is placed in the vicinity of a vertical wall, its two streams, namely, upper and lower streams, would be forced to spread out and deflected upwards and downwards along the wall, resulting in a pair of symmetrical vortices in between.

**Figure 5.** Temporal development of flow patterns within developing scour hole at *X*w = <sup>2</sup>*D*p: (**a1**,**a2**) *t* = 0 h; (**b1**,**b2**) *t* = 0.5 h; (**c1**,**c2**) *t* = 2 h; (**d1**,**d2**) *t* = 12 h; (**e1**,**e2**) *t* = 24 h.

In the context of the current study with a scour hole, Figure 5 depicts the spread-out features of the two jet streams, similar to that observed in Wei and Chiew [11]. More explicitly, both the upper and lower streams are characterized by a pair of outer and inner shear layers with opposite signs, as denoted in Figure 5a1. A side-by-side comparison between Figure 5a1,a2 reveal that V1 and V2 essentially reside within the triangular region between the spread-out jet streams. The zero-vorticity layer (in white) between the positive (in red) and negative (in blue) shear layers, in fact, reflects a layer of zero-shear-stress which determines the separation line that envelops V1 and V2. Accordingly, the counterclockwise V1 and clockwise V2 are associated with the lower shear layer (with positive vorticity) and upper shear layer (with negative vorticity), respectively, which is consistent with those observed in Wei and Chiew [11]. This comparison is important because it indicates that the formation mechanism of V1 and V2 is exclusively related to the deflection effect that is associated with the jet impingement on the wall and has nothing to do with the presence of the bed, although they are no longer symmetrical due to the confinement effect of the latter. On the contrary, a near-bed vortex, V3, which is absent in Wei and Chiew [11], is directly emanated from the flow separation that occurred at the bed.

As the scour hole evolves, it is interesting to note that the shear layer structure associated with the spread-out jet streams seems to be constant and steady during the entire scouring process, although the developing scour hole, to some extent, allows the lower stream to be expanded farther downwards (Figure 5b1,e1). It therefore can be concluded that the presence and development of the scour hole have little impact on the spread-out flow structure, which primarily is dependent on the wall effect. In contrast, the streamline plots on the right column of Figure 5 depicts a considerable variation in the overall structure of the vortex system from the initial to asymptotic state. Specifically, at the initial instant of *t* = 0, Figure 5a2 shows that the presence of the flatbed prevents the formation of the downward flow, which would otherwise occur when the lower stream impinges on the vertical wall in the absence of the bed. Instead, a strong upward flow can be found along the vertical wall, which enhances the strength of V1 and squeezes V2 to the upper right corner of the FOV. On the other side, V3 is still in its embryonic phase. Thus, one could surmise that at the initial instant, it is V1 that is the driving force for the onset of scouring, during which the bed sediment particles are entrained in a counter-clockwise manner and transported to the lateral sides by the vortex tube formed in front of the wall. As soon as an initial local scour hole is excavated around the base of the quay wall, the original "confinement effect" associated with the flatbed diminishes, allowing the jet flow (lower stream) to be deflected downwards along the wall. As a result, a clockwise vortex is expected to be formed inside the scour hole. This is exactly what is shown at the subsequent time of *t* = 0.5 h in Figure 5b2, in which a well-established V3 is present, resembling the horseshoe vortex in a pier scour hole. This vortex, in turn, facilitates the subsequent scouring process, during which the bed sediment would be driven to the upstream by the clockwise flow, finally depositing at the upstream of the propeller or being carried away with the oncoming jet flow. Meanwhile, Figure 5b2 also shows that without the effect of the previously observed upward flow at *t* = 0 h, V1 and V2 appear to be quasi-symmetrical about the propeller axis, similar to those observed by Wei and Chiew [11]. From then on, Figure 5b2–e2 simply show that V3 is exclusively responsible for the scouring action, during which the sediments are swept in the clockwise fashion from the bed bottom and carried upstream largely in the form of bedload (visual observation). More interestingly, the enlargement of the scour hole does not support a further development of V1 and V2 as one could have envisioned. On the contrary, the enhancement of the primary vortex (V3) within the scour hole appears to overwhelm the growth of V1 and V2. In particular, V1 exhibits an evident shrinking trend from *t* = 0.5 h to *t* = 12 h, while V2 seems to be able to maintain its size. Thereafter, the vortex system appears to be stabilized by the presence of the large scour hole. At *t* = 24 h, both the size and position of all the three vortices are found to reach an asymptotic state when the scouring process ceases.
