*3.1. Temporal Evolution*

The temporal evolutions of the experiments in the present study are shown in Figure 5, displaying the development with time of scour depth at the transducers. Due to the many measuring locations, the data are displayed with increased transparency towards downstream for a clearer distinction. To reduce the potential distraction caused by excessive lines, part of the data of minor significance are deleted from the graph, while the general trends can still be shown clearly. It should also be noted that the transducers are not functional when they are buried or the distance to the bed is smaller than 0.03-m. Thus, part of the scour data at the beginning stage are not available, such that some of the curves start at a non-zero value.

Figure 5a shows the scour temporal evolution for the side-by-side arrangemen<sup>t</sup> with aligned flow. Data from just one of the complex piers are displayed, as the scour patterns are symmetric. Scour at two pile columns of any one of the adjacent piers are very close, and the scour depth at each column decreases towards downstream. Scour between the two complex piers, where the flow is usually contracted and accelerated, is minor during the first 300,000 s (≈3.5 days), followed by comparatively rapid scour when the scour holes produced by the two piers expand and merge. It indicates that the current level of proximity for this arrangemen<sup>t</sup> will not lead to significant contraction scour between two piers under clear-water flow regime. The maximum in-between scour depth occurs at the upstream end of the space and decreases towards downstream, which is similar to the natural profile of the merged scour holes.

When there is a 30◦ skew angle (which is common for river bends or braided channels), as shown in Figure 5b, the scour temporal evolutions at all the measuring locations sugges<sup>t</sup> consistent trends with rapid deepening during the first 100,000 s followed by comparatively slow development of the scour holes to reach equilibrium. Similar to the scour features at stand-alone skewed complex piers (Yang et al. [28]) and pile groups (Zhao and Sheppard [4]; Lança et al. [10]), the maximum scour depths at both of the adjacent piers occur at the downstream ends of the upstream pier flanks (pile A4). Thus, only the data of the pile column at the upstream pier flank (pile A1–A4) of each pier are shown. Generally, the scour depth at each pile column increases towards downstream, in contrast to the aligned arrangement. The scour between the two piers initiates rapidly at the beginning of the experiment without significant stagnation and the maximum equilibrium scour depth occurs at the middle section of the in-between space.

Figure 5c shows the scour temporal evolution at two staggered complex piers. The downstream pier shows an "ascend-descend-equilibrium" trend, which is conjectured to be due to the incoming sediment eroded from the upstream pier filling the downstream scour hole. A similar trend can also be observed for the bed-level data between the piers. The sediment particles entrained and eroded away from the scour hole at the upstream pier are transported towards downstream by wake vortices with a certain skew angle to the pier's centerline; it is observed that the inner path of transport may partially overlap with the downstream pier. As a result, the scour depths at the downstream complex pier are significantly smaller than the upstream pier. The maximum scour depth at each pier still occurs at the

first-row piles. However, for the downstream pier, the scour at the inner side (pile A1) is reduced by the upstream sediment supply.

For the tandem pier arrangement, as shown in Figure 5d, the temporal trend is much simpler than the staggered arrangement. The scour at the downstream pier is significantly mitigated by the upstream pier, which leads to strong vortex shedding observed and thereby the weakened scouring capacity in the lee-wake area.

**Figure 5.** Temporal evolution of clear-water scour depths (*U*/*Uc* = 0.9) measured with: (**a**) side-by-side arrangemen<sup>t</sup> without skew angle; (**b**) side-by-side arrangemen<sup>t</sup> with 30◦ skew angle; (**c**) staggered arrangement; and (**d**) tandem arrangement.
