**1. Introduction**

Bridges play an important role in the transportation of goods and people across rivers. In civil engineering, one of the most important issues is to protect bridge piers from collapse. In fact, their foundation may be threatened by localized scour, as a result of the flow constriction of the cross-sectional area, and the subsequent increase of the flow velocity [1]. Thus, in order to ensure the protection of such structures, it is of a high priority to predict the flow field and sediment transport around the bridge piers.

Many researchers have studied the vortice systems around piers, stating that they primarily affect the local scour [2–6]. Melville and Coleman [5] stated that the flow field around a bridge pier is characterized by down-flow, surface roller, and wake vortices, such as the horseshoe vortex, at the base of the pier, and wake vortices behind the pier. According to Melville [2] and Chiew [4], a horseshoe vortex increases the flow velocity near the bed, and the wake vortex carries the eroded bed material downstream. However, the effect of the pier on flow separation, and the consequent sediment transport, depends on turbulence.

Some studies have investigated the stochastics nature of turbulent flow around a pier [2,7–11], but there still remains a lack information concerning the trend of higher order moments for the fluctuating velocities.

As the safety of the pier depends on the depth and volume of the scoured region around it, most researchers focus on the estimation of the maximum scour depth around the pier [5,12–15], developing, from laboratory and field data, empirical relations different from each other, for model or equation parameters. Melville and Coleman [5] proposed a scour depth prediction model depending on several parameters, such as flow depth, pier geometry, and flow intensity. Chavan and Kumar [14], from the experimental data, developed an empirical equation for the estimation of the scour depth in alluvial channels with a downward seepage.

Alluvial channels have granular permeable boundaries; hence, the flow field is a complex interaction between the surface and subsurface flow, as water is either seeping in (upward seepage) or seeping out (downward seepage) from the channel [15]. Shukla and Misra [16] quantified the water loss as a result of seepage as nearly 45% of the total flow volume. Tanji and Kielen [17] observed that the seepage losses in the earthen channels in semi-arid areas range between 20% and 50%. Kinzli et al. [18], and Martin and Gates [19] estimated that water loss as a result of downward seepage was around 15% and 40%, respectively. Moreover, seepage affects the channel morphology [20–22] and increases the streamwise velocity near the bed [23–26].

The aim of this study is to deepen the description of the turbulent flow field around a single vertical bridge pier set in a seepage-affected alluvial channel, and to develop empirical relations for evaluating scour hole characteristics such as length, width, area, and volume, including the downward seepage parameters.

## **2. Experimental Set-Up and Procedure**
