3.1.1. Turbulence Intensities

Around the pier, the distributions of the fluctuating components of the streamwise and vertical instantaneous velocity (σ*u* and σ*w*, respectively), expressed as root mean square (RMS), have been evaluated for the different discharges and percentages of seepage. In Figure 2, σ*u* and σ*w*, scaled with the shear velocity (*u*\*), are expressed as *u*\* = √ (τ/ρ; where τ = γ*RS* is the bed shear stress, ρ is the flow density, *R* is hydraulic radius, and *S* is the bed slope), versus the distance (*z*) from the bed, scaled with the flow depth (*h*), represented as *h*+, are shown.

**Figure 2.** Non-dimensional distributions of turbulence intensities.

Upstream of the pier (U), σ*u* and σ*w* show similar trends. In particular, σ*u* is lower near the bed, because of the reversal flow. With respect of the zero seepage, σ*u* is reduced by 15% in case of 10% seepage, and by 22% averagely in case of 15% seepage. For the different seepage percentages, σ*u* and σ*w* attain higher values at the edge of the scour hole (*h*+ ≈ 0.1), then, increasing in *h*+; while σ*w* shows a nearly constant value, σ*u* slightly decreases, oscillating around a constant value.

Downstream of the pier (D), where there is no obstruction to the flow, for the different seepage percentages, σ*w* shows an increasing trend, attaining higher values than in the section U, because of the wake vortices behind the pier. Near the free surface, σ*w* slightly decreases, because of the reduced strength of the wake vortices in the presence of the lateral flow through the channel boundaries. For the zero seepage percentage, σ*u* shows a nearly constant value, while it slightly decreases, with scattering trends, for the seepage percentages of 10% and 15%, respectively.

Laterally to the pier (S1), in the case of 10% and 15% seepage percentages, near the bed (*h*+ < 0.2), σ*u* and σ*w* increase at an average about 20%–30% and 25%–35% with no seepage value, respectively, because of the enhanced turbulence near the bed.
