# Scour around Piers under Waves: Current Status of Research and Its Future Prospect

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^{2}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Concept of Scour

#### 1.2. Types of Scour

#### 1.2.1. General Scour

#### 1.2.2. Localized Scour

#### 1.2.3. Constriction Scour

#### 1.2.4. Local Scour

#### 1.2.5. Clear-Water Scour and Live-Bed Scour

## 2. Scour under Waves

_{m}is the maximum wave-induced velocity, and T

_{w}is the wave period. For 6 < KC < 100, the vortex shedding is the only governing factor of the scour process under waves [26,27] (see Figure 3). In the case of scour under waves, each shed vortex formed due to the presence of a pier moves the sediment particles away from the vicinity of the pier, directing them downstream. As a result, the scour hole is formed around the pier for every half period of waves.

#### 2.1. Scour Depth

_{rms}and the peak wave period T

_{wp}, following the procedure of Zyserman and Fredsøe [32], with the addition of suspended sediment concentration. They expressed the KC number as the following:

_{rms}is $\sqrt{2}$σ

_{u}, ${\sigma}_{u}^{2}$ is $\underset{0}{\overset{\infty}{\int}}{S}_{u}({\omega}_{a})\mathrm{d}{\omega}_{a}$, S

_{u}(ω

_{a}) is the spectrum of the instantaneous near-bed wave-induced velocity u(t), and ω

_{a}is the angular frequency of wave.

_{r}, of 0.74, 0.38, and 0.23. While changing the D

_{r}from 0.23 or 0.38 to 0.74, they found 1.6 to 2 times the increment of scour depth.

_{cr}is the critical inflow velocity for the initiation of sediment motion, u is the orbital velocity, x

_{rel}is the relative water displacement [= x

_{eff}/(1 + x

_{eff})], and x

_{eff}is the effective water displacement [= 0.03(1 − 0.35u

_{cr}/u)(KC − 6)]. It is worth highlighting that, unlike Equation (2), Equation (4) considers not only the effects of the KC number, but also the effects of critical velocity of sediment on scour depth.

_{eD}, and the seabed ripples on the formation of scour depth. However, they found that these two parameters are less significant in the scour process under waves. Myrhaug and Ong [37] used the data of Dey et al. [14] and presented a stochastic approach for calculating the maximum scour depth around a pier for two kinds of nonlinear random waves: 2D long-crested and 3D short-crested waves. They reported an increment in the wave-induced scour depth, with a reduction of clay content in a sand–clay mixture for both the 2D and 3D waves.

_{s}is the sediment number, R

_{ed}is the grain Reynolds number based for the bed grain diameter, d, and D

_{r}is the relative density.

_{c}, where Θ

_{c}is the critical Shields parameter. However, the S/D decreases with a further increase in Shields parameter, Θ, due to sediment backfill into the scour hole [44].

#### 2.2. Scour-Hole Shape and Size

#### 2.3. Timescale

_{t}(t) as the following:

_{t}(t) curve at t = 0 (Figure 7). The T can also be achieved by differentiating Equation (9) with respect to time, t.

^{0.5}/D

^{2}, s is the relative density of sediment, g is the acceleration due to gravity, and d

_{50}is the median sediment size. It is evident that the T* increases with an increase in KC number. This is because of the fact that the amount of sediment to be transported from the scour hole increases as the KC number increases. By contrast, the T* reduces with an increase in Shields parameter, Θ.

## 3. Closure and Future Prospects

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Development of scour depth around a pier, with time and approach velocity. Here, (d

_{se})

_{max}corresponds to the maximum scour depth at equilibrium condition.

**Figure 3.**Pictorial view of scour hole around a vertical pier. (

**a**) Scour under waves, where the vortex shedding is the main mechanism for 6 < KC < 100. (

**b**) Scour under steady current, where downflow, horseshoe vortex, and wake vortices are the key mechanisms.

**Figure 4.**Nondimensional scour depth, S/D, versus Keulegan–Carpenter number, KC number, for different values of clay fraction n in sand–clay mixtures, where the solid line for n = 0 represents Equation (2), given by Sumer et al. [26].

**Figure 5.**Nondimensional scour depth, S/D, versus Keulegan–Carpenter number, KC number, under waves.

**Figure 6.**Variation of nondimensional scour depth, S/D, with Shields parameter, Θ, for different sets of KC numbers under waves.

**Figure 8.**Temporal variation of nondimensional scour depth, S

_{t}/D, under waves at different points around a circular cylinder.

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**MDPI and ACS Style**

Gazi, A.H.; Afzal, M.S.; Dey, S. Scour around Piers under Waves: Current Status of Research and Its Future Prospect. *Water* **2019**, *11*, 2212.
https://doi.org/10.3390/w11112212

**AMA Style**

Gazi AH, Afzal MS, Dey S. Scour around Piers under Waves: Current Status of Research and Its Future Prospect. *Water*. 2019; 11(11):2212.
https://doi.org/10.3390/w11112212

**Chicago/Turabian Style**

Gazi, Ainal Hoque, Mohammad Saud Afzal, and Subhasish Dey. 2019. "Scour around Piers under Waves: Current Status of Research and Its Future Prospect" *Water* 11, no. 11: 2212.
https://doi.org/10.3390/w11112212