# Quantitative Spatio-Temporal Characterization of Scour at the Base of a Cylinder

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## Abstract

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## 1. Introduction

## 2. Experimental Set Up and Data Collection

_{50}= 3.55 mm, geometric standard deviation, σ = 1.35, and angle of repose, φ = 35°. The approach flow depth, H, was 0.205 m, the approach depth-averaged flow velocity (V) was 0.620 m/s, and the water temperature (T) was 25 °C. The model pier was a circular cylinder with diameter, D, equal to 0.152 m. The cylinder was mounted on the center of the flume approximately 50 flow depths downstream of its entrance to ensure that the flow was fully developed [31]. The experiment lasted for 250 min. The most relevant dimensionless parameters of the experiment are: τ/τ

_{c}= 0.95, H/D = 1.35, D/d

_{50}= 43, Re

_{D}= 81,000, Re

_{H}= 109,000, Fr = 0.44; where τ: bed shear stress; τ

_{c}: critical bed shear stress for sediment entrainment, Re

_{D}: pier diameter-based Reynolds number (Re

_{D}= VD/ν, ν: kinematic viscosity), Re

_{H}: approach flow depth-based Reynolds number (Re

_{H}= VH/ν), and Fr: Froude number (Fr = V/(gH)

^{0.5}, g: gravitational acceleration). The critical shear stress (τ

_{c}) was found experimentally by the gradual increase of the flow velocity and the observation of the flume for sporadic sediment entrainment.

^{2}was represented by more than 6500 pixels. The distance of the cameras from the bed and the cylinder were approximately 180 mm and 400 mm, respectively. Before the beginning of the experiment, water was introduced gradually, while an adjustable tailgate at the downstream end of the flume was raised. As soon as the flow reached the desired depth, the cameras were synchronized using a stroboscopic light, and started recording videos. The target velocity was reached by adjusting the flow discharge and the tailgate. At the completion of the experiment, the flow discharge was reduced and the tailgate was raised. Before draining the flume, the velocity of the flow was greatly decreased and the bed bathymetry was measured with a point gauge to validate the accuracy of the primary measurements.

^{2}of the bed was represented by more than 6000 points at every instant. The accuracy of the measurements was 0.86 mm and the precision was 2.31 mm. The detailed description of the technique along with investigations of its accuracy and reliability are presented in [30]. Overall, this methodology allows for the continuous collection of very high temporal and spatial resolution measurements of the bed topography, while being minimally intrusive. Though numerous experiments using similar configurations have been carried out in the past, this is the first time, to the authors’ knowledge, that such high quality quantitative observations of the scour around a pier have been made possible.

## 3. Results

#### 3.1. Overview of the Scour Hole Evolution

#### 3.2. Overview of the Scour Rate Evolution and Distribution

#### 3.3. Dependence of Scour Depth on Location and Time

^{2}) and the sum of squared errors (SSE). It was found that the temporal evolution of the scour depth at every location with θ < 130° could be optimally (R

^{2}> 0.95) described by a piecewise power function, with one breakpoint. The area of the scour hole with θ ≥ 130° was described less successfully (R

^{2}~ 0.7) by power functions. Table 1 shows the general form of the equations that describe scour as a function of time and Figure 7 illustrates some examples of the curve fitting results. The breakpoint that most accurately separates the two distinct scour rates was placed successfully at t = 9 min for the locations where scour started during the first 3 min of the experiment (see Figure 2). At the locations where scour started later, the breakpoint was placed at succeeding instants that varied significantly.

^{2}> 0.9) with linear curves whose slopes remain relatively constant in time but vary with θ. On the other hand, the radial profiles at θ ≥ 130° cannot be represented with linear functions of r as effectively. Instead second- or third-degree polynomials should be used to approximate the local bed topography along angular planes at the wake (Table 1).

## 4. Discussion

#### 4.1. Interpretation of the Results

#### 4.2. Evaluation of the Measurements

^{2}) it is expected that the results and discussion presented here cannot be significantly affected. Finally, though an investigation of the characteristics of the depositional area would be very interesting, such information is not necessary for the conclusions that are drawn here.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Johnson, P.A.; Jones, J.S. Merging laboratory and field data in bridge scour. J. Hydraul. Eng.-ASCE
**1993**, 119, 1176–1181. [Google Scholar] [CrossRef] - Sheppard, D.M.; Demir, H.; Melville, B.W. Scour at Wide Piers and Long Skewed Piers; National Research Council (U.S.), Transportation Research Board, National Cooperative Highway Research Program, American Association of State Highway and Transportation Officials, and Federal Highway Administration: Washington, DC, USA, 2011. [Google Scholar]
- Baker, C.J. The Turbulent Horseshoe Vortex. J. Wind. Eng. Ind. Aerod.
**1980**, 6, 9–23. [Google Scholar] [CrossRef] - Dargahi, B. The Turbulent-Flow Field around a Circular Cylinder. Exp. Fluids
**1989**, 8, 1–12. [Google Scholar] [CrossRef] - Devenport, W.J.; Simpson, R.L. Time-dependent and time-averaged turbulence structure near the nose of a wing body junction. J. Fluid Mech.
**1990**, 210, 23–55. [Google Scholar] [CrossRef] - Apsilidis, N.; Diplas, P.; Dancey, C.L.; Bouratsis, P. Time-resolved flow dynamics and Reynolds number effects at a wall-cylinder junction. J. Fluid Mech.
**2015**, 776, 475–511. [Google Scholar] [CrossRef] - Paik, J.; Sotiropoulos, F. Numerical simulation of strongly swirling turbulent flows through an abrupt expansion. Int. J. Heat Fluid Flow
**2010**, 31, 390–400. [Google Scholar] [CrossRef] - Escauriaza, C.; Sotiropoulos, F. Initial stages of erosion and bed form development in a turbulent flow around a cylindrical pier. J. Geophys. Res.-Earth
**2011**, 116. [Google Scholar] [CrossRef] - Koken, M.; Constantinescu, G. An investigation of the dynamics of coherent structures in a turbulent channel flow with a vertical sidewall obstruction. Phys. Fluids
**2009**, 21, 085104. [Google Scholar] [CrossRef] - Istiarto, I.; Graf, W.H. Experiments on flow around a cylinder in a scoured channel bed. Int. J. Sediment Res.
**2001**, 16, 431–444. [Google Scholar] - Dey, S.; Raikar, R.V. Characteristics of horseshoe vortex in developing scour holes at piers. J. Hydraul. Eng.-ASCE
**2007**, 133, 399–413. [Google Scholar] [CrossRef] - Debnath, K.; Manik, M.K.; Mazmder, B.S. Turbulence statistics of flow over scoured cohesive sediment bed around circular cylinder. Adv. Water Resour.
**2012**, 41, 18–28. [Google Scholar] [CrossRef] - Kumar, A.; Kothyari, U.C.; Raju, K.G.R. Flow structure and scour around circular compound bridge piers—A review. J. Hydro-Environ. Res.
**2012**, 6, 251–265. [Google Scholar] [CrossRef] - Beheshti, A.A.; Ataie-Ashtiani, B. Scour hole influence on turbulent flow field around complex bridge piers. Flow Turbul. Combust.
**2016**, 97, 451–474. [Google Scholar] [CrossRef] - Melville, B.W.; Chiew, Y.M. Time scale for local scour at bridge piers. J. Hydraul. Eng.-ASCE
**1999**, 125, 59–65. [Google Scholar] [CrossRef] - Kothyari, U.C.; Hager, W.H.; Oliveto, G. Generalized approach for clear-water scour at bridge foundation elements. J. Hydraul. Eng.-ASCE
**2007**, 133, 1229–1240. [Google Scholar] [CrossRef] - Simarro, G.; Teixeira, L.; Cardoso, A.H. Closure to “Flow Intensity Parameter in Pier Scour Experiments” by Gonzalo Simarro, Luis Teixeira, and Antonio H. Cardoso. J. Hydraul. Eng.-ASCE
**2009**, 135, 155. [Google Scholar] [CrossRef] - Link, O.; Castillo, C.; Pizarro, A.; Rojas, A.; Ettmer, B.; Escauriaza, C.; Manfreda, S. A model of bridge pier scour during flood waves. J. Hydraul. Res.
**2016**. [Google Scholar] [CrossRef] - Oliveto, G.; Hager, W.H. Temporal evolution of clear-water pier and abutment scour. J. Hydraul. Eng.-ASCE
**2002**, 128, 811–820. [Google Scholar] [CrossRef] - Lu, J.Y.; Shi, Z.Z.; Hong, J.H.; Lee, J.J.; Raikar, R.V. Temporal Variation of Scour Depth at Nonuniform Cylindrical Piers. J. Hydraul. Eng.-ASCE
**2011**, 137, 45–56. [Google Scholar] [CrossRef] - Umeda, S.; Yamazaki, T.; Ishida, H. Time evolution of scour and deposition around a cylindrical pier in steady flow. In Proceedings of the International Conference on Scour and Erosion, Tokyo, Japan, 5–7 November 2008; pp. 140–146.
- Dodaro, G.; Tafarojnoruz, A.; Sciortino, G.; Adduce, C.; Calomino, F.; Gaudio, R. Modified Einstein sediment transport to simulate the local scour evolution downstream a rigid bed. J. Hydraul. Eng.-ASCE
**2016**, 142. [Google Scholar] [CrossRef] - Radice, A.; Porta, G.; Franzetti, S. Analysis of the time-averaged properties of sediment motion in a local scour process. Water Resour. Res.
**2009**, 45, 12. [Google Scholar] [CrossRef] - Radice, A.; Tran, C.K. Study of sediment motion in scour hole of a circular pier. J. Hydraul. Res.
**2012**, 50, 44–51. [Google Scholar] [CrossRef] - Link, O.; Pfleger, F.; Zanke, U. Characteristics of developing scour-holes at a sand-embedded cylinder. Int. J. Sediment Res.
**2008**, 23, 258–266. [Google Scholar] [CrossRef] - Dargahi, B. Controlling Mechanism of Local Scouring. J. Hydraul. Eng.-ASCE
**1990**, 116, 1197–1214. [Google Scholar] [CrossRef] - Kirkil, G.; Constantinescu, G. Flow and turbulence structure around an in-stream rectangular cylinder with scour hole. Water Resour. Res.
**2010**, 46, W11549. [Google Scholar] [CrossRef] - Escauriaza, C.; Sotiropoulos, F. Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System. Flow Turbul. Combust.
**2011**, 86, 231–262. [Google Scholar] [CrossRef] - Khosronejad, A.; Kang, S.; Sotiropoulos, F. Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour.
**2012**, 37, 73–85. [Google Scholar] [CrossRef] - Bouratsis, P.; Diplas, P.; Dancey, C.L.; Apsilidis, N. High-resolution 3-D monitoring of evolving sediment beds. Water Resour. Res.
**2013**, 49, 977–992. [Google Scholar] [CrossRef] - Sabersky, R.H.; Acosta, A.J.; Hauptmann, E.G. Fluid Flow: A First Course in Fluid Mechanics, 3rd ed.; Collier Macmillan: New York, NY, USA, 1989. [Google Scholar]
- Diplas, P.; Dancey, C.L.; Celik, A.O.; Valyrakis, M.; Greer, K.; Akar, T. The role of impulse on the initiation of particle movement under turbulent flow conditions. Science
**2008**, 322, 717–720. [Google Scholar] [CrossRef] [PubMed] - Mia, F.; Nago, H. Design method of time-dependent local scour at circular bridge pier. J. Hydraul. Eng.-ASCE
**2003**, 129, 420–427. [Google Scholar] [CrossRef] - Yanmaz, A.M.; Kose, O. A semi-empirical model for clear-water scour evolution at bridge abutments. J. Hydraul. Res.
**2011**, 47, 110–118. [Google Scholar] - Guo, J. Semi-analytical model for temporal clear-water scour at prototype piers. J. Hydraul. Res.
**2014**, 52, 366–374. [Google Scholar] [CrossRef] - Dey, S. Clear Water Scour around Circular Bridge Piers: A Model; Department of Civil Engineering, Indian Institute of Technology: Kharagpur, India, 1991. [Google Scholar]
- Euler, T.; Herget, J. Controls on local scour and deposition induced by obstacles in fluvial environments. Catena
**2012**, 91, 35–46. [Google Scholar] [CrossRef] - Roulund, A.; Sumer, B.M.; Fredsoe, J.; Michelsen, J. Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech.
**2005**, 534, 351–401. [Google Scholar] [CrossRef] - Breusers, H.N.C.; Raudkivi, A.J. Scouring; International Association for Hydraulic Research: Rotterdam, The Netherlands, 1991. [Google Scholar]
- Kirkil, G.; Constantinescu, G.; Ettema, R. Detached Eddy Simulation Investigation of Turbulence at a Circular Pier with Scour Hole. J. Hydraul. Eng.-ASCE
**2009**, 135, 888–901. [Google Scholar] [CrossRef] - Apsilidis, N.; Diplas, P.; Dancey, C.L.; Bouratsis, P. Effects of wall roughness on turbulent junction flow characteristics. Ex Fluid
**2016**, 57. [Google Scholar] [CrossRef] - Melville, B.W.; Raudkivi, A.J. Flow characteristics in local scour at bridge piers. J. Hydraul. Res.
**1997**, 15, 373–380. [Google Scholar] [CrossRef] - Melville, B. Pier and Abutment Scour: Integrated Approach. J. Hydraul. Eng.-ASCE
**1997**, 123, 125–136. [Google Scholar] [CrossRef] - Sheppard, D.M.; Melville, B.; Demir, H. Evaluation of Existing Equations for Local Scour at Bridge Piers. J. Hydraul. Eng.-ASCE
**2014**, 140, 14–23. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) View of the hydraulic flume; (

**b**) View of the cameras recording the bed during the experiment.

**Figure 2.**Scour depth (s) contour maps during the first 8 min of the experiments. Flow direction is from left to right. t: time.

**Figure 5.**The cylindrical grid that was used for the statistical analysis of the scour hole’s morphology. r: radial distance from the surface of the pier; θ: angle of the plane around the cylinder.

**Figure 9.**Scour depth against radial distance from the surface of the cylinder, for various instants after t = 9 min, in 5 angular planes, around the cylinder.

**Figure 11.**Average slope of radial profiles, at r = 5 mm, at the front and the sides of (or around) the cylinder during the development phase.

**Table 1.**Quantitative characteristics of the various phases and regions. Parameters

**c**are constants used in the derived equations.

_{i}Initial Scour Phase | Development Scour Phase | |||||
---|---|---|---|---|---|---|

(0 min ≤ t < 9 min) | (9 min ≤ t ≤ 250 min) | |||||

Front | Side | Wake | Front | Side | Wake | |

(0 ≤ θ ≤ 20) | (20 < θ < 130) | (130 ≤ θ < 180) | (0 ≤ θ ≤ 20) | (20 < θ < 130) | (130 ≤ θ < 180) | |

Terminal scour depth (mm) | 46.0 | 70.8 | 23.9 | 116.2 | 114.2 | 80.5 |

Location of max scour depth (θ, r) | (20, 30) | (60, 30) | (175, 180) | (0, 20) | (60, 5) | (175, 100) |

Terminal eroded volume (mm^{3}) | 1.14 × 10^{6} | 4.76 × 10^{6} | ||||

Scour (s) vs. Time (t) | s = t^{c1} | s = t^{c1} + c_{2} | Undefined | s = t^{c1} | s = t^{c1} + c_{2} | Undefined |

Scour (s) vs. Angular Plane (θ) | Undefined | s = c_{3}sin(c_{4}θ) + c_{5} | ||||

Scour (s) vs. radial distance (r) | s = c_{5}r + c_{6} | s = c_{7}r^{3} + c_{8}r^{2} + c_{9}r + c_{10} | s = c_{5}r + c_{6} | s = c_{7}r^{3} + c_{8}r^{2} + c_{9}r + c_{10} | ||

Eroded Volume (V) vs. Time (t) | V = t^{c11} | V = tc_{11} + c_{12} | ||||

Slope of the angular profile (Z) vs. Angular Plane (θ) | Undefined | Z = c_{13}sin(c_{14}θ) + c_{15} | Undefined |

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**MDPI and ACS Style**

Bouratsis, P.; Diplas, P.; Dancey, C.L.; Apsilidis, N.
Quantitative Spatio-Temporal Characterization of Scour at the Base of a Cylinder. *Water* **2017**, *9*, 227.
https://doi.org/10.3390/w9030227

**AMA Style**

Bouratsis P, Diplas P, Dancey CL, Apsilidis N.
Quantitative Spatio-Temporal Characterization of Scour at the Base of a Cylinder. *Water*. 2017; 9(3):227.
https://doi.org/10.3390/w9030227

**Chicago/Turabian Style**

Bouratsis, Pol, Panayiotis Diplas, Clinton L. Dancey, and Nikolaos Apsilidis.
2017. "Quantitative Spatio-Temporal Characterization of Scour at the Base of a Cylinder" *Water* 9, no. 3: 227.
https://doi.org/10.3390/w9030227