Numerical study of scouring downstream of a stilling basin


The aim of the present study is to numerically investigate the scouring phenomenon downstream of a stilling basin for a wide range of Froude number and size of bed material. The numerical model was first verified. The results obtained from the numerical model concerning the maximum depth and profiles of the scoured hole were in agreement with the long-term experimental data. Thereupon, the verified numerical model was employed to simulate the profile of the scour hole for various Froude numbers and bed material sizes downstream of the stilling basin. According to the results of the numerical model as well as experimental data, it was revealed that by using dimensionless scour depth, the upstream profile of the scour hole is independent of time and size of the material. Results show that the bottom of the scour hole in the oscillating jump is of greater length than the steady jump. Moreover, both the numerical and available experimental data were used to propose a relationship for calculation of long-term maximum scour depth in a wide range of affecting parameters.

AbstractSection Article highlights
  • Scour hole depth and geometry downstream of a stilling basin were studied with a verified numerical model.

  • Numerical simulations were made in a wide range of Froude number and bed material size which were not available in the literature.

  • Using available experimental data and numerical model results, an equation was developed for estimating the scour depth.

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  1. 1.

    United States Bureau of Reclamation.

  2. 2.

    Volume of fluid.



Channel width

c :

Denotes the concentration of the suspended sediments, is the fall velocity of the sediments and represents the diffusion coefficient

d 50 :

Median grain size

F :

Volume fraction in the cell

F d :

The densimetric Froude number \(\left (\frac{\rm{V}}{\sqrt{{\rm{g}}{{^{\prime}}} {\rm{d}}_{50}}}\right)\)

F r :

Upstream Froude number

F r2 :

Downstream Froude number \(\left(\frac{\rm{V}}{\sqrt{g{ y}_{t}}}\right)\)

g i :

The gravitational acceleration in the \({x}_{i}\) direction

g′ :

\(=\frac{g\Delta \rho }{\rho }\)

H :

The spillway upstream head

h :

The distance from the bottom to the crest of the spillway

k :

Kinetic turbulent energy per unit mass

L A :

The length of the approach channel

L B :

The length of the basin

L r :

Roller length

L s :

The length of the sediment bed

p :

The height of the spillway

P :

Total pressure

R e :

Reynolds number \((\frac{ \rho {\mathrm{V} y}_{t}}{\mu })\)

t :

The duration of the scouring

t* :

Time required to reach the maximum scour depth equal to \({z}^{*}\)

t n :

The maximum scouring time (quasi-equilibrium time)

u i :

Velocity component in the \({x}_{i}\) direction

V :

The velocity of the flow

W :

Fall velocity of the sediments

y 1 :

The initial depth of the jump

y 2 :

The sequent water depth of hydraulic jump

y t :

The tail water depth

z* :

Half the spillway height

z 1 :

The thickness of the sedimentary bed

Z mn :

Maximum scour depth at quasi-equilibrium time

Z m :

The maximum scour depth at any time

ρ :

Density of the fluid

ρ s :

Density of the sediment

Δρ :

The difference of density between bed material and water (\({\rho }_{s}-\rho\))

\(\tau\) ij :

Stress tensor

υ :

Kinematic viscosity

υ t :

The eddy viscosity or turbulent viscosity

\(\delta\) ij :

Kronecker delta

\(\Gamma\) :

Diffusion coefficient

σ :

Standard deviation of sediment


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Correspondence to Amir Reza Zarrati.

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Hojjati, S.H., Zarrati, A.R. Numerical study of scouring downstream of a stilling basin. Environ Fluid Mech 21, 465–482 (2021).

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  • Scour hole
  • Stilling basin
  • Free hydraulic jump
  • Numerical model