314
CHAPTER 6. SEDIMENT TRANSPORT MODELS
Wang et al.'s Distorted Fall Trajectory Model. Now assume that the model facility
is not large enough to accommodate a length scale of Nl = 11.3, and it is necessary
to distort the model using the guidance of Wang, et al. (1990). Determine the
horizontal length scale and the time scales that would be used if the model vertical
scale is selected as Nz — 25.
From Eqn. 6.152 the model distortion is calculated as
Q =
Nx
Nz
NgNz
(NplN^
<1>(25) VZ'
(1)2(3.36)2 )
1.22
and the horizontal scale ratio is simply
Nx = 1-22 Nz = 1-22 (25) = 30.5
The hydrodynamic time scale is determined from Eqn. 6.147 as
hr
30.5
Nt = —.
= —,
— 61
and the morphological time scale comes from Eqn. 6.151, i.e.,
Note. The guidance provided by Hughes (1983) would have given a horizontal length
scale of Nx = 37.2 (from Eqn. 6.135), and a time scale of Nt — Ntrn = 7.44 (from
Eqn. 6.132).
Xie’s Undistorted Modeling Criteria Various parameters other than
the fall speed parameter have been suggested for use in characterizing
sediment transport processes. Such parameters include relative grain size
(77/d5o) and wave steepness (H/Lo). Xie (1981) conducted numerous twodimensional small-scale movable-bed model tests to examine the scouring
of bed material adjacent to a vertical seawall subjected to nonbreaking
waves. After testing several parameters, including the fall speed parameter, Xie presented a criterion for distinguishing between scour patterns
typical of suspension-dominated and bedload-dominated sediment transport. The criterion depended on the grain size of the bed material and on
the wave conditions, and it was expressed in terms of the parameter
Umax
Ut
(6.156)
where
CHAPTER 6. SEDIMENT TRANSPORT MODELS
Wang et al.'s Distorted Fall Trajectory Model. Now assume that the model facility
is not large enough to accommodate a length scale of Nl = 11.3, and it is necessary
to distort the model using the guidance of Wang, et al. (1990). Determine the
horizontal length scale and the time scales that would be used if the model vertical
scale is selected as Nz — 25.
From Eqn. 6.152 the model distortion is calculated as
Q =
Nx
Nz
NgNz
(NplN^
<1>(25) VZ'
(1)2(3.36)2 )
1.22
and the horizontal scale ratio is simply
Nx = 1-22 Nz = 1-22 (25) = 30.5
The hydrodynamic time scale is determined from Eqn. 6.147 as
hr
30.5
Nt = —.
= —,
— 61
and the morphological time scale comes from Eqn. 6.151, i.e.,
Note. The guidance provided by Hughes (1983) would have given a horizontal length
scale of Nx = 37.2 (from Eqn. 6.135), and a time scale of Nt — Ntrn = 7.44 (from
Eqn. 6.132).
Xie’s Undistorted Modeling Criteria Various parameters other than
the fall speed parameter have been suggested for use in characterizing
sediment transport processes. Such parameters include relative grain size
(77/d5o) and wave steepness (H/Lo). Xie (1981) conducted numerous twodimensional small-scale movable-bed model tests to examine the scouring
of bed material adjacent to a vertical seawall subjected to nonbreaking
waves. After testing several parameters, including the fall speed parameter, Xie presented a criterion for distinguishing between scour patterns
typical of suspension-dominated and bedload-dominated sediment transport. The criterion depended on the grain size of the bed material and on
the wave conditions, and it was expressed in terms of the parameter
Umax
Ut
(6.156)
where