284
CHAPTER 6. SEDIMENT TRANSPORT MODELS
list of cited literature. Presumably, a re-evaluation of the data took place
between the two publications, resulting in a modified form for the scaling
law.
Equations 6.83 and 6.84 are the form of Noda’s scaling criteria that
commonly appear in the literature. These equations specify a relationship
between the horizontal and vertical scales, and the sediment diameter and
immersed relative density scales. The experimenter is free to chose two of
the scales, and the remaining two then become defined. Figure 6.4 is a
graphical representation of the model law as given by Equations 6.83 and
6.84.
Noda’s generalized guidance leads to models in which the bathymetry
has a distortion given as
fi = (Nz)° 32 (A^)-0-386
(6.85)
However, it is possible to have a geometrically undistorted model using
lightweight sediment particles. Assuming that Nx = Nz = Nl, where NL
is the undistorted model length scale, Eqns. 6.83 and 6.84 become
Nd = (NL)~°SSi
(6.86)
Nl = (W,.)1 2
(6.87)
The modeler can choose either Nl, Nd, or Np> and this fixes the other
remaining two parameters. The utility of this undistorted version of Noda’s
law is fairly limited in model length scale by the practical range of sediment
density. For example, one of the lightest material that might be considered
as a model sediment is plexiglas with a relative density of ps/p = 1.16. If
plexiglas is used to model a prototype sand beach, then Np> — 10.25, and
from Eqn. 6.87, Nl — 16.3. The plexiglas particles would need to have a
diameter about 15 times larger than the prototype grain size. Also, as the
particles become lighter, the model sediment diameter increases drastically,
which significantly affects beach percolation and particle accelerations and
causes scale effects on the “dry” portion of the beach, as discussed for
bedload models in the section entitled Lightweight Model Requirements.
Noda (1972) listed the assumptions invoked when applying his movablebed scaling criteria. These included the fact that the law was developed
using two-dimensional results, and extrapolation to three dimensions may
introduce some difficulties. He stated that scaling of the wavelength by
the vertical scale will conserve wave refraction in 3-d models, but the number of waves will not be in accordance with the distorted horizontal scale.
Diffraction and reflection processes will not be preserved in a 3-d model,
nor is the sediment concentration. Hudson, et al. (1979) also noted that
reflections are increased in a distorted model; but they stated that distorted
CHAPTER 6. SEDIMENT TRANSPORT MODELS
list of cited literature. Presumably, a re-evaluation of the data took place
between the two publications, resulting in a modified form for the scaling
law.
Equations 6.83 and 6.84 are the form of Noda’s scaling criteria that
commonly appear in the literature. These equations specify a relationship
between the horizontal and vertical scales, and the sediment diameter and
immersed relative density scales. The experimenter is free to chose two of
the scales, and the remaining two then become defined. Figure 6.4 is a
graphical representation of the model law as given by Equations 6.83 and
6.84.
Noda’s generalized guidance leads to models in which the bathymetry
has a distortion given as
fi = (Nz)° 32 (A^)-0-386
(6.85)
However, it is possible to have a geometrically undistorted model using
lightweight sediment particles. Assuming that Nx = Nz = Nl, where NL
is the undistorted model length scale, Eqns. 6.83 and 6.84 become
Nd = (NL)~°SSi
(6.86)
Nl = (W,.)1 2
(6.87)
The modeler can choose either Nl, Nd, or Np> and this fixes the other
remaining two parameters. The utility of this undistorted version of Noda’s
law is fairly limited in model length scale by the practical range of sediment
density. For example, one of the lightest material that might be considered
as a model sediment is plexiglas with a relative density of ps/p = 1.16. If
plexiglas is used to model a prototype sand beach, then Np> — 10.25, and
from Eqn. 6.87, Nl — 16.3. The plexiglas particles would need to have a
diameter about 15 times larger than the prototype grain size. Also, as the
particles become lighter, the model sediment diameter increases drastically,
which significantly affects beach percolation and particle accelerations and
causes scale effects on the “dry” portion of the beach, as discussed for
bedload models in the section entitled Lightweight Model Requirements.
Noda (1972) listed the assumptions invoked when applying his movablebed scaling criteria. These included the fact that the law was developed
using two-dimensional results, and extrapolation to three dimensions may
introduce some difficulties. He stated that scaling of the wavelength by
the vertical scale will conserve wave refraction in 3-d models, but the number of waves will not be in accordance with the distorted horizontal scale.
Diffraction and reflection processes will not be preserved in a 3-d model,
nor is the sediment concentration. Hudson, et al. (1979) also noted that
reflections are increased in a distorted model; but they stated that distorted