288
CHAPTER 6. SEDIMENT TRANSPORT MODELS
the smaller flume were scaled from the larger flume conditions according to
the Froude criterion for geometrically undistorted hydrodynamic models.
The median sand grain sizes used in the smaller model tests had d50 of 0.15
mm, 0.30 mm, 0.42 mm, and 1.62 mm. Ito and Tsuchiya used sand with
d50 = 0.94 mm for the prototype case, and they also scaled down Saville’s
(1957) large-scale wave tank test results obtained with 0.22 mm sand.
Ito and Tsuchiya (1984) compared the profile development between prototype and model and arrived at an empirical scaling relationship for the
sediment grain size diameter prototype-to-model scale given as
and
Nd = (1.7)° (JV£)0'83
For Nl < 2.2
(6.88)
Nd = (1.7)' (Nl)02
For Nl > 2.2
(6.89)
They also stipulated geometrically undistorted models with hydrodynamics
scaled according to the Froude criterion, and model sediment having the
same specific gravity has the prototype. Example 6.4 illustrates application
of Ito and Tsuchiya’s scaling relationships.
There is some confusion about the correct exponents of the “1.7” factor
in Eqns. 6.88 and 6.89. In Ito and Tsuchiya (1986, 1988), the exponents
of the “1.7” factor are given opposite to what they are above. However,
a plot of the equations that appears in all three papers is consistent with
Eqns. 6.88 and 6.89 (in Ito and Tsuchiya (1988), the exponent “0.83” was
mistyped as “0.87”.)
Ito and Tsuchiya (1984) verified their scaling relationship by conducting
a 2-d beach model of the Ogata coast in Niigata. The model had a length
scale of Nl — 50, which gave a derived grain size diameter scale of Nd =
3.7 using Eqn. 6.89 (misprinted as Nd = 3.2 in their paper).
The morphological time scale was found by Ito and Tsuchiya (1986) to
be close to the Froude time scale for their experiments, and for the length
scale of Nl — 50, Ito and Tsuchiya (1988) reported their sediment diameter
scale was similar to what would be obtained using “Dean’s scaling criteria”
(which is discussed in the section entitled Scale Criteria Dependent on Fall
Speed).
Hallermeier’s Modeling Criteria
Hallermeier (1985) reviewed four available sets of scaling criteria for designing movable-bed models, stating that each of the reviewed models contradicted the others, and each model had its own shortcomings and limitations.
Hallermeier proposed his own condition of similitude for movable-bed
modeling embodied in the dimensional parameter
CHAPTER 6. SEDIMENT TRANSPORT MODELS
the smaller flume were scaled from the larger flume conditions according to
the Froude criterion for geometrically undistorted hydrodynamic models.
The median sand grain sizes used in the smaller model tests had d50 of 0.15
mm, 0.30 mm, 0.42 mm, and 1.62 mm. Ito and Tsuchiya used sand with
d50 = 0.94 mm for the prototype case, and they also scaled down Saville’s
(1957) large-scale wave tank test results obtained with 0.22 mm sand.
Ito and Tsuchiya (1984) compared the profile development between prototype and model and arrived at an empirical scaling relationship for the
sediment grain size diameter prototype-to-model scale given as
and
Nd = (1.7)° (JV£)0'83
For Nl < 2.2
(6.88)
Nd = (1.7)' (Nl)02
For Nl > 2.2
(6.89)
They also stipulated geometrically undistorted models with hydrodynamics
scaled according to the Froude criterion, and model sediment having the
same specific gravity has the prototype. Example 6.4 illustrates application
of Ito and Tsuchiya’s scaling relationships.
There is some confusion about the correct exponents of the “1.7” factor
in Eqns. 6.88 and 6.89. In Ito and Tsuchiya (1986, 1988), the exponents
of the “1.7” factor are given opposite to what they are above. However,
a plot of the equations that appears in all three papers is consistent with
Eqns. 6.88 and 6.89 (in Ito and Tsuchiya (1988), the exponent “0.83” was
mistyped as “0.87”.)
Ito and Tsuchiya (1984) verified their scaling relationship by conducting
a 2-d beach model of the Ogata coast in Niigata. The model had a length
scale of Nl — 50, which gave a derived grain size diameter scale of Nd =
3.7 using Eqn. 6.89 (misprinted as Nd = 3.2 in their paper).
The morphological time scale was found by Ito and Tsuchiya (1986) to
be close to the Froude time scale for their experiments, and for the length
scale of Nl — 50, Ito and Tsuchiya (1988) reported their sediment diameter
scale was similar to what would be obtained using “Dean’s scaling criteria”
(which is discussed in the section entitled Scale Criteria Dependent on Fall
Speed).
Hallermeier’s Modeling Criteria
Hallermeier (1985) reviewed four available sets of scaling criteria for designing movable-bed models, stating that each of the reviewed models contradicted the others, and each model had its own shortcomings and limitations.
Hallermeier proposed his own condition of similitude for movable-bed
modeling embodied in the dimensional parameter