6.2. MOVABLE-BED SCALING REQUIREMENTS
249
These two parameters may be recognized as the coordinates of the classic
Shield’s diagram for incipient motion in unidirectional flow as shown in
Figure 6.3. The third dimensionless variable is the relative density (or
specific gravity) of the sediment, i.e.,
s. = J
(6.7)
and the fourth parameter is'a relative length, i.e.,
t -A
• ~ d
(6-8)
Kamphuis (1985) stated that the characteristic length, A, in the relative
length parameter should be the average wave amplitude (am) for short-wave
models and the water depth (/i) for long-wave models and unidirectional
flow models. The fifth parameter is the relative fall speed, i.e.,
K
(6-9)
For complete similitude in sediment transport, values of all five parameters in Eqns. 6.5 - 6.9 must be the same in the model as in the prototype.
Generally, this is not possible at scales other than prototype; however,
it will be seen shortly that we can formulate several useful “incomplete”
similitudes.
Dalrymple (1989) presented a similar dimensionless grouping of parameters for sediment transport, only he neglected the characteristic length, A,
and included the sediment fall speed and wave height and period such that
f (p,v,rb,d,pa,u,H,T) = 0
(6.10)
Dalrymple’s corresponding set of dimensionless products was given by
Ils — 9
v * d
pv^ pa
y ’ 7id' p'
4 Named in honor of Dr. Robert G. Dean, who popularized the fall speed parameter
in a 1973 publication.
(6.H)
where the parameter,
= 4
(6.12)
0)1
is referred to cis the fall speed parameter or Dean number4. Equation 6.11 represents transport of both bedload and suspended sediment.
249
These two parameters may be recognized as the coordinates of the classic
Shield’s diagram for incipient motion in unidirectional flow as shown in
Figure 6.3. The third dimensionless variable is the relative density (or
specific gravity) of the sediment, i.e.,
s. = J
(6.7)
and the fourth parameter is'a relative length, i.e.,
t -A
• ~ d
(6-8)
Kamphuis (1985) stated that the characteristic length, A, in the relative
length parameter should be the average wave amplitude (am) for short-wave
models and the water depth (/i) for long-wave models and unidirectional
flow models. The fifth parameter is the relative fall speed, i.e.,
K
(6-9)
For complete similitude in sediment transport, values of all five parameters in Eqns. 6.5 - 6.9 must be the same in the model as in the prototype.
Generally, this is not possible at scales other than prototype; however,
it will be seen shortly that we can formulate several useful “incomplete”
similitudes.
Dalrymple (1989) presented a similar dimensionless grouping of parameters for sediment transport, only he neglected the characteristic length, A,
and included the sediment fall speed and wave height and period such that
f (p,v,rb,d,pa,u,H,T) = 0
(6.10)
Dalrymple’s corresponding set of dimensionless products was given by
Ils — 9
v * d
pv^ pa
y ’ 7id' p'
4 Named in honor of Dr. Robert G. Dean, who popularized the fall speed parameter
in a 1973 publication.
(6.H)
where the parameter,
= 4
(6.12)
0)1
is referred to cis the fall speed parameter or Dean number4. Equation 6.11 represents transport of both bedload and suspended sediment.