5.2. RUBBLE-MOUND STRUCTURES
187
given by Dai and Kamel (1969). They stated that the largest uncertainty in
the evaluation of viscous scale effects in porous structures is the magnitude
and characteristics of the interior velocity field.
Shimada, et al. (1986) investigated rubble-mound stability and scale
effects associated with viscosity and wave reflection. In their conclusions
that stated that there will be negligible scale effects for Reynolds numbers
greater than 4 x 105. This suggested critical Reynolds number is higher
than given by Dai and Kamel (1969).
3 Sakakiyama and Kajima (1990) used armor unit fall velocity as the velocity in their
experimental Reynolds numbers, so the absolute values of Reynolds numbers may not
correspond to those values calculated using Eqn. 5.31.
Van der Meer (1988) conducted extensive physical model tests of armor
and riprap stability using irregular waves. He examined the validity of his
stability equation by reproducing small-scale stability tests at larger scale
in the Delta Flume. Van der Meer calculated the armor layer Reynolds
number using Eqn. 5.31 with significant wave height, 773, replacing H and
the median armor size, d50, replacing ta. Good correspondence between the
large- and small-scale models led Van der Meer to conclude that no viscous
scale effects occurred at armor layer Reynolds numbers above 4 x 104, which
was the smallest Reynolds number in his tests.
Sakakiyama and Kajima (1990) derived a theoretical relationship between the stability coefficient (/<△) in Hudson’s formula (Eqn. 5.22) and
the drag coefficient, Cd- They conducted experiments using three sizes of
model Tetrapods ranging from 16 g to 6800 g, and found that the wave
force on an individual armor unit was relatively larger at the smaller scale.
It was concluded that the scale effect was due to the change of relative drag
force as a function of Reynolds number. The test data were for Reynolds
numbers3 less than about 106, and the assumption was made that inertial
forces were small compared to drag forces.
All of the studies discussed above recognized that similitude of armor
stability is impacted by viscous forces in the model when the armor unit
Reynolds number falls below a critical value. However, the investigators
differ by almost two orders of magnitude (6 x 103 - 4 x 105) on what this
lower value should be. As always, stability models should be conducted at
the largest scale possible to remove any doubt about viscous scale effects.
When this is not possible, it appears that sufficient evidence exists to justify
models that have armor layer Reynolds numbers (Eqn. 5.31) as low as
4 x 104.
Finally, it is important to note that earlier scale effects studies employed
monochromatic waves, whereas modern tests utilized irregular waves. The
agreement between Dai and Kamel’s (1969) results and Van der Meer’s
(1988) results seems to indicate that significant wave height (773) corre
187
given by Dai and Kamel (1969). They stated that the largest uncertainty in
the evaluation of viscous scale effects in porous structures is the magnitude
and characteristics of the interior velocity field.
Shimada, et al. (1986) investigated rubble-mound stability and scale
effects associated with viscosity and wave reflection. In their conclusions
that stated that there will be negligible scale effects for Reynolds numbers
greater than 4 x 105. This suggested critical Reynolds number is higher
than given by Dai and Kamel (1969).
3 Sakakiyama and Kajima (1990) used armor unit fall velocity as the velocity in their
experimental Reynolds numbers, so the absolute values of Reynolds numbers may not
correspond to those values calculated using Eqn. 5.31.
Van der Meer (1988) conducted extensive physical model tests of armor
and riprap stability using irregular waves. He examined the validity of his
stability equation by reproducing small-scale stability tests at larger scale
in the Delta Flume. Van der Meer calculated the armor layer Reynolds
number using Eqn. 5.31 with significant wave height, 773, replacing H and
the median armor size, d50, replacing ta. Good correspondence between the
large- and small-scale models led Van der Meer to conclude that no viscous
scale effects occurred at armor layer Reynolds numbers above 4 x 104, which
was the smallest Reynolds number in his tests.
Sakakiyama and Kajima (1990) derived a theoretical relationship between the stability coefficient (/<△) in Hudson’s formula (Eqn. 5.22) and
the drag coefficient, Cd- They conducted experiments using three sizes of
model Tetrapods ranging from 16 g to 6800 g, and found that the wave
force on an individual armor unit was relatively larger at the smaller scale.
It was concluded that the scale effect was due to the change of relative drag
force as a function of Reynolds number. The test data were for Reynolds
numbers3 less than about 106, and the assumption was made that inertial
forces were small compared to drag forces.
All of the studies discussed above recognized that similitude of armor
stability is impacted by viscous forces in the model when the armor unit
Reynolds number falls below a critical value. However, the investigators
differ by almost two orders of magnitude (6 x 103 - 4 x 105) on what this
lower value should be. As always, stability models should be conducted at
the largest scale possible to remove any doubt about viscous scale effects.
When this is not possible, it appears that sufficient evidence exists to justify
models that have armor layer Reynolds numbers (Eqn. 5.31) as low as
4 x 104.
Finally, it is important to note that earlier scale effects studies employed
monochromatic waves, whereas modern tests utilized irregular waves. The
agreement between Dai and Kamel’s (1969) results and Van der Meer’s
(1988) results seems to indicate that significant wave height (773) corre