316
CHAPTER 6. SEDIMENT TRANSPORT MODELS
Examining Eqn. 6.159, there are two conditions by which N * could
approach unity. The first is if Umax
(7» in both the prototype and
model. This would be representative of highly turbulent conditions, such
as exist in the surf zone during energetic wave conditions; and in the limit it
corresponds somewhat to the physical description given by Gourlay (1968)
and Dean (1973) for a suspended grain falling through the water column
under the influence of horizontal currents.
• beach and dune profile response to storm events
The other conditions leading to N * = 1 is if the ratio U * /Umax
is kept
similar between prototype and model. In general the investigator will be
unable to satisfy both the fall speed scale and the grain size scale necessary
to meet this condition. Even if possible, the scaling would be valid for only
one specific hydrodynamic condition because Umax depends on wave period
and wave height, whereas U * is independent of wave height. This would
hamper investigations using irregular waves, as well as studies in which
numerous regular wave periods were of interest.
6.4.3 Suspension-Dominated Modeling Conclusions
In conclusion, efforts aimed at reproducing surf zone profile response in
small-scale movable-bed models during erosive conditions have converged
on scaling criteria that preserve the parameter H/uT between prototype
and a geometrically undistorted model, with the hydrodynamics (waves
primarily) being scaled by the Froude criterion. As Dean (1985) discussed,
this model law preserves similarity in wave form, sediment fall path, waveinduced velocities, break point, breaker type, and wave decay (provided the
model is large enough to preclude viscous and surface tension effects.) The
bottom shear stress will not be correctly scaled using the fall speed parameter model criteria because the bottom boundary layer and ripple formations
are not reproduced. This will result in noticeable scale effects when wave
breaking turbulence is not dominant in the domain being modeled.
The movable-bed scaling criterion given by Eqn. 6.155 is for geometrically undistorted Froude models where the sediment size is selected so
the fall speed parameter is held constant between prototype and model.
Past experience with these and similar scaling criteria, coupled with the
assumptions used in formulating the guidance, restricts application of this
type of physical modeling to coastal sediment problems and processes that
are chiefly erosional in nature, with the erosion occurring in an energetic,
turbulence-dominated region such as the surf zone. Typically, the scaling
is intended to replicate the short-term response of the sea bed to storminduced waves. Examples of situations that may be candidates for modeling
with the fall speed criteria include:
CHAPTER 6. SEDIMENT TRANSPORT MODELS
Examining Eqn. 6.159, there are two conditions by which N * could
approach unity. The first is if Umax
(7» in both the prototype and
model. This would be representative of highly turbulent conditions, such
as exist in the surf zone during energetic wave conditions; and in the limit it
corresponds somewhat to the physical description given by Gourlay (1968)
and Dean (1973) for a suspended grain falling through the water column
under the influence of horizontal currents.
• beach and dune profile response to storm events
The other conditions leading to N * = 1 is if the ratio U * /Umax
is kept
similar between prototype and model. In general the investigator will be
unable to satisfy both the fall speed scale and the grain size scale necessary
to meet this condition. Even if possible, the scaling would be valid for only
one specific hydrodynamic condition because Umax depends on wave period
and wave height, whereas U * is independent of wave height. This would
hamper investigations using irregular waves, as well as studies in which
numerous regular wave periods were of interest.
6.4.3 Suspension-Dominated Modeling Conclusions
In conclusion, efforts aimed at reproducing surf zone profile response in
small-scale movable-bed models during erosive conditions have converged
on scaling criteria that preserve the parameter H/uT between prototype
and a geometrically undistorted model, with the hydrodynamics (waves
primarily) being scaled by the Froude criterion. As Dean (1985) discussed,
this model law preserves similarity in wave form, sediment fall path, waveinduced velocities, break point, breaker type, and wave decay (provided the
model is large enough to preclude viscous and surface tension effects.) The
bottom shear stress will not be correctly scaled using the fall speed parameter model criteria because the bottom boundary layer and ripple formations
are not reproduced. This will result in noticeable scale effects when wave
breaking turbulence is not dominant in the domain being modeled.
The movable-bed scaling criterion given by Eqn. 6.155 is for geometrically undistorted Froude models where the sediment size is selected so
the fall speed parameter is held constant between prototype and model.
Past experience with these and similar scaling criteria, coupled with the
assumptions used in formulating the guidance, restricts application of this
type of physical modeling to coastal sediment problems and processes that
are chiefly erosional in nature, with the erosion occurring in an energetic,
turbulence-dominated region such as the surf zone. Typically, the scaling
is intended to replicate the short-term response of the sea bed to storminduced waves. Examples of situations that may be candidates for modeling
with the fall speed criteria include: