6.2. MOVABLE-BED SCALING REQUIREMENTS
247
Hydrodynamic Similitude Requirements
The hydrodynamic parameters can be given in terms of a complete set of
dimensionless products using the dimensional analysis techniques given in
Chapter 2. As previously noted, there are a large number of combinations
that will produce a complete set, therefore it is necessary to add logic and
experience to the formulation. Kamphuis (1985) gave the hydrodynamic
set as
n -
- LL IL L H < UÏ y 1
/« n
H f [l’ l' l’ l’ r l’ ty\Jl’ l^l\
(61)
The explicit functional relationship between all the variables is unknown; therefore, hydraulic kinematic and dynamic similitude requires that
all dimensionless products must remain the same in the model as in the
prototype. Preserving the values of the first five dimensionless products
in Eqn. 6.1 requires that the model geometry and hydrodynamics be geometrically undistorted. The sixth dimensionless parameter will be constant
provided that model boundary roughness is the same as in the prototype,
and this is approximately satisfied in coastal models if the boundary layer
remains in the turbulent rough region. However, questions arise relative to
bed roughness when bed ripples form, and this topic will be discussed later.
The seventh dimensionless product can be rearranged to get t/yjL/g,
where \/L/g is proportional to the period of simple harmonic motion
(waves) caused by the force of gravity (also see Example 3.3 in Chapter 3). Because gravity-driven harmonic systems conform to the Froude
time scaling, we can see that maintaining the same value of relative time
between prototype and model will require that the hydrodynamics be scaled
according to the Froude criterion.
Finally, the eighth product, v/Ly/gL, is recognized as a flow Reynolds
number with velocity represented by y/gT>. Similitude requires that prototype and model Reynolds numbers be the same. From Chapter 4 we
know that viscous effects are ignored in many modeling situations which
means that Reynolds similitude is usually not met in the model. However, as pointed out by Kamphuis (1985) neglecting viscosity is difficult to
justify for sediment motion confined to the boundary layer because model
boundary layers can be laminar smooth. Unfortunately, there is no practical alternative except trying to assure turbulent flow exists next to the
movable bed.
Through analysis of the above dimensionless parameters, it is concluded
that the hydrodynamic phase of sediment transport models must be geometrically undistorted and scaled using the Froude criterion. At the same
time we recognize that viscous scale effects and prototype-scale bedforms
may adversely impact the model hydrodynamics.
247
Hydrodynamic Similitude Requirements
The hydrodynamic parameters can be given in terms of a complete set of
dimensionless products using the dimensional analysis techniques given in
Chapter 2. As previously noted, there are a large number of combinations
that will produce a complete set, therefore it is necessary to add logic and
experience to the formulation. Kamphuis (1985) gave the hydrodynamic
set as
n -
- LL IL L H < UÏ y 1
/« n
H f [l’ l' l’ l’ r l’ ty\Jl’ l^l\
(61)
The explicit functional relationship between all the variables is unknown; therefore, hydraulic kinematic and dynamic similitude requires that
all dimensionless products must remain the same in the model as in the
prototype. Preserving the values of the first five dimensionless products
in Eqn. 6.1 requires that the model geometry and hydrodynamics be geometrically undistorted. The sixth dimensionless parameter will be constant
provided that model boundary roughness is the same as in the prototype,
and this is approximately satisfied in coastal models if the boundary layer
remains in the turbulent rough region. However, questions arise relative to
bed roughness when bed ripples form, and this topic will be discussed later.
The seventh dimensionless product can be rearranged to get t/yjL/g,
where \/L/g is proportional to the period of simple harmonic motion
(waves) caused by the force of gravity (also see Example 3.3 in Chapter 3). Because gravity-driven harmonic systems conform to the Froude
time scaling, we can see that maintaining the same value of relative time
between prototype and model will require that the hydrodynamics be scaled
according to the Froude criterion.
Finally, the eighth product, v/Ly/gL, is recognized as a flow Reynolds
number with velocity represented by y/gT>. Similitude requires that prototype and model Reynolds numbers be the same. From Chapter 4 we
know that viscous effects are ignored in many modeling situations which
means that Reynolds similitude is usually not met in the model. However, as pointed out by Kamphuis (1985) neglecting viscosity is difficult to
justify for sediment motion confined to the boundary layer because model
boundary layers can be laminar smooth. Unfortunately, there is no practical alternative except trying to assure turbulent flow exists next to the
movable bed.
Through analysis of the above dimensionless parameters, it is concluded
that the hydrodynamic phase of sediment transport models must be geometrically undistorted and scaled using the Froude criterion. At the same
time we recognize that viscous scale effects and prototype-scale bedforms
may adversely impact the model hydrodynamics.