4.3. LONG-WAVE HYDRODYNAMIC MODELS
141
Sizing of the artificial roughness elements can be done theoretically by
assuming an analytical form for the turbulent boundary layer, and then developing scaling relations (Yalin 1971); however, many laboratories simply
add roughness based on past experience with similar modeling projects.
Distorted Long-Wave Model Scale Requirements
The scaling requirements for geometrically distorted long-wave models are
given by Eqns. 4.105 and 4.107, and they allow flexibility in choosing a
suitable horizontal scale. Model distortion is called for when large bodies
of water are to be modeled, such as Chesapeake Bay or San Francisco Bay.
Using an undistorted length scale relationship in these cases would result
in model waters depths so small that surface tension effects and excessive
frictional losses would invalidate the model response.
The distorted scale relationships allow the model to have greater water
depth while taking up less horizontal area. Often this is the single overriding consideration in the decision to employ a distorted model. In addition,
distorted models have less frictional loss, and it is easier to make the model
behave like the prototype by using bottom roughness elements. Finally,
distorted scale models provide easier wave height measurement, particularly for low-amplitude long-period waves that frequently occur in nature
(Hudson, et al. 1979).
Distorted models do have drawbacks. Slopes are steeper in a distorted
model, and this creates differences in wave reflection that need to be considered as a scale effect (Whalin and Chatham 1974). Also, refraction and
diffraction are only reproduced accurately for waves that adhere to the
criterion for long waves given by Eqn. 4.91.
Unidirectional Currents in Long-Wave Models
Just as in short-wave models, currents can be mechanically created in smallscale long-wave models through the use of pumps and manifolds, and the
nonlinear interaction between the long waves and currents will be faithfully
reproduced provided the currents are properly scaled.
If we restrict the current flows to be governed by the same set of equations (Eqns. 4.97-4.100) as the long-wave motion, then the currents must
conform to the same criteria found for long waves. This implies that vertical currents will not be in similitude with the wave motion because of
the geometric distortion of the long waves. Therefore, we are in essence
restricted to horizontal currents in a long-wave model.
The scale for current velocity is found from Condition 1 (Eqn. 4.105) as
141
Sizing of the artificial roughness elements can be done theoretically by
assuming an analytical form for the turbulent boundary layer, and then developing scaling relations (Yalin 1971); however, many laboratories simply
add roughness based on past experience with similar modeling projects.
Distorted Long-Wave Model Scale Requirements
The scaling requirements for geometrically distorted long-wave models are
given by Eqns. 4.105 and 4.107, and they allow flexibility in choosing a
suitable horizontal scale. Model distortion is called for when large bodies
of water are to be modeled, such as Chesapeake Bay or San Francisco Bay.
Using an undistorted length scale relationship in these cases would result
in model waters depths so small that surface tension effects and excessive
frictional losses would invalidate the model response.
The distorted scale relationships allow the model to have greater water
depth while taking up less horizontal area. Often this is the single overriding consideration in the decision to employ a distorted model. In addition,
distorted models have less frictional loss, and it is easier to make the model
behave like the prototype by using bottom roughness elements. Finally,
distorted scale models provide easier wave height measurement, particularly for low-amplitude long-period waves that frequently occur in nature
(Hudson, et al. 1979).
Distorted models do have drawbacks. Slopes are steeper in a distorted
model, and this creates differences in wave reflection that need to be considered as a scale effect (Whalin and Chatham 1974). Also, refraction and
diffraction are only reproduced accurately for waves that adhere to the
criterion for long waves given by Eqn. 4.91.
Unidirectional Currents in Long-Wave Models
Just as in short-wave models, currents can be mechanically created in smallscale long-wave models through the use of pumps and manifolds, and the
nonlinear interaction between the long waves and currents will be faithfully
reproduced provided the currents are properly scaled.
If we restrict the current flows to be governed by the same set of equations (Eqns. 4.97-4.100) as the long-wave motion, then the currents must
conform to the same criteria found for long waves. This implies that vertical currents will not be in similitude with the wave motion because of
the geometric distortion of the long waves. Therefore, we are in essence
restricted to horizontal currents in a long-wave model.
The scale for current velocity is found from Condition 1 (Eqn. 4.105) as