144
CHAPTER 4. HYDRODYNAMIC MODELS
where ,VZ has replaced N^. Substituting the long-wave period scale ratio
(given by Eqn. 4.107) for NT in Eqn. 4.117 results in the equality NL = Nx
that is necessary for diffraction similitude.
Waves that do not obey the shallow water wave approximation (i.e.,
dispersive waves) will not correctly simulate diffraction in a geometrically
distorted model if the wave period is scaled by the distorted Froude time
scale (Eqn. 4.107). However. Whalin and Chatham (1974) noted that in
instances where diffraction was the primary phenomenon of interest, diffraction of dispersive waves will be correctly reproduced if the wave period is
scaled as the square root of the horizontal length scale, Nt — V^’x ■ Of
course all other features of the wave action will not be in similitude.
In summary, it can be concluded that
Both refraction and diffraction in Froude-scaled. longwave hydrodynamic physical models are correctly reproduced for both geometrically undistorted and geometrically distorted models.
4.3.2 Long-Wave Model Laboratory and Scale Effects
Laboratory effects and scale effects in long-wave models are the two most
important factors affecting model results, and it is critical that the experimenter be fully aware of their potential impacts.
Laboratory Effects
As in short-wave models, laboratory effects in long-wave models arise because of model boundary effects on the flow, through unintentional nonlinear wave effects brought about by mechanical generation of waves and
currents, and from simplification of prototype forcing conditions. The few
applications of long-wave physical models conducted in two-dimensional
wave flumes will encounter the same problems as discussed for short-wave
models. However, reflection problems will be enhanced because long waves
reflect more of their energy, and active absorption systems have more difficulty dealing with longer wavelengths. In addition, geometrically distorted
long-wave models in flumes have steeper slopes than prototype which also
contribute to increased reflection.
1 hree-dimensional long-wave models are much more common, and their
major laboratory effect is reflection of long-wave energy by model boundaries. Reflection of intermediate and long waves from harbor or inlet structures is substantial, and these reflected waves must be absorbed (or at
least reduced in magnitude) at the outer boundaries of the model. Long
waves are hard to absorb, and in order to absorb as much wave energy
CHAPTER 4. HYDRODYNAMIC MODELS
where ,VZ has replaced N^. Substituting the long-wave period scale ratio
(given by Eqn. 4.107) for NT in Eqn. 4.117 results in the equality NL = Nx
that is necessary for diffraction similitude.
Waves that do not obey the shallow water wave approximation (i.e.,
dispersive waves) will not correctly simulate diffraction in a geometrically
distorted model if the wave period is scaled by the distorted Froude time
scale (Eqn. 4.107). However. Whalin and Chatham (1974) noted that in
instances where diffraction was the primary phenomenon of interest, diffraction of dispersive waves will be correctly reproduced if the wave period is
scaled as the square root of the horizontal length scale, Nt — V^’x ■ Of
course all other features of the wave action will not be in similitude.
In summary, it can be concluded that
Both refraction and diffraction in Froude-scaled. longwave hydrodynamic physical models are correctly reproduced for both geometrically undistorted and geometrically distorted models.
4.3.2 Long-Wave Model Laboratory and Scale Effects
Laboratory effects and scale effects in long-wave models are the two most
important factors affecting model results, and it is critical that the experimenter be fully aware of their potential impacts.
Laboratory Effects
As in short-wave models, laboratory effects in long-wave models arise because of model boundary effects on the flow, through unintentional nonlinear wave effects brought about by mechanical generation of waves and
currents, and from simplification of prototype forcing conditions. The few
applications of long-wave physical models conducted in two-dimensional
wave flumes will encounter the same problems as discussed for short-wave
models. However, reflection problems will be enhanced because long waves
reflect more of their energy, and active absorption systems have more difficulty dealing with longer wavelengths. In addition, geometrically distorted
long-wave models in flumes have steeper slopes than prototype which also
contribute to increased reflection.
1 hree-dimensional long-wave models are much more common, and their
major laboratory effect is reflection of long-wave energy by model boundaries. Reflection of intermediate and long waves from harbor or inlet structures is substantial, and these reflected waves must be absorbed (or at
least reduced in magnitude) at the outer boundaries of the model. Long
waves are hard to absorb, and in order to absorb as much wave energy