7.8. ADDITIONAL WAVE GENERATION TOPICS
441
Lean (1967) presented a simplified theory for predicting wave reflection from permeable wave absorbers of simple shape made of uniformly
porous material. The method invoked linear long-wave theory, and it was
assumed that the resistance coefficient of the absorber material is known
and the small-amplitude waves do not break upon entering the absorber.
Lean examined absorbers backed by vertical walls, uniformly-sloping bottoms, and parabolically-sloping bottoms. For a given overall wave absorber
length, Lean found that lower reflection coefficients are possible when the
porous absorber material is placed over plane-sloping and parabolicallysloping bottoms, rather than placing absorber material over a constantdepth bottom. He recommended that the absorber length should be at
least 75% of the incident wavelength to achieve reflection coefficients below
10%, and there will always be some reflection, even for very long absorbers.
Le Méhauté (1972) proposed a passive wave absorber in which the incident waves progressively encounter regions of increased energy dissipation
(less porosity). In each section a portion of the energy is dissipated while
the remainder is either transmitted or reflected. Le Méhauté’s approach
was to optimize the progressive wave absorber to minimize reflection while
gradually dissipating the energy. This allowed the overall length of the
absorber to be shorter than one wavelength. Small-scale experiments qualitatively supported Le Méhauté’s theoretical development.
Keulegan (1972) derived expressions for the damping of waves by screens
made from high porosity (~ 95% - 97%) aluminum wool, rubberized ‘ horsehair” and polyurethane foam. Model test results were provided for specific
wave conditions in tabular form, and an example design for a wave absorber was given. The reflection characteristics of parallel equally-spaced
mesh screens were discussed in a companion report (Keulegan 1973). In
this report, Keulegan derived a theoretical model, and he reported fair
agreement between model and observations. An empirically-based expression was also presented.
Madsen (1983) gave an analytical solution for reflection of normallyincident shallow-water waves from a vertical porous wave absorber situated
on a flat bottom in front of a solid vertical wall. The absorber was assumed
to be homogeneous and rectangular in shape, and the solution is only for
nonbreaking first-order waves. Estimates of regular wave reflection coeffi
cients were made using a combined numerical integration and iteration that
required specification of absorber width and porosity, stone diameter, wa
ter depth, wave period, and incident wave height. Madsen emphasize is
method could not be extended to irregular wave trains because the so ution
is strongly nonlinear, thus superposition of solutions would not be vai
Svendsen (1985) noted that reflections from bottom depth transitions
can be made negligible if
441
Lean (1967) presented a simplified theory for predicting wave reflection from permeable wave absorbers of simple shape made of uniformly
porous material. The method invoked linear long-wave theory, and it was
assumed that the resistance coefficient of the absorber material is known
and the small-amplitude waves do not break upon entering the absorber.
Lean examined absorbers backed by vertical walls, uniformly-sloping bottoms, and parabolically-sloping bottoms. For a given overall wave absorber
length, Lean found that lower reflection coefficients are possible when the
porous absorber material is placed over plane-sloping and parabolicallysloping bottoms, rather than placing absorber material over a constantdepth bottom. He recommended that the absorber length should be at
least 75% of the incident wavelength to achieve reflection coefficients below
10%, and there will always be some reflection, even for very long absorbers.
Le Méhauté (1972) proposed a passive wave absorber in which the incident waves progressively encounter regions of increased energy dissipation
(less porosity). In each section a portion of the energy is dissipated while
the remainder is either transmitted or reflected. Le Méhauté’s approach
was to optimize the progressive wave absorber to minimize reflection while
gradually dissipating the energy. This allowed the overall length of the
absorber to be shorter than one wavelength. Small-scale experiments qualitatively supported Le Méhauté’s theoretical development.
Keulegan (1972) derived expressions for the damping of waves by screens
made from high porosity (~ 95% - 97%) aluminum wool, rubberized ‘ horsehair” and polyurethane foam. Model test results were provided for specific
wave conditions in tabular form, and an example design for a wave absorber was given. The reflection characteristics of parallel equally-spaced
mesh screens were discussed in a companion report (Keulegan 1973). In
this report, Keulegan derived a theoretical model, and he reported fair
agreement between model and observations. An empirically-based expression was also presented.
Madsen (1983) gave an analytical solution for reflection of normallyincident shallow-water waves from a vertical porous wave absorber situated
on a flat bottom in front of a solid vertical wall. The absorber was assumed
to be homogeneous and rectangular in shape, and the solution is only for
nonbreaking first-order waves. Estimates of regular wave reflection coeffi
cients were made using a combined numerical integration and iteration that
required specification of absorber width and porosity, stone diameter, wa
ter depth, wave period, and incident wave height. Madsen emphasize is
method could not be extended to irregular wave trains because the so ution
is strongly nonlinear, thus superposition of solutions would not be vai
Svendsen (1985) noted that reflections from bottom depth transitions
can be made negligible if