EM 1110-2-1100 (Part II)
30 Apr 02
(3) Note that Equation II-7-8 indicates that Cr approaches the value of a at higher values of the Iribarren
number. Thus, the highest reflection coefficients for stone and concrete unit armored structures are around
0.5. As expected, vertical plane slopes (infinite Iribarren number) would have a reflection coefficient near
unity. For typical rigid vertical bulkheads, owing to the irregularity of the facing surface, a value of Cr = 0.9
might be used.
c. Reflection from beaches.
(1) When the reflecting slope becomes very flat, the incident wave will break on the slope, causing an
increase in energy dissipation and commensurate decrease in the reflection coefficient. Thus, beaches are
generally very efficient wave absorbers, particularly for shorter period wind-generated waves. An added
complexity is that as the incident wave conditions change, the beach profile geometry will change, in turn
changing the reflection coefficient somewhat. Laboratory measurements of wave reflection from beaches
suffer from scale effects in trying to replicate the prototype beach profile, surface roughness, and porosity.
Also, it is harder to select a beach slope angle for the Iribarren number owing to the complexity of beach
profiles. Thus, data plots follow the form of Equation II-7-8, but with significant scatter in the data points.
Seelig and Ahrens (1981) suggest that a = 0.5 and b = 5.5 be used for beaches. Since the slope angles are
small, the Iribarren number will be relatively small, yielding relatively low reflection coefficients.
(2) An interesting phenomenon (known as Bragg reflections after a similar phenomenon in optics) occurs
when the shallow nearshore seabed has uniformly spaced bottom undulations. A resonance develops between
the incident surface waves of certain periods and the bottom undulations, causing a reflection of a portion of
the incident wave energy (see Davies and Heathershaw (1984), Mei (1985), Kirby (1987)). Resonance and
reflection are maximum for that portion of the incident wave spectrum having a wavelength that is twice the
length of the bottom undulations. There is an approximately linear increase in the reflection coefficient with
the increase in the number of bottom undulations. Reflection also increases if the amplitude of the bottom
undulations increases or the water depth over the undulations decreases. For appropriate undulation
geometries and water depths, reflection coefficients in excess of 0.5 are possible.
(3) It has been suggested (Mei 1985) that Bragg reflections that develop on a nearshore bar system will
set up a standing wave pattern seaward of the bar system which, in turn, causes the bar system to extend in
the seaward direction. Theoretical, laboratory, and field studies indicate that it is possible to build a series
of shore-parallel submerged bars tuned to the dominant incoming wave periods, that will act as a shore
protection device. The feasibility of building these bar systems and their economics need to be studied
further.
d. Reflection patterns in harbors.
(1) Figure II-7-24 depicts the plan view of a wave crest approaching and reflecting from a barrier that
has a reflection coefficient Cr. The incident wave crest is curved owing to refraction and possibly to
diffraction. The actual bottom contours in front of the barrier are as shown. The reflected wave crest pattern
can be constructed by:
(a) Constructing imaginary mirror image hydrography on the other side of the barrier.
(b) Constructing the wave crest pattern that would develop as the wave propagates over this imaginary
hydrography (this would involve the use of refraction and diffraction analyses as described in previous
sections).
(c) Constructing the mirror image of the imaginary wave crest pattern to define the real reflected wave.
Harbor Hydrodynamics
II-7-29
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