V. TYPES OF STRUCTURES AND RANGE OF CONDITIONS TESTED 
Table 1 summarizes the sources of wave reflection coefficients for struc-— 
tures and beaches and the range of conditions tested. Three types of structure 
are considered: smooth, impermeable slopes with no overtopping; revetments 
armored with one or more layers of riprap with no overtopping; and rubble-mound 
breakwaters armored with stone or dolos. 
The water depth at the toe of the structure, d,, is taken as a character- 
istic water depth, g is the acceleration due to gravity, and a representative 
armor unit diameter, d, is determined from 
2-3)" © 
where W is the armor weight, and y the specific weight of the armor mate- 
rial. A measure of the wave breaker height that could occur at the toe of the 
structure, Hp, is given by Goda (1975) as 
d 
gb, = O17 Lo{1-0 = exp [-4.712 = (1.0 + 15 n!-233)]h (7) 
lo) 
where Lo is the deepwater wavelength given by linear wave theory, and m the 
tangent of the slope of the seabed seaward of the structure. 
Other variables summarized in Table 1 include dimensionless ratios using 
Hj, the incident wave height (significant height for irregular waves) at the 
toe of the structure; T, the wave period (period of peak energy density for 
irregular waves); and L, the wavelength at the toe of the structure. 
Only those tests with fully turbulent hydraulic conditions are considered 
in order to minimize the influence of viscous effects (Jonsson, 1966). The 
Reynolds number, Re, proposed by Madsen and White (1976), 
R2 20 
Re“ T vu tand 8) 
where R is the wave runup and v the kinematic viscosity of water (about 
0.009 square centimeter per second at 20° Celsius), is used to establish which 
tests are fully turbulent. For smooth slopes only those tests with Re > 3 x 10" 
are analyzed; for rough slopes only tests with Re > 10* are considered (Jonsson, 
1966; Madsen and White, 1976). 
VI. TECHNIQUES FOR PREDICTING REFLECTION AND ENERGY 
DISSIPATION COEFFICIENTS 
Section IV showed the strong dependence of the magnitude of the reflection 
coefficient on the amount of wave energy dissipated (also on the amount of wave 
energy transmitted in the case of a permeable or overtopped structure). In this 
section, factors that influence the reflection coefficient are systematically 
investigated, and empirical prediction formulas are developed. Types of wave 
energy dissipation considered include losses in energy due to structure-induced 
wave breaking and wave modification, breaking at the toe of a structure or 
in the surf zone seaward of the structure, structure surface roughness, and 
internal flow in permeable sections of a structure. 
13 
