facilities, and result in the development of great strains on mooring lines. 

 Therefore seawalls, bulkheads, and revetments inside of harbors should dissi- 

 pate rather than reflect incident wave energy whenever possible. Natural 

 beaches in a harbor are excellent wave energy dissipaters, and proposed harbor 

 modifications which would decrease beach areas should be carefully evaluated 

 prior to construction. Hydraulic model studies are often necessary to evalu- 

 ate such proposed changes. The importance of wave reflection and its effect 

 on harbor development are discussed by Bretschneider (1966), Lee (1964), and 

 LeMehaute (1965); harbor resonance is discussed by Raichlen (1966). 



A measure of how much a barrier reflects waves is given by the ratio of 

 the reflected wave height IL. to the incident wave height Hi which is 

 termed the reflection coefficient x> hence x = H^/Hj . The magnitude of x 

 varies from 1.0 for total reflection to for no reflection; however, a small 

 value of X does not necessarily imply that wave energy is dissipated by a 

 structure since energy may be transmitted through some structures such as per- 

 meable, rubble-mound breakwaters. A transmission coefficient may be defined 

 as the ratio of transmitted wave height H^ to incident wave height H^, In 

 general, both the reflection coefficient and the transmission coefficient will 

 depend on the geometry and composition of a structure and the incident wave 

 characteristics such as wave steepness and relative depth d/L at the struc- 

 ture site. 



2. Reflection from Impermeable, Vertical Walls (Linear Theory) . 



Impermeable vertical walls will reflect most incident wave energy unless 

 they are fronted by rubble toe protection or are extremely rough. The reflec- 

 tion coefficient x is therefore equal to approximately 1 .0, and the height of 

 a reflected wave will be equal to the height of the incident wave. Although 

 some experiments with smooth, vertical, impermeable walls appear to show a 

 significant decrease of x with increasing wave steepness, Domzig (1955) and 

 Goda and Abe (1968) have shown that this paradox probably results from the 

 experimental technique, based on linear wave theory, used to determine x* 

 The use of a higher order theory to describe the water motion in front of the 

 wall gives a reflection coefficient of 1.0 and satisfies the conservation of 

 energy principle. 



Wave motion in front of a perfectly reflecting vertical wall subjected to 

 monochromatic waves moving in a direction perpendicular to the barrier can be 

 determined by superposing two waves with identical wave numbers, periods and 

 amplitudes but traveling in opposite directions. The water surface of the 

 incident wave is given to a first- order (linear) approximation by equation (2- 

 10) 



and the reflected wave by 





Consequently, the water surface is given by the sum of v] ^ and n^., or, 

 since % = H^, 



2-112 



