and the transmission coefficient will dépend upon the geometry and composition of a structure and the incident wave characteristics such as wave
steepness and relative depth d/L, at the structure site.
2.52 REFLECTION FROM IMPERMEABLE, VERTICAL WALLS (LINEAR THEORY)
Imperméable vertical walls will reflect almost ail incident wave
energy unless they are fronted by rubble toe protection or are extremely
rough. The reflection 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, imperméable
walls appear to show a significant decrease of x with increasing wave
steepness, Domzig (1955), Goda and Abe (1968) hâve shown that this paradox
probably results from the experimental technique, based on linear wave
theory, used to détermine 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,
(2-10)
and the reflected wave by,
/2nx
2nt\
T] = — cos ---- + ~~~
r
2
\ L
T )
Conséquently, the water surface is given by the sum of
and nr
since
V = rj. + T]r =
which reduces to
2îtx
2nr
tj = H. cos —— cos — .
(2-79)
Equation 2-79 represents the water surface for a standing wave or ctapotis
which is periodic in time and in x having a maximum height of 2H^ when
both cos(2ttx/L) and cos(2îit/T) equal 1. The water surface profile as a
function of 2irx/L for several values of 27it/T are shown in Figure 2-61.
There are some points (nodes) on the profile where the water surface
2-113