Figure 6. Diffraction zone notation. 
than more exact theories of wave diffraction which are valid for periodic waves 
over a horizontal bottom and are represented by a Fresnel integral. For this, 
it will be assumed that the energy travels laterally along a wave crest as well 
as along a wave ray. The lateral speed of propagation is assumed to be equal 
to the group velocity of a periodic wave of average period. (Actually, since 
the problem is confined to very shallow-water waves, and the longest waves of 
the spectrum diffract most, the limit of the diffraction zone is defined by an 
angle such as the velocity of propagation of wave energy along the crest and 
is simply VgD, where D is the water depth.) This lateral transmission of 
energy results in a decrease of wave energy from the exposed area to the shaded 
area, such that (Fig. 7) 
D 
H2dx = i H? ds (26) 
A 0 
where s is the distance along a crest from the end of the groin. Figure 7 
shows from simple geometrical relationships that 
Q V2 
OD ee ea PET 
Gp @, 25) 2 
oA = -% tan (45° - a,) (27) 
oC) = Litany (4570+ oF) 
therefore, 
: ‘ an Uecann (4 eac)) us 
He ee ee H*dx (28) 
SO ley A) eh cae) ISO Say) 
20 
