IV. Retreating Shorelines ...
239
k may be written :
k = (D/A) 3/4
(15)
D = grain size diameter taken as Ds0, A = semi-excursion of water
participles right over the bottom.
In order to maintain the same shear stress over the bottom, r must remain
the same, or"
r~x = (D/A) 3/4 p.U2max = constant
Um~ can be written "
....
osh
+...
Um,x T
(16)
(17)
H -- d 1/3
or
H --- d TM
which shall remain the same over the profile subjected to shear stresses by
the oscillating water movement brought about by the wave action. Consider
one particular storm of extreme intensity and a narrow range of periods
which is normal. Wave heights decrease relatively little moving from the
offshore towards the relatively steep bottom. Energy loss will mainly take
place by bottom friction and little or less by top-breaking and internal
friction. The wave height H, in relation to depth d, may be approximated
as :
(19)
(20)
Eq. (18) may for one particular storm wave period be written as •
(D/A)3/4.H 2 constant
(21)
(18)
tE d ] ]2
=
(D/AW. F cosh Fc-/+...]
IT
This equation in its first approximation is fairly accurate for the area outside
the breaker zone. One therefore has"