6. Wave Run-up and Overtopping
191
It was reported that the run-up reaches a maximum for imperméable structures, whereas, the permeability of the structure has an influence on the
run-up only for lower values of £m.
Cm = tan a
W2
m
(6-14)
For larger values of (i.e., “£m” > 6) smooth and rock slopes were found
to yield the same levels of run-up. The formulae for the 2% run-up level
for the mean wave period for a double layered rubble mound slope were
proposed as follows,
RU2%/Hs = 0.96£m for Cm < 1.5
Ru2%/Hs = 1.17^46 for e™ > 1.5
(6.15)
(6.16)
6.2.2 Recent run-up équation
For plane progressive waves, based on the maximum depth-integrated wave
momentum flux Hughes [2003, 2004] presented a new non-dimensional
parameter. The parameter mentioned as the wave momentum flux parameter (FW), was well-defined as,
Pmf —
(6-17)
where
Mp = depth-integrated wave momentum flux
As (A/j^max consists of force per unit length of wave crest, it was claimed
that maximum depth integrated wave momentum flux would deliver a good
représentation of wave processes at Coastal structures.
For establishing an empirical équation for estimating the wave momentum flux parameter for finite amplitude, Hughes [2003, 2004] considered,
non-linear waves based on a numerical solution technique (Fourier approximation) and the resulting empirical équation, was given as,
l' Mf\
_ . / d \ ‘4’
2.026
Ao = 0.639 ( — )
\ a J
Ar = 0.180 ( — )
(6.18)
(6.19)
(6.20)