ERDC/CHL CHETN-III-70
July 2005
Figure 2. Maximum wave runup on smooth impermeable plane slope
Summary of Irregular Wave Runup Prediction for Smooth Slopes: Hughes (2003b)
recommended the following equations for prediction of irregular wave runup on smooth,
impermeable slopes for nonbreaking (surging/collapsing) waves and breaking (plunging/spilling)
waves as delineated by values of Hmo /Lp.
Nonbreaking (surging/collapsing) waves (Hmo/Lp < 0.0225):
1/ 2
⎛M ⎞
Ru 2%
= 1.75 ⎡1 - e-(1.3cot α) ⎤ ⎜ F2 ⎟
1.0 ≤ cot α ≤ 4.0
for
(10)
⎣
⎦ ρgh
h
⎝
⎠
Breaking (plunging/spilling) waves (Hmo/Lp > 0.0225):
1/ 2
⎛M ⎞
Ru 2%
= 1.75 ⎡1 + e-(0.47 cot α) ⎤ ⎜ F2 ⎟
1.5 ≤ cot α ≤ 4.0
for
(11)
⎣
⎦ ρgh
h
⎝
⎠
The formulas are for structure slopes steeper than 1:4 (cot α = 4).
More recently Hughes (2004b) modified Equation 11 for breaking (plunging/spilling) waves to
include irregular runup on smooth, impermeable slopes as mild as 1:30. The newer equation was
given as:
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