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> Fig. 13. Measured versus predicted nonbreaking solitary wave run-up--Liformula.
Breaking solitary wave run-up
Notation
Hughes-Runup-CEv51
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1100
S.A.
Hughes
/
Coastal
Engineering
51 (2004) 10851104
triangular
wedge
derivation
presented
earlier
is
not
and
predicted
R/h was
0.12
for
all
data,
and
the
RMS
appropriate
for
steeper
slopes
and
a
more
accurate
error
dropped
to
0.034
when
the three
out-lying
points
description
of the
wedge
volume
is needed.
Never-
were
discarded.
Also
note
that structure slope
has
a
theless,
Eq.
(43)
yielded
reasonable
estimates
for
relatively
minor
influence
for
nonbreaking
solitary
slopes
between
1/30
and
1/10.
waves.
A
theoretical
run-up
equation
for
nonbreaking
3.4.2.
Nonbreaking
Solitary
Wave
Run-up
solitary
waves
was presented by
Li
and
Raichlen
Nonbreaking
wave
run-up
data
from
Synolakis
(2001)
as
(1986,
1987)
for
a
plane
impermeable
slope
with
5=4
cota
=2.08,
and
data
from
Hall
and
Watts
(1953)
for
R
H
1=2
2:
831
cota
slopes
with
cot a
=1.0,
2.14
and
3.73
were
used
to
h
h
Li
examine
the
utility
of
the
wave
momentum
flux
9=4
H
parameter
for
estimating
nonbreaking
solitary
wave
3=2
0:
293
cota
45
run-up.
In this
case,
relative
wave
run-up
R/h was
h
shown
to be
directly
proportional
to the
maximum
Predictions
using
Eq.
(45)
are
compared
to
the
depth-integrated
wave
momentum
flux
parameter
with
a
very
good
fit
to the
122
data
points
provided
by the
nonbreaking
run-up
data
in
Fig.
13
.
Good
corre-
expression
spondence is
seen
except
for
the
milder
slope
with
cota
=3.73.
It is
interesting
to
note
that
R
M
F
substitution
of
Eq.
(31)
for
M
F
/(qgh
2
) in
Eq.
(44)
1:82cota
1=5
44
qgh
2
h
results in an
expression
containing
terms
with
H/h
raised to
powers
that are
approximately
the
same
as in
Goodness-of-fit
is
shown
in
Fig.
12
for
the
nonbreaking
Eq.
(45).
wave
run-up
data.
With
the
exception
of a
few
outlying
points,
the
empirical
Eq.
(44)
does
remarkably
well.
Overall
root-mean-squared
error
between
measured
4.
Summary
and
conclusions
The
goal
of
this
study
was
to
develop
new
formulas
for
wave
run-up
on smooth,
impermeable
plane
slopes
based
on a
new
parameter
representing
the
maximum
depth-integrated
wave
momentum
flux
occurring
in a
wave.
These
formulas
should
be as
good
as
existing
formulas
for
estimating
run-up
due
to
waves
that
break
on the slope
and
better at
estimating
nonbreaking
wave
run-up.
A
crude
run-up
formula
was
derived
based
on the
simple
argument
that the
weight
of
water
contained
in
the
run-up
wedge
above
still
water
level
at
maximum
run-up
is
proportional
to the
maximum
depth-inte-
grated
wave
momentum
flux
in the
wave
at or
near
the
toe of the slope.
The
derived
general
formula
included
an
unknown
function
of slope that needed to be
determined
empirically.
Existing
published
wave
run-up
data
for
regular,
irregular
and
solitary
waves
were
used
to establish
the
empirical
slope
functions
for
the
new
wave
run-
up
formulas.
Reasonable
predictive
capability
for
Fig.
13.
Measured
versus
predicted
nonbreaking solitary
wave
run-
regular
waves
was demonstrated
for
all
but
the
up--Li
formula.
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