S.A. Hughes / Coastal Engineering 51 (2004) 10671084
1069
Iribarren number (n and no) also known as the surf
similarity parameter. This parameter was introduced
number of waves in the surf zone. Since that time,
the Iribarren number has appeared in many empirical
whether breaking would occur on a plane slope. As
formulas related to beach processes and coastal
structures.
and Nogales suggests the parameter no gives the ratio
The deepwater Iribarren number is directly
of the beach or structure slope bsteepnessQ to the
proportional to the wave period and to the beach
or structure slope, and no is inversely proportional to
square root of wave steepness as defined by the local
wave height (H) at the toe of the slope divided by the
the square root of local wave height. Water depth is
deepwater wave length (Lo). Note that often the
not included in the deepwater Iribarren number, but
parameter no is calculated using a finite-depth local
it is implicitly included in the local Iribarren number
based on local wave length. Most successful
wave height near the slope toe rather than a true
applications of the deepwater Iribarren number
deepwater Ho. For example, in laboratory experi-
pertain to surf zone processes where the waves
ments, it is common to specify H as the wave height
undergo depth-limited breaking on the slope. Con-
measured over the flat-bottom portion of the wave
sider two waves having significantly different wave
facility before significant wave transformation occurs
heights but the same value of wave steepness, H/Lo.
due to shoaling. In some cases, HcHo, but this is not
always assured. For the discussion in this paper, we
Depth-limited breaking will occur at different depths
will assume that no is based on the local wave height
on the slope, and the magnitude of the dimensional
flow parameters at breaking will be different; but this
at or near the toe of the slope rather than Ho.
does not seem to matter for some surf zone processes
plane and composite slopes. His analysis for the case
where waves break on the slope resulted in a
approximation, waves in the surf zone decay in a
dimensionally nonhomogeneous equation for maxi-
self-similar manner with breaker height proportional
mum runup R given as
to water depth, so it can be argued that the wave
bores resulting from these two different waves
tana
R
behave much the same after breaking provided they
2:3 rffiffiffiffiffiffi
1
H
H
have the same deepwater wave steepness prior to
T2
breaking. Likewise, we should expect somewhat
similar flow characteristics in the broken waves as
Recognizing that the coefficient 2.3 has units of ft1/2/s,
Eq. (1) can be expressed as a dimensionally homoge-
However, prior to depth-limited wave breaking,
neous equation in terms of deepwater Iribarren
deepwater wave steepness based on local wave
number with the introduction of the gravity constant
height (and by extension the deepwater Iribarren
in Imperial units, i.e.,
number) is not necessarily a good descriptor of flow
kinematics because local water depth is not included.
R
1:0no
2
This is illustrated by noting that deepwater wave
H
steepness can be represented as the product of
This form of Hunt's equation (with different dimen-
relative wave height (H/h) and relative water depth
(h/gT2), so that
sionless coefficient) is presently used to estimate
irregular wave runup on plane impermeable slopes
1=2
!1=2
no
H
H
h
2p
3
Hughes, 2002).
gT 2
tana
Lo
h
The surf similarity parameter was popularized by
Fig. 1 plots the variation of (H/Lo)1/2 for different
number and showed its applicability to a number of
values of relative depth. The solid lines are constant
surf zone processes including: a criterion for wave
values of relative wave height (H/h) between 0.1 and
breaking, differentiation of breaker types, wave setup,
0.7. The heavy-dashed curve is the wave steepness