S.A. Hughes / Coastal Engineering 51 (2004) 10671084

1069

Iribarren number (n and no) also known as the surf

wave runup and rundown, wave reflection, and

similarity parameter. This parameter was introduced

number of waves in the surf zone. Since that time,

by Iribarren and Nogales (1949) as an indicator for

the Iribarren number has appeared in many empirical

whether breaking would occur on a plane slope. As

formulas related to beach processes and coastal

discussed by Battjes (1974), the derivation of Iribarren

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,

suggested by Battjes (1974).

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

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

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