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

Table 2

The hydrodynamic interaction of waves with

Common dimensionless wave parameters

coastal structures is complex, and steady progress

Parameter

Value

has been made toward understanding wave/structure

h/L; h/gT2; kh

interactions. However, some engineering aspects of

Relative depth

Relative wave height

H/h

coastal structure design are still not fully described by

H/L; H/Lo; H/gT2

Wave steepness

theory. Examples include rubble-mound armor stabil-

Ho/Lo; Ho/gT2

Deepwater wave steepness

ity, wave runup on permeable slopes, and wave

paffinffiaffiffi

t ffiffi

Local Iribarren number, n

H=L

overtopping of protective structures.

ptffiaffiffiaffiffiffiffi

ffinffi

Deepwater Iribarren number, no

Engineers have established useful design guidance

Ho=Lo

by augmenting theoretical reasoning with empirical

or paffinffiaffiffiffiffi

tffi ffi

coefficients determined from small-scale laboratory

H=Lo

testing. The balance between theoretical and empirical

and other parameters such as those given in Table 1.

contribution to coastal structure design guidance

This helps reduce the number of independent varia-

varies widely. For example, estimation of nonbreaking

bles that need to be examined during laboratory

wave forces on vertical walls is largely theory with

testing. Table 2 lists the more common dimensionless

some empirical adjustments, whereas estimation of

wave parameters that are used in coastal structure

irregular wave runup on permeable structures is

design guidance.

almost entirely empirical.

With the exception of relative wave height, H/h,

Waves are usually included in empirical design

the wave parameters listed in Table 2 strictly

relationships by one or more wave parameters

pertain to uniform, periodic waves of permanent

considered to be representative of the incident wave

form. It is customary to use first-order wave theory

condition. Common regular and irregular wave

to calculate values for wave length. These dimen-

parameters are listed Table 1. Sometimes, these wave

sionless parameters are also used to characterize

parameters are combined to form dimensionless

irregular waves trains by substituting wave heights,

variables that may include relevant fluid parameters

wave periods, and wave lengths representative of

irregular waves, such as wave heights Hmo, Hrms,

Table 1

H1/3, and H10%; wave periods Tp and Tm; and wave

Common wave and fluid parameters

lengths Lp, Lop, Lm and Lom. (See list of symbols at

Regular wave parameters

end of paper for definitions of these irregular wave

H--wave height

Ho--deepwater wave height

parameters.)

L--local wave length

Lo--deepwater wave length

Correlations between dimensionless wave param-

k--wavenumber [=2p/L]

T--wave period

eters and process responses observed in experiments

Irregular wave parameters

form the basis for much coastal structure design

Hmo--zeroth-moment

Hs--significant wave height

guidance and some nearshore beach processes. Often,

wave height

[=H1/3]

justification for using a particular wave parameter is

Hrms--root-mean-squared

H10%--10% of waves are

not based on a physical argument, but simply because

wave height

higher

it produced the least scatter in the correlation. Only

Tp--spectral peak wave

Tm--mean wave period

relative wave height, H/h, is applicable to solitary

period

Lp--wave length associated

Lop--deepwater wave length

waves, although there are some definitions for solitary

with Tp

with Tp

wave length which would allow use of the other wave

Lm--wave length associated

Lom--deepwater wave length

parameters.

with Tm

with Tm

Fluid and other parameters

2. The Iribarren number

q--fluid density

g--gravitational acceleration

l--coefficient of dynamic

m--coefficient of kinematic

viscosity

viscosity

One parameter of proven usefulness for wave

a--beach or structure slope

h--water depth

processes on beaches and at coastal structures is the

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