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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
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]
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
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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