IV. Retreating Shorelines
3.3
Theoretical Analysis
171
A theoretical analysis has been given by Silvester (op. cir.)
Sitarz [J.A. Sitarz, 1963, Contribution h l'6tude de r6volution des plages h partir
de la consistance des profiles d'6quilibre. Trav. Centre Etud. Rech. Oceanogr.,
10-20] has developed equations, based upon energy principles, for profiles
beyond the breaker-line to the limit of active bed disturbance. He has determined
a relationship for the width of the surf zone for swell and storm-wave profiles,
plus the cross-sectional area of the water in this zone, from which its average
depth can be derived. The offshore profile is given by :
x = ky 2 where k = 0.95/[(s-1)l/2DH 3/2]
(11)
where x is the distance seawards from the breaker line ; y is the depth below
SWL (Still Water Level) ; s is the ratio (density of sediment)/(density of
seawater) = 2.65 ; D is the median sediment diameter at some appropriate depth
(in ram) ; and H is the wave height just offshore from the breaker zone (in m).
The above equation indicates that the milder slopes occur with larger values of k,
which in turn result from finer sediment or smaller wave heights. The usual value
of s (= 2.65) is applicable to most sand situations. It appears strange that wave
period does not enter this relationship, since it determines in part the waterparticle oscillation. Also, the mass-transport "velocity" at the bed is strongly
dependent upon period or depth to wave length ratio. Taken overall it is period
that dictates the refraction pattern and hence the proportion of the deep-water
height occurring near the breaker zone.
To complete the swell-built profile it is necessary to continue the offshore bed
slope or curve up the beach face to the berm. The beach face is best measured at
the site, but some general values are grapheA in fig. 2 for three conditions of
exposure. The D (mm) in fig. 2 represents median diameters of sediment
particles in the swash zone. The berm height should be measured where possible,
since calculations contain too many variables for practical purposes.
3.3
Theoretical Analysis
171
A theoretical analysis has been given by Silvester (op. cir.)
Sitarz [J.A. Sitarz, 1963, Contribution h l'6tude de r6volution des plages h partir
de la consistance des profiles d'6quilibre. Trav. Centre Etud. Rech. Oceanogr.,
10-20] has developed equations, based upon energy principles, for profiles
beyond the breaker-line to the limit of active bed disturbance. He has determined
a relationship for the width of the surf zone for swell and storm-wave profiles,
plus the cross-sectional area of the water in this zone, from which its average
depth can be derived. The offshore profile is given by :
x = ky 2 where k = 0.95/[(s-1)l/2DH 3/2]
(11)
where x is the distance seawards from the breaker line ; y is the depth below
SWL (Still Water Level) ; s is the ratio (density of sediment)/(density of
seawater) = 2.65 ; D is the median sediment diameter at some appropriate depth
(in ram) ; and H is the wave height just offshore from the breaker zone (in m).
The above equation indicates that the milder slopes occur with larger values of k,
which in turn result from finer sediment or smaller wave heights. The usual value
of s (= 2.65) is applicable to most sand situations. It appears strange that wave
period does not enter this relationship, since it determines in part the waterparticle oscillation. Also, the mass-transport "velocity" at the bed is strongly
dependent upon period or depth to wave length ratio. Taken overall it is period
that dictates the refraction pattern and hence the proportion of the deep-water
height occurring near the breaker zone.
To complete the swell-built profile it is necessary to continue the offshore bed
slope or curve up the beach face to the berm. The beach face is best measured at
the site, but some general values are grapheA in fig. 2 for three conditions of
exposure. The D (mm) in fig. 2 represents median diameters of sediment
particles in the swash zone. The berm height should be measured where possible,
since calculations contain too many variables for practical purposes.