290
L. Erikson et al. / Coastal Engineering 52 (2005) 285302
estimated by comparing the duration of a complete
( gsinb)) so that,
swash cycle with the period of the incident waves. If
the duration of the swash cycle exceeds the incident
qffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffi
Ts
1
wave period, then interaction is expected. Because
pffiffi arctan e ln Ae A2 1
e
2 e
Tsg
friction has been introduced to describe the swash
front's position, the predicted motion is asymmetric
13
and the time for the up-rush to reach the maximum
pffiffi
where Ae 1=cosarctan e and e f u2=2yhgsinb.
point of landward displacement, Tsu, is shorter than
0
The parameter e expresses the ratio between friction
the time required for the back-wash to return to the
and gravity. At the limit where e approaches zero, the
SWS, Tsb. The duration of the up-rush can be derived
by noting that u su=0 at the time of maximum
Tsg as a function of e, as well as Tsu/Tsg and Tsb/Tsg.
landward retreat (setting usu=0 in Eq. (2)); the
The figure shows that the swash duration is always
duration of the back-wash can be obtained by setting
shorter if friction is included, and that the duration of
the travel distance of the back-wash equal to the up-
the back-wash is always longer than the up-rush.
rush (xsb=xsu). The total swash duration is given by
Ts=Tsb+Tsu,
pffiffiffiffiffiffiffiffiffiffiffiffiffi
4. Experimental setup
ln A A2 1 u0
Guu0
12
Ts
4.1. Wave flume
g tanGbsinb
g tanGusinb
A 27-m section of a wave tank at the Engineering
where A=1/cos( Gb), and the b and u subscripts of G
Research and Development Center, U.S. Army Corps
refer to values for back-wash and up-rush, respec-
of Engineers in Vicksburg, Mississippi was used for
tively. If fb=fu=f and yhb=yhu=yh, then the effects of
the experiment. The tank measured 0.91 m in width,
friction can be assessed by dividing Eq. (12) by the
and 0.91 m at maximum depth. Waves were generated
by a horizontally displacing piston-type paddle in a
water depth of at least 0.5 m. The experimental setup
is shown in Fig. 3.
Uniform sand with a median grain size diameter
1.0
(D50) of 0.13 mm and a fall speed of 1.4 cm/s was
used in the experiment. The beach profile beneath the
0.8
still water line was graded to represent an equilibrium
profile. Foreshore slopes above the initial still water
line were tanb=0.20 (1:5, vertical to horizontal) or
0.6
tanb=0.07 (1:15), depending on the case.
0.4
4.2. Instrumentation
Ts/Tsg
Tsu/Tsg
0.2
A total of 14 standard capacitance gauges were
Tsb/Tsg
used in the experiment, 3 of which were at or
landward of the SWS. The gauges are estimated to
0.0
measure with an accuracy of 0.5%. Two digital
0
1
2
3
4
Non-dimensional parameter, ε
video cameras (Sony, models PC100E and TRV6E)
were used to record the vertical elevation of the
water surface at the SWS and the run-up lengths.
calculated swash durations, including friction, of the up-rush, back-
The cameras were of the PAL (Phase Alternative
wash and full cycle, respectively. Tsg is the calculated swash
System) Western European and Australian standard
duration without friction.
Previous Page
