286
L. Erikson et al. / Coastal Engineering 52 (2005) 285302
collapsed bores that move up and down a slope as a
The impetus for this study was to gain some
mass of water was first described by Ho et al. (1963)
insight into swash behavior due to waves generated
and Shen and Meyer (1963). They derived a set of
by moving vessels although it is believed that the
governing equations, based on the non-linear shallow
results are applicable to a wider range of wave
water equations (NLSWE) together with mathemat-
conditions. A moving ship typically generates a set of
ical and physical interpretations of singularities at the
waves at both its bow and stern as a consequence of
point of bore collapse and maximum run-up.
pressure gradients along the hull. These waves are
often referred to as wash waves and, when measured
hypothesis. He noted that during the up-rush, and
some distance from the navigation route of a vessel
initial stages of the back-wash, the leading edge
they consist of a group of waves that increase in
behaved like a unit mass moving up and down the
height to some maximum and subsequently decrease.
foreshore under the action of gravity, neglecting
When these waves reach the shore there is often
friction.
significant interaction between subsequent waves
such that when a wave reaches the shoreline and
water theory to field data from a number of natural
travels up a beach face it is not always able to
sandy beaches with steep foreshore slopes
complete a full swash cycle before the next wave
(tanb=0.093 to 0.15). A comparison between
comes along. This second wave either overtakes the
measurements and inviscid theory replicated the
first wave during its up-rush stage (catch-up) or
gross flow behavior of the up-rush well, but
collides with the first wave during the back-wash
overestimated the maximum run-up by as much as
stage. This interaction between waves continues with
65%. He speculated that the difference in magni-
each incoming wave, and with respect to the hydro-
tude was due to not accounting for bed friction and
dynamics, the end result is that the maximum run-up
infiltration (median grain size diameters of
will not correspond to the up-rush of the highest wave
in the train. This is particularly true for mild foreshore
slopes (tanbb0.1) where the time it takes for a swash
added a stress term for bed friction to the non-
lens to travel up and down is longer than for steeper
linear shallow water theory and solved the equa-
slopes (Mase and Iwagaki, 1984).
tions with measured values to obtain an inferred
The objective of this study was to develop a simple
friction value of 0.1 for the up-rush. Similarly,
physically-based approach to describe the shoreline
motion while accounting for interaction between
rush and back-wash friction factors by iterating on f
subsequent waves in the swash zone. A particular
using the non-linear shallow water theory (also
focus on vessel generated waves was also the intent. A
termed dballistic modelT) and compared the results
description of the shoreline motion due to collapsing
to measured data obtained at Duck in 1994
bores at the still water shoreline is particularly suitable
(D50=0.22 mm). Analysis of over 2000 individual
for modeling swash interaction and, thus, this already
swash events showed that an up-rush friction
well established approach was modified to incorporate
swash interaction. An equation describing the onset of
coefficient fb=0.04 gave the best results with
swash interaction, including the effects of friction is
respect to the minimum overall error between
derived. The equation is tested and numerical results
calculated and measured swash trajectories. The
of the model with and without swash interaction for
authors also noted that during the field campaign,
data from a laboratory experiment conducted in part
the foreshore slope decreased from about 0.19 to
for this study are presented.
0.06 and that the foreshore seemed to adjust in
order to minimize swash interaction. By iterating on
f, they essentially accounted for swash interaction
by adjusting the friction terms.
2. Literature review
The catch-up and absorption mechanism of
The hypothesis that the time-varying position of
swash interaction was explicitly modeled by Mase
the leading edge of the shoreline can be described by
and Iwagaki (1984) employing empirical data and
Previous Page
