Geoscience Reference
In-Depth Information
rip cells also exist on long straight beaches with little
variation in offshore topography, another mechanism must
also act to provide lateral variations in wave height. This is
thought to be that of standing
edge waves
(Fig. 6.48),
which form as trapped waveforms due to refraction and
refracting wave interactions with strong backflowing wave
swash on relatively steep beaches. Edge waves were first
detected on natural beaches as short-period waves acting
at the first subharmonic of the incident wave frequency,
decaying rapidly in amplitude offshore. The addition of
incoming waves to edge waves give marked longshore vari-
ations in breaker height, the summed height being great-
est where the two wave systems are in phase. It is thought
that trapped edge waves may be connected with the for-
mation of the common cuspate form of many beaches;
these have wavelengths of a few to tens of meters, approx-
imately equal to the known wavelengths of measured edge
waves. Results concerning the effects of edge waves and
“leaky” mode standing waves (where some proportion of
energy is reflected seaward as long waves at infragravity
frequency, 0.03-0.003 Hz) indicate that both shoreward
and seaward transport may result, dependent on
conditions. Usually, water entrained under groups of large
waves in arriving wavepackets is preferentially transported
seaward under the trough of the bound long period
group wave.
The familiar longshore currents are produced by
oblique wave attack upon the shoreline; these may be
superimposed upon the rip cells described earlier. Such
currents, which give a lateral thrust in the surf zone, are
caused by
Sign convention
+z, w
Plane surface
parallel to
y
normal to
x
+y,v
t
yy
+x,u
Wave crests normal
to plane (shore)
t
xx
c
a
x
w
u
Wave group energy
per unit area
E = 0.5
e.g. flux of
x-momentum
per unit vol. is
(ru)u = t
xx
r
=
Water
density
h
ga
2
r
bottom
Fig. 6.46
Definition diagram for the radiation stress,
, exerted on
the positive side of the
xy
plane by wave groups approaching from
the left hand side. The radiation stress is the momentum flux
(i.e. pressure) due to the waves.
30
20
Setup
10
Still water level
xy
, the flux toward the shoreline (
x
-direction) of
momentum directed parallel to the shoreline (
y
-direction).
This is given by
0
-5
Theory
Experiment
is the angle
between wave crest and shore (shore-parallel crests
xy
0.25
E
sin 2
, where
Setdown
0
;
Fig. 6.47
Wave setup and setdown as produced by radiation stress
caused by incoming waves in an experimental tank.
shore-normal
90
). The
xy
value reaches a maximum
when sin 2
1, or when the angle of wave incidence is
45
. Field data give the longshore velocity component,
u
l
,
as 2.7
u
max
sin
cos
.
radiation stress
xx
remaining after wave reflection and
bottom drag and is balanced close inshore by a pressure
gradient due to the sloping water surface (Fig. 6.48). In
the breaker zone the setup is greater shoreward of large
breaking waves than smaller waves, so that a longshore
pressure gradient causes longshore currents to move from
areas of high to low breaking waves. These currents turn
seaward where setup is lowest and where adjacent currents
converge.
What mechanism(s) can produce variations in wave
height parallel to the shore in the breaker zone? Wave
refraction is one mechanism; some rip current cells are
closely related to offshore variations in topography. Since
6.6.3
Estuarine circulation dynamics
Water and sediment dynamics in estuaries are closely
dependent upon the relative magnitude of tide, river, and
wave processes. The incoming progressive tidal wave is
modified as it travels along a funnel-shaped estuary whose
width and depth steadily decrease upstream. For a 2D
wave that suffers little energy loss due to friction or reflec-
tion (a severe simplification), the wave energy flux will
remain constant, causing the wave to amplify and shorten
as it passes upstream into narrower reaches. This is the
Search WWH ::
Custom Search