Outer Earth processes and systems - Physical Processes in Earth and Environmental Sciences - page 270

latitudes, small to moderate buoyancy fluxes are soon
turned by the Coriolis force, and they may be trapped
along-source in the mid- to inner shelf where they form
coastal currents or linear fronts. Mixing vortices develop
along the free shear layer of the fronts and offshore cir-
culating shelf waters. Plumes are very sensitive to the
effects of coastal upwelling or downwelling currents
caused by winds. They may reach some way out into the

mid-shelf or right across the shelf break, depending upon
their dynamic characteristics and those of the shelf. Low
slopes encourage long passage, whilst the development of
vorticity on steeper slopes encourages turning and termi-
nation. The large buoyancy flux of many late spring and
summer Arctic rivers, for example, causes plumes to
extend for up to 500 km offshore, well into the Arctic
Ocean.

6.6 Ocean-land interface: coasts

Coasts are dynamic interfaces between land and sea where
energy is continuously being transferred by the action of
traveling waves, including the tide. This incoming wave
energy flux also interacts with energy inputs from the land,
in the form of river flows. The nature of any coastal inter-
face varies according to the type and magnitude of these
various energy fluxes and also to the geological situation
determined by bedrock type (more or less resistant). Like
any interface the coast may be largely static in time and
space or it may be highly mobile, either advancing seaward
when sedimentary deposition dominates, a prograding
coastline , or retreating landward when erosion and net
transport outward to the shelf dominates, a retreating
coastline .

a wide surf zone in which the waves steepen slowly, show
low orbital velocities, and surge up the beach with very
minor backwash effects.
The shallow water nature of incoming coastal waves
means that the wave trains are no longer made up of dis-
persive waveforms, as for deepwater waves (Section 4.9).
Instead, the speed depends only upon water depth and so
the impact of waves upon shallow topography leads to a
number of interesting features, chiefly the familiar curva-
ture or refraction of approaching oblique wave crests as
they “feel bottom” at different times (Fig. 6.45).

6.6.2 Waves arriving at coasts: The role of
radiation stress

6.6.1 Nearshore wave behavior The forward energy flux or power associated with waves

approaching a shoreline (Section 4.9) is, Ecn , where E is
the wave energy per unit area, c is the local wave velocity,
and n

As the typical sinusoidal swell of the deep ocean passes
landward over the continental shelf the dispersive wave
groups (Section 4.9) undergo a transformation as they
react to the bottom at values of between about 0.5 and
0.25 of wavelength,

0.5 in deepwater and 1 in shallow water. Because
of this forward energy flux there exists a shoreward-
directed momentum flux or radiation stress outside the
zone of breaking waves. This radiation stress is the excess
shoreward flux of momentum due to the presence of
groups of water waves, the waves outside the breaker zone
exerting a thrust on the water inside the breaker zone.
This thrust arises because the forward velocity associated
with the arrival of groups of shallow-water waves gives rise
to a net flux of wave momentum (Fig. 6.46). For wave
crests advancing toward a beach there are two relevant
components of the stress,

. In this transformation to shallow-
water waves, wave speed and wavelength decrease whilst
wave height, H , increases. Peaked crests and flat troughs
develop as the waves become more solitary in behavior
until oversteepening causes wave breakage. Waves break
when the water velocity at the crest is equal to the wave
speed. This occurs as the apical angle of the wave reaches a
value of about 120 . In deepwater the tendency toward

breaking may be expressed in terms of a limiting wave
steepness given by H /

xx , with the x -axis in
the direction of wave advance and the other,

ij . One is

0.14. Breaking waves spill,
plunge, or surge (Figs 6.43 and 6.44); the behavior varies
according to steepness of the beach face. Steep beaches
possess a narrow surf zone in which the waves steepen rap-
idly and show high orbital velocities. Wave collapse is
dominated by the plunging mechanism and there is much
interaction on the breaking waves by backwash from a pre-
vious wave-collapse cycle. Gently sloping beaches show

yy , with the
y -axis parallel to the wave crest. These components are
xx

E /2 for deepwater or 3 E /2 for shallow water, and

yy 0 for deepwater or E /2 for shallow water. Radiation

stress plays an important role in the origin of a number of
coastal processes, including wave setup and setdown,
generation of longshore currents, and the origin of rip
currents (Fig. 6.47).