Outer Earth processes and systems - Physical Processes in Earth and Environmental Sciences - page 264

6.5.1 Shelf tides

Tidal strength may also vary because of the nature of the
connection between the shelf or sea and the open ocean.
In the case of the Mediterranean Sea, for example, the
connection with the Atlantic has become so narrow and
restricted that the Atlantic tide cannot reach any signifi-
cant range over most of its area. Locally, in the Straits of
Gibraltar, the Straits of Messina, and the Venetian Adriatic,
for example, the tidal currents (but not necessarily the tidal
range) may be greatly amplified when water levels between
unrelated tidal gyres or standing waves interrelate.
Another cause of spatially varying tidal strength is the
resonant effect (Section 4.9) of the shelf acting upon the
open oceanic tide (Fig. 6.36) and creating standing waves .
Resonance greatly increases the oceanic tidal range in
nearshore environments and leads to the establishment of
very strong tidal currents. Most shelves are too narrow and
deep (Fig. 6.36) to show significant resonance across
them, that is, L

In the oceans the twice-daily tidal wavelength, , is very

large (about 10 4 km) compared with water depth, h (say
5 km), and is thus still of shallow-water (long-wave) type
(i.e. h /

0.1). From Section 4.9 the maximum tidal
wave velocity in the open oceans is thus given approxi-
mately by u ( g h ) 0.5 , about 220 m s 1 . The open ocean

tidal wave decelerates as it crosses the shallowing waters of
the shelf edge. This causes wave refraction of obliquely
incident waves into parallelism with the shelf break and
partial reflection of normally incident waves. At the same
time the wave amplitude, a , of the transmitted tidal
wave is enhanced. This follows from the energy equation
for gravity waves E

g a 2 ( gh ) 0.5 (Section 4.9); the
supremacy of the square versus the square root terms
means that the overall wave amplitude must increase. The
tidal current velocity of a water particle (as distinct from
the tidal wavelength) also increases because this depends
upon the instantaneous amplitude of the wave.

0.5

. In most cases, for example in the
shelf of the eastern USA, a simple slow linear increase of
tidal amplitude and currents occurs across the shelf. Open
coastal basins like estuaries, bays, and lagoons must receive
the 12-hourly oceanic tidal wave and a standing wave (of
period 12 h) may be set up, with a node at the mouth and
an antinode at the end (by no means the only resonant
possibility). In the limiting scenario, with L

0.25

Shoreface Inner shelf Mid shelf Outer shelf

, we
have . The Bay of Fundy, Maritime Canada,
is the world's most spectacular example of a gulf that res-
onates with the c. 12 h period of the semidiurnal ocean
tide. The gulf has a length of about 270 km (calculated
from the gulf head to the major change of slope at the
shelf edge) and is about 70 m deep on average, giving
the required approximately 12 h characteristic resonant
period. The standing resonant oscillation has a node at its
entrance, which causes the tidal range to increase from

0.25 Surface boundary layer

Mixed b.l.

T 4 L / gh

Fig. 6.34 Simple division of shelf waters into mixed, surface, and
bottom boundary layers. Inner shelf mixed b.l. has tide and wave
mixing, though the degree of mixing is seasonally variable. Outer
shelf is often stratified into a surface b.l. with geostrophic flows and
a friction-dominated benthic boundary layer.

Riverine estuary

or delta distibutary

Buoyant
plume

Seasonal thermocline

Internal waves

Fig. 6.35 Major controls on cross-shelf water and sediment transport.