Outer Earth processes and systems - Physical Processes in Earth and Environmental Sciences - page 265

6

Plan Plan

Shelf depths
100 m
50 m
25 m

4

2

Flood tide Ebb tide

t = 0 t = 6/12T

Pressure force P ressure force

0 0

0.5 1.0 1.5

Shelf width in tidal wavelengths

x -section x -section

Fig. 6.36 Tidal wave resonance across shelves of different width and
water depth.

Coriolis f orce Coriolis force

3 m to a spring maximum of some 15.6 m along its length
to the antinode.
The Coriolis force acts as a moderating influence on
tidal streams in semi-enclosed large shelves, like the north-
western European shelf, the Yellow Sea, and the Gulf of
St. Lawrence. In the former, the progressive anticlockwise
tidal wave of the North Atlantic enters first into the Irish
Sea and the English Channel and then several hours later it
veers down into the North Sea proper through the
Norway-Shetland gap in a great anticlockwise rotary wave
(whose passage north to south was noted by the monk
Bede in the eighth century). Why should such rotary
motions occur? The answer is that the tidal gravity wave,
unlike normal surface gravity waves due to wind shear or
swell (Section 4.9), has a sufficiently long period that it
must be deflected by the Coriolis force. Since the water on
continental shelf embayments like the North Sea is
bounded by solid coastlines, often on two or three sides,
the deflected tide rotates against the sides (Figs 6.37 and
6.38) as a boundary wave . Such waves of rotation against
solid boundaries are termed Kelvin waves , the propagating
wave being forced against the solid boundaries by the
effects of the Coriolis parameter, f . The water builds up as
a wave whose radial slope exerts a pressure gradient that
exactly balances the Coriolis effect at equilibrium
(Fig. 6.39). Tidal currents due to the wave are coast paral-
lel at the coast (Fig. 6.40a) with velocities at maximum in
the crest or trough (reverse) and minimum at the half-
wave height. The wave decays in height exponentially sea-
ward toward an amphidromic node of zero displacement.
The resonant period in the North Sea is around 40 h, a
figure large enough to support three multinodal standing
waves (Fig. 6.41). The crest of the tidal Kelvin wave is a

Cotidal lines and amphidromic point

3

4 2

5 1

6 Ap 0

7 11

8 10

t = 9

Times in 1/ n of 12 h tidal period

Fig. 6.37 The development of amphidromic circulation within a
partly enclosed shelf sea by Coriolis turning of the tidal wave into
a Kelvin wave of circulation.

radius of the roughly circular basin and is also a cotidal line
along which tidal minima and maxima coincide.
Concentric circles drawn about the node are lines of equal
tidal displacement. Tidal range is thus increased outward
from the amphidromic node by the rotary action. Further
resonant and funnelling amplification may of course take
place at the coastline, particularly in estuaries (see
Section 6.6.3). Not all basins can develop a rotary tidal
wave: there must be sufficient width, since the wave decays
away exponentially with distance. The critical width is
termed the Rossby radius of deformation , R , given by the
ratio of the velocity of a shallow-water wave to t he magni-
tude of the Coriolis parameter, that is, R g h / f . At