2.4 The Influence of Current on the Evolution of Waves at the Global Scale
4 7
Fig. 2.4. Wave propagation rays in the Southern Ocean under circumpolar current
conditions: cp~ -ray "turning" points without any current; cp; -ray "turning" points
with current
( *)
2k{} v;
cos 'P =
.
Rg ( 1 + z; v{} ± V 1 + ~ v{})
(2.30)
Unlike wave propagation without currents, considered in the previous section, in this case the turning point depends not only on the latitude 'P and
the initial propagation angle /30 (see (2.8)), but also on the current velocity.
For waves originally propagating in the southern direction, and small
values of the ratio wV/g « 1, the expression (2.30) can be written as:
( *)
kTJgcos(cpo) cos(/3o)
coscp ~
(
)
.
w2 1- 2wyTJ
g
(2.31)
According to (2.31) for v{} = 1 ms- 1 and the wave period T = 11 s (with
w "' 0.5 rads- 1 ), the angle cp* is changed additionally due to current, by
approximately 10°, i.e. the turning point is shifted along a latitude over
1000 km south or northward depending on the current velocity direction (see
Fig. 2.4).
Estimates of the influence of the current on waves obtained in this section
reveal that the current is reflected and the waves cannot reach the Antarctic
shores (see Fig. 2.4). This occurs in the case of propagation of northwest
waves typically generated by westerly and northwesterly winds. Thus, superposition of incident and reflected waves should be observed to the north