80
If the ocean surface is regarded as a "free-surface", i.e., if X = 1, (A9) admits two classes of
wave processes. The fast processes, the Poincare waves (see also Section 3), for which
Iml » f3lk II (k 2 + k 2), are such that
x
x
y
m = ± U 0
2 + g h (k} + k/) ] 1/2 .
(AIO)
These waves are - asymptotically - not affected by the Earth's curvature, since (AlO) does
not encompasses 13. The slow processes contained in (A9) emerge when small angular
frequencies are considered, i.e., m 2 «/0 2 . The corresponding wave processes, called
"planetary waves" or "Rossby waves", obey the following dispersion relation
-ghf3k
m = f 2 + g h (k 2x+ k 2) .
(All)
o
x
y
The phase speed of the Poincare and Rossby waves are displayed in Fig. Al - in a nonasymptotic form.
11= 3500 m
~
,,---.
10 2
---.. '"
h = 500m
:.1:'
-I
E
'"
....."
-'<
+
"0
. .
Q)
10 1
0- -'<
'J)
' - '
U
3"
'" ~
c.. II
V-::.. 10°
, "
"
10 3
10
4
10 5
length cale : k.- I = ky - I (m)
Figure Al. Phase speed of the waves characterized by dispersion relation (A9) (free surface)
and by (A13) (rigid lid) for an ocean depth of h = 3500 m and h = 500 m. We have taken
10 = 8xlO- 5 S-I and 13 = 2xlO- ll m- I s-I, i.e., typical mid-latitudes values.
It is far from clear that fast processes, such as the Poincare waves, need to be included into a
climate models - since climate is presumably determined by much slower phenomena. In the
World Ocean, the fast external waves contain a very small amount of the total energy (e.g.
Zhang and Endoh, 1992). In a climate model, it is thus tempting to ignore these processes. An
elegant way of filtering them out is to drop the time-derivative of 1] in (AI), which thus
transforms to
If the ocean surface is regarded as a "free-surface", i.e., if X = 1, (A9) admits two classes of
wave processes. The fast processes, the Poincare waves (see also Section 3), for which
Iml » f3lk II (k 2 + k 2), are such that
x
x
y
m = ± U 0
2 + g h (k} + k/) ] 1/2 .
(AIO)
These waves are - asymptotically - not affected by the Earth's curvature, since (AlO) does
not encompasses 13. The slow processes contained in (A9) emerge when small angular
frequencies are considered, i.e., m 2 «/0 2 . The corresponding wave processes, called
"planetary waves" or "Rossby waves", obey the following dispersion relation
-ghf3k
m = f 2 + g h (k 2x+ k 2) .
(All)
o
x
y
The phase speed of the Poincare and Rossby waves are displayed in Fig. Al - in a nonasymptotic form.
11= 3500 m
~
,,---.
10 2
---.. '"
h = 500m
:.1:'
-I
E
'"
....."
-'<
+
"0
. .
Q)
10 1
0- -'<
'J)
' - '
U
3"
'" ~
c.. II
V-::.. 10°
, "
"
10 3
10
4
10 5
length cale : k.- I = ky - I (m)
Figure Al. Phase speed of the waves characterized by dispersion relation (A9) (free surface)
and by (A13) (rigid lid) for an ocean depth of h = 3500 m and h = 500 m. We have taken
10 = 8xlO- 5 S-I and 13 = 2xlO- ll m- I s-I, i.e., typical mid-latitudes values.
It is far from clear that fast processes, such as the Poincare waves, need to be included into a
climate models - since climate is presumably determined by much slower phenomena. In the
World Ocean, the fast external waves contain a very small amount of the total energy (e.g.
Zhang and Endoh, 1992). In a climate model, it is thus tempting to ignore these processes. An
elegant way of filtering them out is to drop the time-derivative of 1] in (AI), which thus
transforms to