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is increased, until the regular flow pattern breaks down
into fully irregular flow [
Pfeffer et al.
, 1980;
Buzyna et al.
,
1984].
In its “purest” form, SV has been observed as the peri-
odic tilting back and forth of the main wave troughs. In
association with this observation, the lateral distribution
of eddy energy within the wave was observed to shift back
and forth between the inner and outer sides of the chan-
nel. This observation led some to suggest a kinematic form
for the wave as the superposition of dominant waves with
the same zonal wave number and with lateral structures
(a)
Y
.5
L
H
L
H
O
O
O
O
O
0
H
L
H
L
-.5
.5
(b)
O
O
O
O
H
L
L
H
0
L
H
L
H
φ
1
(y)
=
A
1
sin
πy
,
(1.21)
-.5
.5
φ
2
(y)
=
A
2
sin 2
πy
,
(1.22)
(c)
both propagating azimuthally at different phase speeds.
This type of behavior has been reproduced in a class
of simple, low-order numerical models in which a small
number of wave modes are allowed to interact through
mutual advection in a quasi-geostrophic model.
Weng
and Barcilon
[1987], for example, followed a much ear-
lier approach pioneered by
Lorenz
[1963b] and applied it
to a nonlinear version of the Eady model including the
first two lateral modes (cf. equations (1.21) and (1.22))
to obtain solutions in which eddy energy oscillated in
y
through nonlinear interference between the two gravest
y
modes with the same
x
wave number (e.g., see Figure 1.14).
In practice, however, observed 'structural vacillations'
are often more complicated than this picture would sug-
gest, for example, with transient small-scale features grow-
ing and decaying within a large-scale pattern dominated
by a single azimuthal wave number. Oscillations often
appear to be strongly intermittent and irregular, and the
phenomenon suggests the growth of small-scale insta-
bilities within the large-scale pattern (either barotropic
or baroclinic) that do not reach sufficient amplitude to
disrupt the main pattern.
Read et al.
[1992] found that
the onset of SV occurs quite suddenly at a well-defined
point in parameter space, again with evidence of intermit-
tency in time. The irregular character of the oscillations
becomes steadily more apparent as
is increased, and
the large-scale pattern becomes gradually more distorted
until it begins to break up into irregular flow. This does
not seem to be readily consistent with notions of chaos
in the formal sense, and its precise nature is still not fully
understood (see
Read et al.
[1992] for further discussion).
SV is frequently regarded as an intermediate state prior
to the full onset of irregular wave flow or “geostrophic
turbulence.”
At the highest rotation rates, the wave number spectrum
is observed to fill up to become a broadband contin-
uum, though a limited band of wave numbers still tends
to dominate the spectrum. The most detailed laboratory
measurements of the transition to irregular flow with
L
H
L
H
0
O
O
O
O
O
O
O
O
H
L
H
L
-.5
.5
(d)
O
O
O
O
L
H
L
H
0
L
L
H
H
-.5
.5
(e)
L
H
L
H
O
O
O
O
0
L
L
H
H
4π
X
-.5
0
2π
Figure 1.14.
Stream function fields from a wave number 6 flow
at mid-depth in the
x
y
plane of a zonal channel (where
x
is the
zonal direction and
y
the lateral or meridional direction) during
a structural vacillation cycle, as obtained in a low-order quasi-
geostrophic model. Adapted from
Weng and Barcilon
[1987]
with permission of John Wiley & Sons, Inc.
−
increasing
were carried out by
Buzyna et al.
[1984]
[see also
Pfeffer et al.
, 1980] and
Hide et al.
[1977], in
the former case using the large annulus at Florida State
University. Both studies showed the gradual broadening
of the wave number spectrum and increasing significance
of nonharmonically related azimuthal components as the
fully developed irregular regime was entered (some exam-
ples from the study by
Buzyna et al.
[1984] are shown
in Figure 1.15). At extreme parameter values, the time-
averaged spectrum does not display strong peaks at any
particular individual wave number but appears as a broad
