Geoscience Reference
In-Depth Information
Bretherton
[1967], represents an upper asymptotic limit to
a critical layer. An earlier explanation of the QBO in fact
suggested that the stratospheric mean-flow oscillation is
driven by critical layer attenuation of a spectrum of grav-
ity waves [
LindzenandHolton
, 1968]. Similarly,
Dunkerton
[1981] and
McIntyre
[1994] considered wave transience
and wave breaking as chronologically more important pri-
mary causes of the zonal mean-flow oscillation in the
atmosphere. Hence, the laboratory experiment of Plumb
and McEwan has also been criticized for its apparent
fundamental difference to the QBO [
Dunkerton
, 1981].
However, the DNS of the laboratory experiment [
Wedi
and Smolarkiewicz
, 2006] suggests in fact the opposite:
The laboratory experiment with its distinct gravity wave
sources, a chronology of wave interference, critical layer
formation, and subsequent downward propagation of the
critical layer, leaving behind a uniform zonal mean zonal
flow, portray a picture of the laboratory experiment that
is much closer to the real atmosphere than perhaps orig-
inally thought. DNS means here integrating the Navier-
Stokes equations under the Boussinesq approximation
for salty water without any parametrizations, resolving
the fluid motion down to the Kolmogorov length scale
η
=
(ν
3
/)
1
/
4
,where
ν
is the kinematic viscosity and
denotes the kinetic energy dissipation rate. In this case grid
sizes are
x
=
QBO and convective processes, while finding equatorial
Kelvin and Rossby gravity waves unimportant relative
to other types of wave forcing. Moreover, the reanalysis
dataset ERA-15 [
Gibson et al.
, 1999] shows no significant
spectral signals of equatorially trapped planetary waves
[
Tindall
, 2003].
Consistently, successful numerical modeling of a real-
istic 3D atmospheric QBO as well as realistic representa-
tions of tropospheric and stratospheric global circulations
require the parametrization of nonorographic, vertically
propagating gravity waves [
Scaife et al.
, 2000;
Giorgetta
et al.
, 2002;
Orr et al.
, 2010].
9.2.1. Laboratory Experiment
The laboratory experiment of
Plumb and McEwan
[1978] was conducted in a transparent cylindrical annulus
(radii
a
= 0.183 m and
b
= 0.3 m) filled with density-
stratified salty water to a height of
z
ab
= 0.43 m. The lower
boundary consisted of a thin rubber membrane oscillating
with a constant frequency
ω
0
=0.43s
−
1
and amplitude
= 0.008 m [
Plumb and McEwan
, 1978]. After some time,
a zonal mean zonal flow (visualized by polystyrene pel-
lets) can be observed for approximately 30-40 min in one
direction and then 30-40 minutes in the other direction,
driven exclusively by the gravity wave trains excited by the
boundary oscillation.
The laboratory experiment was repeated by the GFD-
Dennou Club at the University of Kyoto. A photograph
of their cylindrical annulus can be seen in Figure 9.2. Two
main differences to the original Plumb and McEwan setup
exist: (i) the oscillating membrane was placed at the top
of the annulus initiating an oscillation with an apparent
upward
propagation of the mean flow as opposed to a
downward
propagation in the original experiment and (ii)
several water tank sizes were available (Shigeo Yoden, per-
sonal communication). For example, the setup described
(η)
;see
Moin and Mahesh
[1998] for a
review of DNS. With these grid sizes the dissipation scale
of the density is not resolved but justified a posteriori (see
Section 3e in
Wedi and Smolarkiewicz
[2006]).
In large-scale numerical simulations,
Horinouchi and
Yoden
[1998] found a critical-layer mechanism and con-
tributing waves consistent with
Lindzen and Holton
[1968]
to be responsible for QBO-like oscillations. Notably,
the latter study used an “aqua-planet” idealization with
parametrized convection, exciting a spectrum of shorter-
scale gravity waves. The intercomparison study of sev-
eral global circulation models (GCMs) [
Horinouchi et al.
,
2003] corroborates a correlation between the simulated
O
1
25.0
15.0
5.0
-5.0
-15.0
-25.0
40
10
30
20
100
1965
1970
1975
1980
1985
1990
Figure 9.1.
Quasi-biennial oscillation as analyzed in ERA40 in a time-height representation. The figure shows the equatorial
analyzed (unfiltered) zonal mean zonal wind between 200 hPa and 1 hPa averaged between
1
◦
±
latitude for the period 1965-
1990. The contour interval is 5 m
/
s.
