Geoscience Reference
In-Depth Information
of upper or lower boundaries in a zonally periodic chan-
nel, forcing gravity wave motions in a stratified fluid, or,
in the other case, by meridional meandering of the lat-
eral boundaries of a zonally periodic equatorial
β
-plane,
forcing Rossby wave motions in a rotating stratified fluid.
Hence, the differentiation between the two systems is on
the basis of the forces that drive the motion.
The remarkable laboratory experiment of
Plumb and
McEwan
[1978] demonstrates the principal mechanism of
the periodically reversing winds of the QBO. The labo-
ratory setup consists of a cylindrical annulus filled with
density-stratified salty water forced at the lower boundary
by an oscillating membrane. At sufficiently large forcing
amplitude the wave motion generates an oscillation in
the zonal mean zonal flow with relatively long periods
compared to the period of the forcing oscillations. The
laboratory experiment is often employed to explain the
basic mechanism of the atmospheric QBO [
Baldwin et al.
,
2001].
In the laboratory, the averaged momentum flux has
been attributed almost exclusively to viscous internal
wave dissipation [
Plumb
, 1977;
Plumb and McEwan
, 1978;
McIntyre
, 2003], in analogy to equatorial Kelvin and
Rossby gravity wave attenuation by infrared cooling and
hence consistent with the theory of
Holton and Lindzen
[1972]. The latter theory motivated the laboratory experi-
ment and its corresponding conceptual synthesis [
Plumb
,
1977;
Plumb and McEwan
, 1978;
Plumb and Bell
, 1982]
that established the fundamental picture of the QBO as
forced by large-scale upward propagating waves, with the
amplitude and the rate of downward propagation deter-
mined by the waves' phase speeds and intensity, respec-
tively [
Lindzen
, 1987].
Notwithstanding, the two-wave model with oppositely
traveling Kelvin and Rossby gravity waves [
Holton and
Lindzen
, 1972;
Plumb
, 1977] is incomplete. Observations
showed that there must be an additional easterly gravity
wave mode required to account for the easterly accelera-
tion of the QBO [
Lindzen and Tsay
, 1975]. Furthermore,
tropical upwelling, a climatic mean upward motion of
the tropical atmosphere, was shown to necessitate con-
tributions to the mean-flow momentum budget of other
wave types. In particular,
Dunkerton
[1997] argued that
shorter-scale gravity waves contribute up to 70% to the
forcing, thus indicating a considerable uncertainty about
the precise origin and the nature of the waves responsi-
ble for driving the QBO. Consistently, high-resolution 3D
simulations demonstrated insufficient provision of wave
momentum flux by the classical two-wave model, given
realistic amplitudes of Kelvin and Rossby gravity waves
[
Takahashi and Boville
, 1992]. By relaxing the simplify-
ing assumptions characteristic of 1D and 2D mechanistic
models, Takahashi and Boville found wave-wave interac-
tions of Kelvin and Rossby gravity waves, and subsequent
modifications of the background wind, to be important
for the simulated QBO period.
Following
Andrews et al.
[1987] and
McIntyre
[2003],
a “critical layer” is a not necessarily zonally continuous
height band, in which a group of waves are attenuated
by a variety of dissipative processes. A critical surface or
level, first elucidated by
Bretherton
[1966] and
Booker and
9.2. QUASI-BIENNIAL OSCILLATION
The QBO represents the dominant variability in Earth's
equatorial stratosphere, exhibiting quasi-regular zonal
mean wind reversals with an average period of approxi-
mately 28 months. Figure 9.1 shows the unfiltered zonal
mean zonal wind over a 25 year period as analyzed by
the ERA40 reanalysis dataset [
Uppala et al.
, 2005], clearly
showing the alternating quasi-regular wind regimes of
easterly and westerly winds and the distinct downward
propagation between 20 and 40 km height at a rate of
approximately 1 km per month. The QBO fundamen-
tally results from the interaction of vertically propagating
waves with the horizontal background flow.
The principal interaction of waves with a mean flow
[
Eliassen and Palm
, 1961] may be illustrated in a vis-
cous, nonrotating Boussinesq fluid [
Plumb
, 1977] by the
momentum equations averaged in a horizontally periodic
domain as
=
i
ν
∂
2
U
∂z
2
∂U
∂t
−
∂F
i
∂z
,
(9.1)
where
U
:=
u
xy
denotes the horizontally averaged (
mea
n)
flow,
ν
denotes the kinematic viscosity, and
F
i
:=
u
w
xy
expresses the
i
ith contribution to the averaged nonlin-
ear momentum flux from a spectrum of waves. Most
atmospheric research of the QBO is now devoted to find-
ing the precise physical origins of the right-hand side
of equation (9.1) and their realizability in the context
of numerical weather prediction and climate modeling.
Long-term observations of temperature fluctuations of
Jupiter's equatorial stratosphere suggest a similar mech-
anism for the quasi-quadrennial oscillation (QQO) [
Lie
and Read
, 2000]. Furthermore, it has been suggested that
dissipative wave-mean flow interactions are responsible
for superrotation phenomena on Venus [
Leovy
, 1973;
Fels
and Lindzen
, 1974;
Hou and Farrell
, 1987;
Yamamoto
and Takahashi
, 2003], the redistribution of chemical con-
stituents in solar-type stars [
Charbonnel and Talon
, 2005],
and the recently observed equatorial oscillation on Sat-
urn [
Schinder et al.
, 2011]. Moreover, gravity wave-driven
shear flow oscillations in the equatorial plane of the solar
radiative interior have been proposed to help explain the
solar internal rotation, an outstanding problem in stellar
physics [
Rogers et al.
, 2008].
