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(a)
(b)
Waves propagating
right
Waves propagating
right
+
U
Wave
interference
Critical layer
progresses
downward
S
=
-8
-
U
-
U
Filtering
Filtering
(c)
(d)
Waves propagating
left
Waves propagating
left
-
U
Wave
interference
Critical layer
progresses
downward
S
=+
8
+
U
+
U
Filtering
Filtering
Figure 9.4.
The principle mechanism of the oscillation in the laboratory experiment of
Plumb and McEwan
[1978] is shown
in four representative phases of the flow (reproduced from Figure 19 in
Wedi and Smolarkiewicz
[2006]): (a) There is a zonal
mean zonal flow
8; (b) wave-wave mean-flow
interaction generates a critical layer that propagates downward generating a zonal mean zonal flow +
U
; (c) the reversed mean
flow arriving at the oscillating membrane filters the waves of opposite direction to allow only waves with horizontal wave number
s
= +8; (d) wave-wave mean-flow interaction generates a critical layer for the opposite traveling waves generating a downward
propagating zonal mean zonal flow
−
U
allowing gravity waves with a single dominant horizontal wave number
s
=
−
−
U
.
convection parametrization [
Miura et al.
, 2007], appear
to have a substantial influence on the predictive skill of
MJO events in actual forecast simulations. The inter-
action of planetary-scale, lower-tropospheric moisture
anomalies with convective processes have been suggested
as a fundamental mechanism of the MJO [
Majda and
Stechmann
, 2009]. The effects of moist physics are not
least manifested in the fact that convectively coupled
equatorial waves map to linear waves with a smaller effec-
tive equivalent depth than what would be assumed for dry
conditions.
All this makes the MJO complex to study in a
laboratory-scale environment and a laboratory analogue
to the MJO does not (yet) exist. In fact, the search for an
explanation of the MJO has been called the “search for the
Holy Grail of tropical atmospheric dynamics”[
Raymond
,
2001], and the next section attempts to contribute to this
search by reproducing the following prominent features of
the MJO at laboratory scales: the slow eastward propaga-
tion of a near dispersionless solitary phenomenon and its
anomalous horizontal quadrupole structure in the upper
part of the domain.
9.3.1. LES of Laboratory Analogue for MJO-Like
Tropical Dynamics
The same numerical apparatus with time-dependent
curvilinear coordinates that has been successfully applied
for the QBO analogue is employed here to con-
struct/propose a virtual laboratory-scale experiment,
where the generation of solitary structures is excited
and maintained via zonally propagating meanders of the
meridional boundaries of a zonally periodic
β
-plane. The
proposed experimental setup of the laboratory analogue
for MJO-like tropical dynamics and its scaled mapping
onto the equatorial troposphere is given in Table 9.1. From
the dimensions it becomes clear that DNS of the proposed
experiment is still (just) out of reach when considering a
minimum requirement of 4300
×
4000
×
110 grid points
