Geoscience Reference
In-Depth Information
which induces convective vertical motions. Weak, moder-
ate, and strong heating is defined by the boundary value
of the density ratio 0
3D organization of the solitary structure that emerges is
moving slowly to the right. A broader quadrupole struc-
ture spanning the whole meridional extent can be seen
in the anomalous wind field. One can identify one area
with predominantly upward motions and one area with
predominantly downward motions that move to the right
with the quadrupole structure. Overall the 3D organisa-
tion is reminiscent of the suggested archetypical MJO
structure illustrated in Figure 9.6a in Moncrieff [2004].
ρ b )/ρ b =0.0016, 0.0048, 0.0096,
respectively. The velocity values at the lower and lateral
boundaries are set to zero ( v j
b = 0) unless specified other-
wise. The upper boundary is free slip, with
j (z = H 0 ) =0
F
and
F ρ (z = H 0 ) = 0. The ambient flow prescribed as
u e =0.05m / s ( v e =0,w e =0 ) is used together with
the lateral boundary meander to mimic an extratropical
anomalous flow regime.
The particular coordinate mapping employed for the
simulation of lateral bo u nda ry meande rs assumes the
identity transformations t = t , x = x ,and z = z ,and
9.4. DISCUSSION
DNSs or LESs of geophysical laboratory experiments
represent a stringent challenge for model numerical cores.
In order to minimize numerical uncertainties, the pre-
sented numerical formulation uses time-dependent, gen-
eralized curvilinear coordinates, pairing the mathematical
apparatus of Riemannian geometry with modern CFD.
While a realistic simulation of a laboratory experiment
does not necessarily guarantee that the same numerics
perform well at global scales on the sphere, convergence
in the the limit of grid sizes x =
y S (x , y , t)
y N (x , y , t)
y
y = y 0
y S (x , y , t) ,
(9.6)
where y S and y N are the southern and northern domain
boundaries, respectively, and y 0 denotes the domain size
in meridional direction. Numericall y , t he elements of
the Jacobi matrix are evaluated in (t , x ) leading to the
required subset of (nontrivial) coefi c ients [ WediandSm o-
larkiewicz , 2004] G 1
G 1 ∂y/∂y , G 1
G 1 ∂y/∂x ,
=
=
(η) builds con-
fidence in the overall numerical procedure. Moreover,
with increasing resolution of weather and climate sim-
ulations, it is relevant how the numerics of a model
deals with the influence of small-scale fluctuations on
the larger scale flow when such a mechanism is only
partially or not at all parametrized. In particular, “vir-
tual” laboratory setups provide another diagnostic tool
to study the dynamics of selected flow phenomena while
examining the role of implicit or explicit dissipation.
This has been demonstrated in the DNS of the labora-
tory experiment of Plumb and McEwan for the QBO
[ Wedi and Smolarkiewicz , 2006]. The basic mechanism in
the laboratory experiment and in the numerical simula-
tions is the sequence of gravity wave excitation by simple
fluctuations of the upper or lower boundary, subsequent
wave-wave mean-flow interactions, critical layer forma-
tion followed by wave breaking, and the emergence of
a long-time zonal mean zonal flow oscillation entirely
driven by the wave momentum flux changes. All of these
gravity wave processes and subsequent zonal mean-flow
changes are found in the atmosphere, and hence the accu-
racy of different numerical choices for the simulation of
wave-driven flow phenomena is equally relevant to future
weather and climate predictions.
For example, a comparison of the zonal mean zonal
flow reversal in numerical simulations of the QBO ana-
logue with a flux form Eulerian and a semi-Lagrangian
advection algorithm [ Wedi , 2006] showed the onset of
critical layers in different spatial positions for the latter,
creating different bifurcation points for the flow develop-
ment. Since, in general, flux form schemes have higher-
order truncation errors proportional to the differentials
O
G 2
G 1 ∂x /∂y ,a nd G 2
G 1 ∂x/∂x with
G 1
=
=
=
∂y/∂x ∂x/∂y) 1 .
The simulations on the zonally periodic β -plane are
represented by 128
(∂y/∂y ∂x/∂x
64 grid points and the exper-
imental parameters and their corresponding (rescaled)
atmospheric values are summarized in Table 9.1. The
model uses a time step t =0.1s.
The meridional boundaries are specified by the super-
position of two waves with frequencies ω 1 =2 π/T 1 and
ω 2 =2 π/T 2 ,
×
128
×
2 + a cos ω 2
t
y 0
ω 1
y S (x , y , t) =
2
sin k x x
t ,
ω 1 + ω 2
2
×
(9.7)
and y N (x , y , t) =
y S (x , y , t) ,where y 0 denotes the
domain size in the meridional direction (and analogously
x 0 specifies the domain size in the zonal direction) and
k x =2 π/λ with zonal wavelength λ . Such a forcing
prescribes a boundary meander (a similar forcing is pro-
vided in case d of Table 1 of Malanotte-Rizzoli et al.
[1988]) propagating eastward with the mean phase veloc-
ity 1 + ω 2 )/ 2 k x and pulsating with the frequency 2
ω 1 )/ 2. Unless specified otherwise, the boundary forcing
is activated only after some fixed initial period and the
forcing amplitude a is one-tenth of the meridional extent
of the domain. As in the case for the QBO analogue,
equations (9.6) and (9.7) together with (9.2) allow for
a time-dependent meridional boundary forcing free of
small-amplitude approximations.
The 3D simulation, including stratification and bottom
boundary thermal forcing, is illustrated in Figure 9.5. The
 
Search WWH ::




Custom Search