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outer region, and how the second peak of the symmetric tangential wind is
induced.
The outline of this paper is as follows. A brief description of the model
and the experimental design is given in Sec. 2. Results from the nonlinear
simulations are discussed in Sec. 3. Finally, a summary is given in Sec. 4.
2. Model Description
2.1
. The model
To study the interaction between the core vortex and asymmetric
perturbation, in particular to study how the asymmetry influences the
symmetric flow, we construct a nonlinear barotropic model. The governing
equations in a non-dimensional form on an
f
plane are given as the
following:
∂u
∂t
u
∂u
∂x
v
∂u
−
∂φ
+
+
∂y
− v
=
∂x
,
(2.1a)
∂v
∂t
+
u
∂v
∂x
+
v
∂v
∂y
+
u
=
−
∂φ
∂y
,
(2.1b)
−∇
2
φ,
−
2
J
(
u, v
)
− ζ
=
(2.1c)
)=
∂
∂x
∂
∂y
−
∂v
∂u
∂y
=
∂v
∂x
−
∂
∂y
where
J
(
u, v
and
ζ
,
u
and
v
are the horizontal
∂x
wind velocity components;
φ
, the geopotential height, and
ζ
is the vorticity.
10
−
5
s
−
1
, and the characteristic value for
The Coriolis parameter is
f
=5
×
10
4
s. A non-dimensional time
time is
18 corresponds
to 1 h. The characteristic values for the velocity and horizontal length scales
are
T
=1
/f
=2
×
t
=0
.
C
= 50 m/s and
L
=
CT
= 1000 km, and the Rossby number equals 1
for the vortex.
The numerical solution technique employed is the fourth-order Runge-
Kutta scheme with a time increment of 0.002. The Matsuno scheme
8
is
applied to calculate the advection terms, and the second-order centered
difference is used for the approximation of other space derivatives. A
second-order diffusion is applied every 0.18 time with the non-dimensional
coecient being 1
.
4
×
10
−
6
to ensure the numerical stability. The model
covers a 2
×
2 (2000 km
×
2000 km) area with a grid resolution of 0.002 in
both
directions. The lateral boundary condition is radiative. All
simulations are carried out for 24 h. Most of the results shown are up to
12 h during which the major axisymmetrization process occurs.
x
and
y