EPSC Abstracts,
Vol. 3, EPSC2008-A-00025, 2008
European Planetary Science Congress, © Author(s) 2008
Cyclonic Rossby vortices and a possibility of nano- and microscale dust particle
transport from troposphere into stratosphere
Yu.N. Besedina and S.I. Popel
Institute for Dynamics of Geospheres RAS, Moscow, Russia ([email protected] / Fax: +7-495-1376511)
Abstract
The effect of dust particle capture by Rossby vortices
in Earth’s atmosphere is discussed. Numerical
experiments modeling behavior of spherical particles
in Rossby vortices are carried out. It is shown that
nano- and microscale dust particles (with the sizes not
exceeding 10 µm) can exist in the vortex during
several days. This allows such particles to propagate
together with the vortex for long distances of order
10000 km. If a high enough cyclonic vortex of
synoptic scale crosses subtropical latitudes where the
altitudes of the tropopause vary between 11 km and 16
km, then the effect of the capture of dust particles in
the vortex can result in their transport from
troposphere into stratosphere.
Introduction
An important problem of geophysics of intergeospheric interactions is the determination of
mechanisms of dust particle transport from
troposphere into stratosphere and ionosphere. There
are some facts arguing that this transport is possible.
The first observation of noctilucent clouds in 1885 is
thought to be due to the formation of dust in the huge
volcanic eruption of Krakatoa in 1883 [1]. The
noctilucent clouds are argued to be dust structures at
the mesospheric altitudes [2]. Furthermore, fires
caused by a regional conflict with the use of nuclear
weapon can result in dust (soot) particle ascent up to
the altitudes of the upper stratosphere [3]. The
presence of the soot in the stratosphere was detected
during intensive forest fires [4–6].
Transport of substance and, in particular, of dust into
the stratosphere is thought sometimes to be associated
with powerful convection existing in tropical latitudes
[7]. It should be noted that for typical convection in
Earth’s atmosphere, the convective transport of the
substance to the stratospheric altitudes is prevented by
small temperature gradient in the region of tropopause.
Furthermore, climatic models (see, e.g., [3]) applied
for the description of the dust ascent to the
stratospheric altitudes as a result of the powerful
convection use an assumption that the horizontal
resolution in calculations is relatively rough. The
atmospheric convection occurs at the spatial scales
smaller than the scales which are admitted within this
approximation. In the model [3], an important factor
influencing the intensive ascent of the soot particles is
their heating by short–wave electromagnetic radiation.
We note that both volcanic ash (large particles of the
material of Earth’s crust called also as tephra) and
small sulfate aerosols absorb far less radiation and,
consequently, their ability of to ascend is far weaker
than that for the soot particles [8].
The above facts point out the importance of
consideration of other (not convection) mechanisms of
the dust ascent which can explain an appearance of the
dust in stratosphere even in the case of not such
powerful impacts on the atmosphere as nuclear
explosions and/or volcanic eruptions. However, we
have to take into account that the convective transport
can lead to the concentration of the dust in the upper
part of the troposphere [7].
In this paper we explain nano- and microscale particle
transport from troposphere into the stratosphere by
vortices of synoptic scale which are modelled by
soliton solutions of the nonlinear Charny–Obukhov
equation (Rossby vortices). The vortices of synoptic
scale are present permanently in the atmosphere and
can reach the stratospheric altitudes. Our consideration
is based on the data [9] of laboratory experiments
arguing that Rossby waves of large amplitude capture
and transfer dust particles.
Dust in Rossby Vortices
The solitons (vortices) Rossby are formed in rotating
systems. Their dynamics is described by the nonlinear
Charny–Obukhov equation [9]
∂ ( ∆ψ − ψ )
∂ψ
+ J (ψ , ∆ψ ) = 0,
∂t
∂x
∂a ∂b ∂a ∂b
J ( a, b ) =
,
−
∂x ∂y ∂y ∂x
+ vR ( y )
where the axes Ox and Oy are chosen in parallel of
latitude and meridian directions respectively, ψ is the
dimensionless function of the current related to zonal
(u) and meridian (v) velocity components by
u=−
∂ψ
∂ψ
, v=
.
∂y
∂x
Using the polar coordinates we find the following
soliton solution
ψ = p0 F0 ( r ) + RUF1 ( r ) sin θ ,
where
⎧ ⎛ J 0 ( kr )
⎞
− 1 ⎟ + 1,
⎪ g 0 ⎜⎜
J 0 ( kR ) ⎟⎠
⎪
F0 ( r ) = ⎨ ⎝
⎪ K 0 (κ r )
⎪ K (κ R ) , r > R
⎩ 0
r≤R
⎧ ⎛ κ ⎞ 2 J 1 ( kr ) κ 2 + k 2
r,
−
⎪⎜ ⎟
k 2R
⎪ ⎝ k ⎠ J 1 ( kR )
, F1 ( r ) = ⎨
⎪ K 1 (κ r )
⎪ − K (κ R ) , r > R
1
⎩
r≤R
vR ,
U
the values k and g0 are determined from the condition
of continuity of the function ψ at r=R, the coefficients
R, and p0 are free parameters, J0 and J1 are Bessel
functions, K0 and K1 are McDonald functions, uR is
the dimensionless Rossby velocity, U is the speed of
the soliton (moving along x–direction). Here and
below, the velocities uR and U are normalized to the
isothermal sound speed in the air, the linear sizes
(with the exclusion of dust grain sizes) to the Rossby
radius, and the time to the value 1/Ω, where Ω is the
frequency of Earth’s rotation.
We have carried out numerical calculations of the
behaviour of a spherical dust particle with taking into
account Stokes resistance as well as the pressure head.
In Fig. 1, the trajectories of dust particles having
different sizes are presented for a cyclonic Rossby
vortex of the radius of 100 km.
κ2 = 1+
that the dust particles with the sizes smaller or of order
10 µm can be transferred by a vortex of the radius of
100 km to the above distances (in the horizontal
direction).
Discussion
Thus dust particles with the sizes less or of order
10 µm can be captured by a cyclonic Rossby vortex
during the time of order the time of the vortex
existence. This allows the particles to be transferred to
the distances of several thousand kilometers in the
horizontal direction. The vortex propagation through
the subtropical region is of significant interest because
this region possesses some specific features such as
discontinuities of tropopause, upward flows [3], etc. In
the subtropical region there is a sharp (several
kilometers) decrease in the tropopause altitude when
one goes from the equator to the pole. The cyclonic
vortices have the velocity component in this direction.
Consequently, even in the case of the horizontal
propagation, high enough cyclonic vortices of
synoptic scale can transfer the captured nano- and
microscale dust particles into the lower stratosphere.
Dust particles transferred to stratosphere can have
very big existence time and influence the climate near
Earth’s surface during several years [3]. Hence, the
proposed mechanism of the dust particle transport into
stratosphere can be important from the viewpoint of
the climate modeling.
Acknowledgements
This study was supported by the Division of Earth
Sciences, Russian Academy of Sciences (the basic
research programs “Nanoparticles in Natural and
Technogenic Systems” and “Geophysics of intergeospheric interactions”), by the RFBR (project no.
06–05–64826), and by the ISTC (project no. KR–
1522).
Fig. 1 Trajectories of dust particles of different sizes in an
atmospheric Rossby vortex of the radius of 100 km. Thin (bold)
lines correspond to the dust particle size of 1 cm (1 mm).
Numerical investigation of the dependence of time T
of the existence of dust particle in the vortex on the
dust particle diameter a has shown that for the vortices
of different sizes the following relationship is fulfilled
with a good accuracy, T~ a-0.5. The investigation has
shown also that in the vortex with the radius of 100
km dust particles with the sizes not exceeding 100 nm
can exist inside the vortex during several days. The
time of the vortex existence has the same order of
magnitude. Such small particles can be transferred by
the vortex to the distances of order 10000 km. The
time of existence of dust grains in larger vortices and
the distance which the particles pass together with the
vortex are even larger.
The consideration of vertical dust motions caused by
the friction in the boundary layer of the vortex shows
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