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(
18.3
) of the variational formalism (Sect.
18.2
). The Reynolds number is estimated
using molecular viscosity as
10
9
12
. Consequently the molecular viscosity term can
be neglected so that the flow is an ideal flow, but the nonlinear terms of the governing
equations are fully retained, portion of which is expressed by eddy viscosity.
The entropic balance (
18.5
) is the sole diagnostic Euler-Lagrange equation and
should be always satisfied for the all other prognostic Euler-Lagrange equations as
discussed in Sect.
18.3
and in Fig.
18.3
as the completeness of solution. The vorticity
(
18.6
) is derived from the entropic balance (
18.6
).
Using the variational analysis method (
Sasaki 1970
) with the constraints (
18.5
)
and (
18.6
), it may be possible to get entropy, flow velocity, vorticity, the potentials
˛
and
from the conventional and radar observation data. It is noted that the Lagrange
multiplier potentials
ˇ
are not easily expressed in terms of conventional
meteorological field variables (which can be seen as a weakness of this approach),
except in this article they are well interpreted as divergent part and rotational part
respectively (Fig.
18.1
). In the Sects.
18.11
and
18.12
of this article, preliminary
research on uses of the radar data was described. The results are promising, although
shown only for one case in each of the chapters. With the new radar variables DZ
and DZ
DR
etc., we may be able to extract cloud microphysical information from
the storm. We plan to further test for a number of other cases by this approach to
establish a solid basis for tornado data assimilation, because of the applicability of
the entropic balance equation as a constraint with the radar observation in variational
formulation.
˛
and
ˇ
Appendix 1 Some Key Questions on Tornadogenesis
Accurate forecasting of tornadogenesis is one of the unsolved problems, in spite
of a great number of observations and research made over many decades. In
recent years, significant progress has been made to understand the mechanism of
tornadogenesis. However, there still remain key questions and difficult problems in
fully understanding tornadogenesis and tornado.
Some of the key questions that need to be answered by any proposed theory of
tornadogenesis are:
1. How does the mesocyclone develop? Note that mesocyclone and wall cloud are
known as observed with tornadogenesis.
2. Why are hydrometeors able to be overshot against the upper air westerlies
of much stronger wind speed than that of low level south-easterly inflow to
tornadic storm?
3. Why are the locations of tornado and major precipitation regions spatially
separate, not coincident?
4. Why is dry air aloft important for tornadogenesis?
5. Why do multiple vortices sometime develop before and during tornadogenesis?
6. How does the tornado develop in a hook echo, at the south-west corner, not at
the center, of a supercell, and why is it associated with wall cloud?
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