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Fig. 18.5 Entropic vortex
. Entropic vortex exists by the gradient of entropy in a baroclinic field.
The horizontal vortex is formed due to the vertical entropy gradient at the upper levels above the
entropic source and overshoots the hydrometeors to upstream against the headwind westerlies. The
vertical vortex is formed at the middle levels due to the horizontal gradient between the source and
the sink of entropy. The entropic vortex formation is explained by the entropic right-hand rule
derived from the entropic balance theory
However, it does not satisfy the Boltszmann's third law of thermodynamics, that
is, the entropy S should be zero at the zero absolute temperature T, namely S D
0
at T D
0
, justified by statistical thermodynamics as the entropy defined by S D k
ln W, where k is Boltsmann's constant and W is the weight of configuration,
andthenSD
0
for W D
1
for perfect configuration and no ambiguity (
Atkins and
de Paula 2002
).
This article uses the third law of the thermodynamics, instead of the conventional
potential temperature. An example is shown in Appendix 4 in conjunction with an
entropic analysis of tornado.
The baroclinic and barotropic states are viewed also from solenoidal state. The
solenoid,
, is a key term of vorticity generation in (
18.25
), and it appeared as a
vector product of the spatial gradient of specific volume and the pressure gradient,
or the spatial gradients of entropy and temperature,
WD r
.1=/
rp Dr
.1=/
rp
:
(18.32)
The solenoid defined above is written in terms of temperature and entropy with
simplification as
(18.33)
which basically is in agreement with that obtained by
Dutton
(
1976
) in a conven-
tional method.
A supercell has properties of baroclinicity, as it is axially asymmetric along the
vertical axis (Figs.
18.5
and
18.6
), whereas a tornado has confined in entropic sink
core, like a singularity, axially-symmetric, surrounded by circular entropic source
DrT rS
;
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