Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 452

flow velocity direction (rotational component) and produces the same vorticity of
Fig. 18.1 . It is called as conjugate vortex (or vorticity) in this article. Combination
of the original vortex and its conjugate produces multi-vortexes as well as single
vortex. It answers the question 5. The answer for the questions 6 and 8 may be
easily found from Fig. 18.4 .
The answer for the questions 7 and 8 is discussed in Sect. 18.7 . The question 9
may be answered in Sect. 18.5 . The answer to the historically long-standing question
10 is a tough one, but may be hinted by the entropic balance theory discussed in this
article and in an example shown in the following Appendix 4. It is challenging for
continuing research to find a full answer for the question 10.

Appendix 4 Entropy Variation and Tornadogenesis

The entropy variation due to cloud-physical phase change is computed at the alti-
tudes of 1-3 km where condensation and evaporation to provide thermodynamical
effects for development of mesocyclones and tornado, and the atmospheric pressure
of approximately 750 mb and temperature of 0 ı C .273 ı K

as an example. For
simplicity for this preliminary investigation, we assume also that S 0 D 0

/

and only
consider the diabatic effects of water molecules on S of the surrounding air on a
moving coordinates with tornado.
The entropy change c S of the surrounding air due to water vapor condensation

100 ı C and 1,013 mb is estimated as 109.0 J ı K 1 mol 1 ,andthat
of evaporating of water droplet

measured at

J ı K 1 mol 1 . Since moisture measurement
is not considered in this preliminary investigation and insufficient measurement
and knowledge on the cloud-physical phase changes of actual cloud, the estimates
were made simply based on the measurements of heat in published chemical
experiments. Their values are adjusted to the value of

109

0 ı C and 750 mb for
representing the altitude of 1-3 km, using the standard adjustment processes ( Atkins
and de Paula 2002 ; Watanabe 2003 ).
The adjustment amount due to the temperature change .100 ı C— T S >

J ı K 1 mol 1 and that due to pressure change 0 ı C / D 16:6 p S (1,013 mb — >

750 mb) D 2.1 J ı K 1 mol 1 .
After the adjustments, the entropy change of the surrounding air due to con-
densation of water vapor is;

J ı K 1 mol 1 c S D .109:0 16:6 C 2:1/ D

J ı K 1 mol 1 , and for that due to evaporation of water droplets is 94:5 e S D

J ı K 1 mol 1 .
Thus we get the entropy difference between the entropic source and sink
separated by the distance d;

J ı K 1 mol 1 D 123:5 . 109:0 16:6 C 2:1/

J ı K 1 mol 1 .
Similarly, the absolute entropy S is calculated by adding the entropy changes
due to melting of ice,

d S D .94:5 . 123:5// D 218:0

J ı K 1 mol 1
from the Boltzmann's third law of thermodynamics, resulting S D .94:5 C 22:0 C
0:8/

J ı K 1 mol 1 and the residual entropy, 22:0 0:8

J ı K 1 mol 1 D 117:3 J ı K 1 mol 1 .