Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 451

7. Why does the tornado touch down in the perpendicular direction to the ground?
Note that tornado should touch down to the ground in a parallel direction if the
tornado is generated by the upward tilting theory of horizontal vortex.
8. Why is the tornado a phenomenon of low altitudes (

< 2-3 km) of the atmo-

sphere?
9. What is the role of upward tilting of low level horizontal vorticity for tornado-
genesis ?
10. What are necessary and sufficient conditions to separate tornadogenesis from
non-tornadogenesis, in spite of several favorable conditions (such as favorable
environmental soundings, supercell, mesocyclones, and RFD)?

These questions seemed to be well answered by the entropic balance theory
( Sasaki 2009 , 2010 ).

Appendix 2 Answer to the Questions 1, 2, 3 and 4

Firstly we consider a simple case where the linear slope between the entropic source
and sink as shown in Fig. 18.5 and the flow velocity (rotational component) is
horizontal and southerly. For this case, the direction of the vorticity is vertical

as given by ( 18.5 ) that is expressed by the entropic right-hand rule (Fig. 18.1 ), and
isshowninFig. 18.5 where the rotational flow direction of the vorticity

!

! is shown

by an arrow with double solid lines. The vorticity represents mesocyclone existed

indeed in the linear entropy slope between the entropic source and sink. It may
answer the question 1.
The entropic anomaly in the air above the top of convective supercell is negative
due to evaporation of the hydrometeors in the dry westerlies and radiative cooling,
while the having the positive entropic source below. Accordingly, the maximum
spatial gradient of the entropy anomaly between the points just above the supercell
(S 0 <0

!

) and at the convective center of the supercell (S 0 >0 ) is directing straight

downwards. With the upper air westerlies wind vector and the entropic spatial
gradient vector, the vorticity

is that of the horizontal vortex tube as shown at the
top of the supercell in Fig. 18.5 . The upper vortex seems the key to overshoot the
hydrometeors generated in the supercell updraft, westwards against the headwind
westerly jet. This may answer the question 2. From the above answer to the
questions 1, and 2, it is apparent that the question 3 is answered from the above
answer to the questions 1 and 2. To answer the both questions 1, 2 and 3, it is noted
that the dry air plays the key roles, and it may answer the question 4.

!

Appendix 3 Answer to the Questions 5, 6, 7, 8, 9 and 10

The “wrap-around mechanism” is explained in a simple way by using the diag-
nostic E-L equation ( 18.5 ) and the entropic right-hand rule (Fig. 18.1 )of( 18.6 ).
Figure 18.6 is prepared which has opposite sign of spatial entropy gradient and the