Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 440

top, wherein they blow away towards the downstream side, east-side, of the storm
in the anvil.
However, some of the lifted hydrometeors are overshot towards the upstream
direction of westerlies, against the strong headwind. It is due to the horizontal vortex
(represented by the vorticity

!/ as shown in Fig. 18.4 where the rotational flow

direction of is shown by an arrow with double solid lines. The horizontal vortex

is formed within the vertical but slanted, towards head-wind direction, by a dipole
of entropic source and sink. The overshot hydrometeors will be evaporating and
sublimating in the ambient dry air, cooling the air. The descending hydrometeors
with cooled air meet with dry middle-level south-westerly jet and are cooled
further and produce rear flank downdraft. Thus, major entropic sink forms nearly
at the same altitude as the entropic source, but further west. The horizontal spatial
gradient of entropy is generated by this entropic source and sink, (Fig. 18.4 )and
the mesocyclones are generated. There, the diagnostic E-L equation ( 18.5 )andthe
entropic right-hand rule play important roles.
The wrap-around mechanism discussed in Sect. 18.7 and shown in schematic
Figs. 18.9 and 18.10 is a nonlinear process, similar to the folding process of the
baker's transformation of nonlinear dynamics (Fig. 18.10 ), and produces an axially-
symmetric vortex in the vertical axis. This mechanism produces the hook echo,
low-level mesocyclone, wall cloud, and tornado. The mechanism is well explained
by the diagnostic E-L equation and the entropic right-hand rule, both of which are
derived by the entropic balance theory.

!

18.9 Comparison with a Well Documented VORTEX2 Result

The entropic balance theory is tested with a well-documented casefrom the most
recent observational experiment, VORTEX2. Figure 18.13 is a schematic diagram
of the supercell and tornadogenesis that occurred on June 5, 2009 in Goshen County,
Wyoming ( Markowski et al. 2012a ,b).
Entropic balance theory implies that the mesocyclone develops in the baroclinic
field between the entropic source (primarily due to condensation) and sink (pri-
marily due to evaporation), as shown in Fig. 18.4 . It is deduced from the theory
that tornado is developed due to the wrap-around of the positive entropic anomaly
air around the subsiding negative core at the area of the center of the tornado.
Indeed, the subsiding core is shown by DRC (descending reflectivity core) and high
value of vertical vorticity in Fig. 18.13 . From entropic balance theory, we found
that the transition from mesocyclone to tornado is characterized by the transition
from baroclinic stage to barotropic stage (Figs. 18.11 and 18.12 ). The transition is
nonlinear, analogous to the baker's transformation, common in nonlinear dynamics,
called in this study as the wrap-around mechanism because of its higher dimension
than that of the baker's transformation (Fig. 18.10 ). It is important to note that