Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 423

either parallel or perpendicular approach of a vortex tube to the ground. These
numerical simulations and theories lead unrealistic results of touching the ground
in parallel, not perpendicular, direction (Question 7 in Appendix 1). However, in
contrary, many visual observations have suggested perpendicular touch down of
tornadoes to the ground. To solve this controversy, the dynamic pipe effect (DPE)
theory developed by Leslie ( 1971 ), Smith and Leslie ( 1978 ) was applied by Trapp
and Davies-Jones ( 1997 ) for tornado touch down perpendicularly to the ground.
Their theory is based on dynamical pressure deficit on the barotropic Boussinesq
(balance) approximation, not including explicitly any thermo-dynamical term, and is
consequently insufficient to explain the transition between baroclinic and barotropic
stages.
On the other hand, the wrap-around mechanism developed on the basis of the
entropic balance theory ( Sasaki 1999 , 2009 , 2010 ) seems better to explain the
transition as we will discuss it in details in Sect. 18.7 . Also, the wrap-around
mechanism together with the kinematic boundary condition at the ground better
explains the important findings that all observed tornado funnels hit perpendicularly
when they touch the ground, contrary to the expectation from the upward tilting of a
horizontal vortex tube. The numerical simulation experiments of tornadogenesis by
Noda ( 2002 ), Noda and Niino ( 2005 , 2010 ) seem to suggest not tilting, but a vertical
coupling mechanism because the helicity (relative or normalized) increases to one
at the mature stage, meaning less solenoidal effects in the vorticity equation and
parallel alignment of updraft and the vorticity axis in their simulation experiments
of tornadogenesis.
Recent VORTEX2 results seem to provide supporting evidence for the entropic
balance theory ( Markowski et al. 2012a , b ) and will be discussed in Sect. 18.9 .Meth-
ods for estimating the entropy anomaly from radar reflectivity and dual-polarization
radar data are presented in Sect. 18.10 . Section 18.11 presents preliminary results of
the application of dual-polarization WSR-88D radar data ( Kumjian et al. 2010 )by
the second author of the present article, and Sect. 18.12 by the third author of this
article for rapid-scanning, mobileX-band radar data. The entropic balance theory
(and derived the entropic right-hand rule and the wrap-around mechanism) and other
directly related observations, theories and models in references are briefly reviewed
in Sect. 18.2 .

18.2 Entropic Balance Theory for Tornadogenesis

The entropic balance theory developed for tornadogenesis ( Sasaki 1999 , 2009 ,
2010 ) is briefly summarized in Sects. 18.2 , 18.3 , 18.4 , 18.5 , 18.6 ,and 18.7 with
addition of further explanation. A tornado is approximated by inviscid and Coriolis-
force free flow because high Reynolds number R e with the molecular viscosity of
the air and high Rossby number R o at the middle latitudes are used,

R e D 10 8 12 and D 10 2 4 : R o (18.1)