Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 453

From ( 18.6 ), the vorticity ! is written as

! D v ˇ .1= S / S : (18.51)

where Vrot represents the rotational component of flow velocity.
Usin the estimated values of S and S, ( 18.51 ) becomes

ds 1 ! D V ˇ 1:86. D 273:0=117:3/= (18.52)

where d is distance between the entropic source and sink.
For an example of mesocyclone cases, v ˇ is taken 10 m/s and d as 5 km, then
( 18.52 ) leads s 1 . For tornado by wrap-around mechanism cases,

( 18.52 ) with 50 m/s of V ˇ and 100 m of d leads

! D 0:0037

s 1 . The former and latter
seem appropriate order of magnitudes for mesocyclones and tornado respectively.

! D 0:93

Acknowledgements The authors would like to express their appreciation for Dr. Paul Markowski
and his colleagues of VORTEX2 for allowing us to use their schematic diagram of summarizing
their findings in this article (Fig. 18.13 ). The first author would like to express his appreciation to
the encouragement and support given to this research by The Office of Vice President for Research,
and National Weather Center (NWC), The University of Oklahoma, USA, and Weathernews,
Inc., Japan. Also, the first author would like to express his appreciation to faculty and scientists
especially of NWC, The University of Tokyo, Kyoto University, Japan, and Ewha Women's
University, South Korea for their useful discussion, and to Vivek Mahale of the university of
Oklahoma for his assistance of computer graphics.

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