Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 434

Fig. 18.8 Multi-vortexes .
Schematic illustration of
formation of four vortexes for
an example explained with
the wrap-around mechanism.
The wrap-around mechanism
is modeled by the entropic
right-hand rule which is
derived from the entropic
balance theory
In a successful numerical simulation of tornadoes with horizontal resolution of
75 m, Noda ( 2002 )and Noda and Niino ( 2005 , 2010 ) clearly showed the particle
trajectory which started at the point of about 500 m AGL, 25 km away in the
NW direction from the tornado vortex center, moved downward continuously,
and converged on the order of 100 m in diameter outside of the tornado vortex.
Similar results were shown in other numerical simulations of tornadoes. The
helicity ( 18.17 ), ( 18.18 ), and ( 18.19 ) play important roles and provide a theoretical
background to explain the above features of the trajectory and unique characteristics
of entropy, which seem in agreement with the numerical simulations and detailed
analyses of observations. The downdraft agrees with the entropic balance theory,
which says intensification of the cyclonic circulation around a tornado is due to the
downdraft. Also, the downdraft on the west-side of a tornadic supercell adiabatically
transports and converges the entropy into or in the neighborhood of a tornadic vortex
with a small area. The entropy from the broader areas outside of 25 km distance
from the tornado vortex and several hundreds meters or more above the ground also
converges downwards and decreases the gradient of entropy outside of the vortex.
The weak baroclinicity in the shallow layer of the atmosphere near the ground that
is expected from the entropic theory seems in agreement with the mobile Doppler
radar observations and surface observations ( Davies-Jones et al. 2001 ). Also, the
entropic balance theory suggests a converged, concentrated, axially (in vertical
direction) symmetric, wrap-around entropy field in and near the mature tornado
vortex core, similar to a nonlinear attractor, as will be discussed further in the next
chapter.