Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 430

Entropic Balance Model
of
Tornadic Supercell

Meandering Westerlies

Dry

Moisture

Dry Upper
Westerlies

Overshooting Hydrometeors
against Headwind Westerlies

Dry Middle & Low Levels
South - Westerly Jet Stream

Entropic Source
Condensation

Entropic Balance
Theory

Meso-
Cyclone

Entropic Sink
Evaporation

Wrap-Around
Mechanism Hook Echo

Rear Flank
Downdraft (RFD)
Dry Line

Wall Cloud

Upward-Tilting
Horizontal Vortex Tube
Moist Southerly
Flow

Tornado

RFD Front

Fig. 18.4 Schematic diagram of tornadogenesis based on the entropic balance theory .
Meandering westerlies transport water vapor evaporated from Gulf Stream into the deeper inland
of the central US great plain area and meet with the dry air to onset supercell. The moisture of the
southerly flow condenses and releases the latent heat to the surrounding air resulting in entropy
increase (18.26b) that is shown by circled plus sign, called entropic source, in the figure. The
hydrometeors such as raindrops and ice particles created by the condensation are lifted by the
updraft of thermal convection of the storm reaching near the cloud top and blow away towards
the downstream side, east-side, of the storm. However, the lifted hydrometeors are overshot
towards upstream direction against the upper-air westerlies. It is due to the upper air horizontal
vortex as shown in this figure where the rotational flow direction of is shown by an arrow

with double solid lines . The overshot hydrometeors will fall down evaporating because of dry
air surrounding and cooling the air. The descending hydrometeors with cooled air meet with dry
middle-level south-westerly jet and are cooled further to produce the rear frank downdraft. Thus,
entropic sink forms nearly at the same altitude of the entropic source at the west of the source.
Horizontal spatial gradient of entropy is generated by the pair of the entropic source and sink. A
vortex, mesocyclone, is formed and the wrap-around mechanism is organized. The wrap-around
mechanism becomes activated by the mesocyclone existed between the entropic source and sink
and produces circular belt of entropic source around the sink. The circular system is an ensemble
of specific combination of the vorticity under the entropic right-hand rule and its conjugate
vorticity. The conjugate vorticity has anti-symmetric entropy gradient and anti-symmetric flow
velocity (rotational component), but results in the same vorticity, under nonlinear processes similar
to folding of the baker's transformation. The wrap-around mechanism is a nonlinear process,
similar to attractor, to generate hook echo, low-level mesocyclone, wall cloud and tornado. These
processes are explained by the diagnostic E-L equation, the entropic right-hand rule and wrap-
around mechanism which are derived by the entropic balance theory

!

where is the density of the air, the second term of the right side of ( 18.25 )isthe

solenoid term. Note that the vorticity diffusion term due to molecular viscosity ( / ,

! , is omitted because of the high Reynolds number of the flow. The solenidal

effect is significant at the supercell stage, but it will be decreased during the