Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 384

Figure 6.52. Spiral bands of radar reflectivity (dBZ e ) around a tornado marked by a WEH on
June 5, 2009 in southeastern Wyoming, as detected by the MWR-05XP, X-band, mobile,
phased array Doppler radar from the Center for Interdisciplinary Remotely-Piloted Aircraft
Studies (CIRPAS) at the Naval Postgraduate School. Range rings shown every 2 km.

transient phenomena, and is regarded as the simplest (and definitely not the most
accurate) one can make. For radial profiles of azimuthal wind in the core that are
''smoother'' than that of a Rankine vortex, the hydrostatic pressure drop in (6.51)
is less (e.g., for a Burgers-Rott vortex the pressure drop is only 59% of that in a
Rankine combined vortex).
In nature only part of the pressure deficit in a tornado is a hydrostatic
consequence of the warm, buoyant air column above it. The maximum wind
speed in a tornado in a hydrostatic atmosphere is referred to as the ''thermody-
namic speed limit''; the seminal work on this topic was instigated by a scientific
report authored by Doug Lilly at NCAR in 1969, which was not published in the
refereed literature.
To make the simplest estimate of maximum horizontal wind speeds in
tornadoes we apply the hydrostatic approximation to the vertical equation of
motion

p 0 0 ¼ 0 @ =@ z þ B ð 6 : 52 Þ

We integrate the hydrostatic equation (6.52) from the surface to the tropopause
and find that at r ¼ 0 the center of the tornado
ð p 0 ð z ¼ z trop Þ

ð z trop

0 dp 0 ¼ Bdz ¼ CIN þ CAPE CAPE 0 p 0 ð r ¼ 0 ; z ¼ 0 Þð 6 : 53 Þ

p 0 ð z ¼ 0 Þ 0

where p 0 ð z ¼ z trop Þ¼ 0 (i.e., we assume that the tornado vortex induces no
perturbation pressure at the tropopause). The perturbation pressure at the surface