Internal tornado pressures

Something that I have been musing over for the last few days with out success so I will open it up for debate!

I am considering what allows some tornados to wedge and some remain a narrow pipe?

I gather that there might be a correlation between internal pressure and wind speed in that for a 200 mph wind the internal pressure would have to be much lower to maintain a narrow vortex but if the internal pressure decreased then the diameter of the tornado would increase. Also if the pressure remained the same but the wind speed increased then the diameter of the tornado would increase

I am just wondering if this can be modelled – i.e. there is some loose correlation between hurricane central pressure and wind speeds.

Tornado diameter = internal pressure (some maths) wind speed
As we know, the flow balance within a tornado is approximately cyclostrophic, which means that the primary forces involved are the pressure gradient force and the centrifugal force (which is actually just the negative of the centripetal force), though friction does affect the flow immediately above the surface. Centrifugal force is directly proportional to wind speed and responds to the wind, so the main "cause" for the wind would be the pressure gradient force. 200mph winds in a large tornado would imply that the central pressure of the tornado is lower than it is a comparatively small tornado that also has 200mb winds. I realize we all know this, but just a refresher for those who may not...

From experience and observation, it seems that there is some relationship between tornado size and LCL/LFC height. Swirl ratio affects the single-vortex vs. multi-vortex mode (*), but I wonder if there is also some affect on tornado width. Many of the "wedge" pictures occur with storms in a low-LCL and low-LFC environment, with the opposite being true for smaller tornadoes. Now, the term "wedge" refers to an aspect ratio of the tornado condensation funnel -- if the funnel is wider than it is tall, it's usually considered a "wedge". Therefore, if the LCL is low (thus the funnel would be 'short' in comparison to the high LCL case) the tornado doesn't have to be as wide in order to be considered a "wedge". For example, width of the tornado at ground would have to be quite wide if the LCL was 2500m (by the commonly-accepted definition, the tornado at the ground would need to be more than 2500m wide). So, it's likely more scientifically worthwhile to investigate factors that affect the width of the tornado, without regard to whether the tornado is a "rope" or a "wedge". My "hunch" is that tornado size is primarily affected by the amount of streamwise vorticity and low-level CAPE (which is affected by LFC height and low-level lapse rates).

EDIT: Forgot to note that the size of the funnel may not be a good indicator of the size of the "tornado", since the wind envelope may be larger than the condensation indicates, which would seem to be the case in areas of low mean RH (in which case the air must reach a lower pressure before saturation occurs). This is an interesting topic, and there are a lot of folks more qualified, so I'm interested to read.

See C.R. Church, J.T. Snow, G.L. Baker and E.M. Agee. 1979: Characteristics of Tornado-Like Vortices as a Function of Swirl Ratio: A Laboratory Investigation. Journal of the Atmospheric Sciences: Vol. 36, No. 9, pp. 1755–1776.
D. C. Lewellen, W. S. Lewellen and J. Xia. 2000: The Influence of a Local Swirl Ratio on Tornado Intensification near the Surface. Journal of the Atmospheric Sciences: Vol. 57, No. 4, pp. 527–544.
Joshua Wurman. 2002: The Multiple-Vortex Structure of a Tornado. Weather and Forecasting: Vol. 17, No. 3, pp. 473–505. ;