Statistical Mechanics of Tornado Intensity Distributions

We examined how the exponential tornado intensity distribution is synthesized in view of statistical mechanics.

We hypothesize that 1) the kinetic energy producing a tornado is partitioned to individual atmospheric molecules in a tornado, 2) the direction of the velocity vector of individual atmospheric molecules is stochastic in the phase space, and 3) the principles of statistical mechanics, i.e., the ergodic theorem and the principle of equal weight, can be applied for the phase space. The tornadic rotation is regarded as the net macroscopic rotation consisting of many molecules in clockwise and counterclockwise rotational states. The theoretical tornado intensity distribution is derived as a probability for independent trials. This statistical distribution is very similar to that for some physical systems, e.g., ferromagnetic substances made from many magnetic dipole moments.

From the expression of the theoretical tornado intensity distribution, we can define entropy and characteristic temperature for the system, and find that the theoretical distribution might be approximated by the Maxwell-Boltzmann distribution characterized by the temperature. We show the physical meaning of the characteristic temperature and its calculation procedure using atmospheric sounding data.

Some verification is presented for the climatological distributions in the United States, Europe, and Japan, and some family tornado events in the United States. For the climatological distribution of 1990-2009 U.S. tornadoes, theoretical energy-temperature relationship is precisely found. This result also gives an insight for the degree of freedom of motion for atmospheric molecules in a tornado. For some U.S. family tornadoes, collaboration of the theory and proximity sounding data approximately reproduced the observed distributions.