Velocity distribution of particles in an arbitrary-arrangement of rotating gases

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In a quasi-rigid rotating convective cell, gas particles can exhibit a Maxwell-Boltzmann distribution when viewed from a co-rotating frame. However, when analyzing gases with arbitrary rotational axes and varying speeds from an inertial frame, the particle velocities may not conform to this distribution. The discussion raises the question of how air flowing into a tornado might deviate from Maxwell-Boltzmann characteristics as the tornado's speed and rotation increase. It also inquires about numerical parameters that could quantify this deviation for calculations in non-equilibrium thermodynamics. Understanding these dynamics is crucial for accurate modeling in complex fluid systems.
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If we have a "quasi-rigid" rotating convective cell where the gas overall rotates at the same angular velocity, we could establish a non-inertial frame of reference co-rotating with this convective cell such that the particles of the gas (seen from that frame of reference) may follow a Maxwell-Boltzmann distribution.

But with what statistical distribution may we characterize the temperature function of a system of gases whose fluid rotations occur around various arbitrary axes and speeds with cells of a varying size, evaluated from an inertial, observing frame? In this case, the particle velocities may or may not follow a Maxwell-Boltzmann distribution.
 
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Will air flowing into a tornado have particle velocity distribution that deviates from the Maxwell-Boltzmann distribution as that tornado increases in speed and rotational rate? Are there any numerical parameters that can be used to usefully characterize the amount of this deviance from Maxwell-Boltzman characteristics for certain kinds of calculations in non-equilibrium thermodynamics?
 

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