Fluid equations assume that there's a single characteristic velocity for the atoms at each point in space. So, for physical systems where local velocity distributions are wide or even multi-modal, fluid equations won't capture the physics.

In plasma physics, Laser Wakefield dynamics is an example of a system that can't be modeled as a fluid.

I sort of doubt these considerations apply to the atmosphere, but this is one of the main heuristics for when you can't use a fluid equation.