It's a bit simpler that that if I understand their premise. Consider an object oscillating as x ~ sin(wt). This will have a velocity, an acceleration, but also all the higher-order derivatives such as jerk, snap, crackle, pop, etc. None of these will ever disappear since a sinusoid is forever differentiable, and even more obviously for rotating systems subject to gravity such as the Earth.
So, they are asking whether these higher-order terms are being accounted for properly when solving e.g. Navier-Stokes of a rotating fluid. This figure in the linked El-Nabuski paper caught my eye because they were showing phases-space plots such as the following:
Similar to what I am finding in the wave equation models for ENSO and QBO:
This characteristic phase-space is related to the Mach-Zehnder-like modulation that I'm calculating re the analytical solutions to the LTE simplification of Navier-Stokes. Curious on what the deeper connection since the solution is replete with the *nonlocal-in-time* higher-order jerk, etc terms.