Discussion
Which situation invalidates the thermal wind relation?
Answer: A
The relation inherits the geostrophic breakdown near the equator, since dividing by a vanishing Coriolis parameter gives an unbounded shear for any temperature gradient. Mid-latitude free tropospheric flow is exactly where it works best. A barotropic layer simply gives zero thermal wind, which is a valid rather than an invalid result, and speed-only shear is an ordinary baroclinic case.
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