Discussion
Which two relations are combined to obtain the thermal wind?
Answer: A
Differentiating the geostrophic relation with respect to pressure and substituting the hydrostatic relation eliminates the geopotential and leaves the vertical shear expressed through the horizontal temperature gradient. The thermal wind therefore inherits the validity conditions of both parent relations, failing wherever either fails. Continuity, the thermodynamic equation and the vorticity and divergence equations play no part in the derivation, though they are of course members of the same governing set and are used elsewhere in this subject for other purposes.
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