Discussion
Which property does the geostrophic wind have on an f-plane?
Answer: D
With \( f \) constant, the geostrophic wind is the gradient of geopotential rotated through ninety degrees and divided by \( f \), and the divergence of such a field vanishes identically. It follows that all horizontal divergence, and hence all vertical motion, is carried by the ageostrophic wind. The geostrophic wind certainly possesses vorticity, it is parallel to the isobars by construction, and its variation with height is the thermal wind, which is a separate relation with its own conditions.
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