Discussion
Which of the following is not required for the thermal wind relation to hold?
Frictionless flow
Geostrophic balance
Hydrostatic balance
A non-zero Coriolis parameter
Answer: A
Friction is not part of the derivation: the relation follows from combining geostrophic and hydrostatic balance, and both of those require a non-zero Coriolis parameter. Friction does of course invalidate geostrophic balance within the boundary layer, but it enters through that route rather than as a separate condition. Distinguishing what a derivation actually uses from what happens to be true alongside it is a habit worth cultivating. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.
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