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Which dependence on layer depth does the thermal wind have?

  • A.Inversely proportional to depth
  • B.Independent of depth, since the relation gives a shear per unit height rather than a total wind change
  • C.Logarithmic in the pressure ratio
  • D.Linear in the geometric depth of the layer measured in metres between its top and bottom surfaces

Answer: C

Integrating the hydrostatic relation gives a factor of the natural logarithm of the ratio of the bounding pressures, so the accumulated wind change depends on that logarithm. In geometric terms this is close to linear over a shallow layer but departs over a deep one because density falls with height. The relation does give a shear per unit pressure, but the question concerns the accumulated change across the layer. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

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