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Which regime does a Rossby number much greater than one indicate?

  • A.The flow is in exact geostrophic balance with the pressure gradient opposing Coriolis exactly
  • B.Friction dominates
  • C.The motion is hydrostatic so that pressure may safely be used as the vertical coordinate here
  • D.Rotation is unimportant

Answer: D

A large Rossby number means the inertial acceleration greatly exceeds the Coriolis acceleration, so the Earth's rotation may be neglected, which is the case for a tornado, a dust devil or water leaving a basin. Geostrophy requires the opposite limit. Friction is measured by a different ratio, and the hydrostatic approximation depends on the aspect ratio of the motion rather than on the Rossby number. The popular claim that bath water circulates according to hemisphere fails precisely because of this scaling.

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