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Which terms appear in spherical coordinates but not in Cartesian ones?

  • A.The pressure gradient terms
  • B.The frictional terms, which represent the turbulent transfer of momentum towards the surface below
  • C.The metric or curvature terms
  • D.The Coriolis terms, which arise from the rotation of the frame rather than from its curvature

Answer: C

Expressing the acceleration in spherical coordinates produces additional terms involving the tangent of latitude and the radius, which account for the changing orientation of the unit vectors as a parcel moves. They are small for most purposes but not negligible near the poles or for very fast flows. Coriolis, pressure gradient and friction all appear in any coordinate system, since they represent physics rather than geometry, and confusing the two kinds of term is a common source of error.

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