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Which term makes the equations of motion nonlinear?

  • A.The Coriolis term, whose magnitude depends on the latitude at which the parcel happens to be located
  • B.The pressure gradient term
  • C.The frictional term, which involves the second derivative of the velocity with respect to height
  • D.The advective term

Answer: D

The advective term is the velocity multiplied by the gradient of velocity, so it is quadratic in the unknown and is the source of the nonlinearity that makes the equations intractable analytically. It is also what produces turbulence and chaos. The Coriolis term is linear in velocity, the pressure gradient depends on a different field, and the frictional term as usually parameterised is linear too, though the eddy viscosity within it may not be. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

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