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Which technique is used to obtain a dispersion relation?

  • A.Linearising about a basic state and assuming a wave form
  • B.Integrating the full nonlinear equations forward in time until a steady wave solution eventually emerges
  • C.Averaging over many observations
  • D.Solving the elliptic inversion problem for the streamfunction given a specified potential vorticity field

Answer: A

Small perturbations are superposed on a specified basic state, products of perturbations are discarded, and a solution proportional to a complex exponential is substituted, giving an algebraic condition on frequency and wavenumber. This is the standard method throughout the subject. Numerical integration and observational averaging can confirm the result but do not derive it. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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