Chaotic response of the 2D semi-geostrophic and 3D quasi-geostrophic equations to gentle periodic forcing

  title={Chaotic response of the 2D semi-geostrophic and 3D quasi-geostrophic equations to gentle periodic forcing},
  author={Dorian Goldman and Robert J. McCann},
Symmetries and Hamiltonian structure are combined with Melnikov's method to show a set of exact solutions to the 2D semi-geostrophic equations in an elliptical tank responding chaotically to gentle periodic forcing of the domain eccentricity (or of the potential vorticity, for that matter) which are sinusoidal in time with nearly any period. A similar approach confirms the chaotic response of the quasi-geostrophic equations to gentle periodic forcing by an external shearing field. Our approach… 

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