Locally-induced nonlinear modes and multiple equilibria in planetary fluids

Abstract

It is demonstrated that nonlinear Rossby modes, such as modons and IG eddies, can be excited in planetary fluids by a sufficiently strong forcing of potential vorticity. When a weak forcing is balanced with a weak dissipation, two (linear and nonlinear) equilibrium states can be produced, depending on the initial condition. When the fluid is inviscid, a sufficiently strong steady forcing may generate a sequence of propagating nonlinear eddies. A weak forcing, by contrast, only generates linear Rossby waves. The criterion which divides the high amplitude nonlinear state and the low amplitude linear state may be interpreted in terms of a ratio of a time necessary to force the eddy to a time for a fluid particle to circulate about the nonlinear eddy once.

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Yamagata, T., Sakamoto, K. & Arai, M. Locally-induced nonlinear modes and multiple equilibria in planetary fluids. PAGEOPH 133, 733–748 (1990). https://doi.org/10.1007/BF00876230

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Key words

  • Nonlinear coherent structures
  • modons
  • IG eddies
  • local multiple equilibria
  • long Rossby waves
  • potential vorticity