Linear Dynamics of the Semi-geostrophic Equations in Eulerian Coordinates on R3

Stefania Lisai, Mark Wilkinson

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Abstract

We consider a class of steady solutions of the semi-geostrophic equations on R3 and derive the linearised dynamics around those solutions. The linear PDE which governs perturbations around those steady states is a transport equation featuring a pseudo-differential operator of order 0. We study well-posedness of this equation in L2(R3, R3) introducing a representation formula for the solutions, and extend the result to the space of tempered distributions on R3. We investigate stability of the steady solutions of the semi-geostrophic equations by looking at plane wave solutions of the associated linearised problem, and discuss differences in the case of the quasi-geostrophic equations.

Original languageEnglish
Article number54
JournalJournal of Mathematical Fluid Mechanics
Volume23
Issue number3
Early online date5 May 2021
DOIs
Publication statusPublished - Aug 2021

Keywords

  • Atmospheric/oceanic fluid dynamics
  • Linear stability
  • Quasi-geostrophic equations
  • Semi-geostrophic equations

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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