Magnetohydrodynamic shallow water waves: Linear analysis

Kevin Heng, Anatoly Spitkovsky

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincaré modes and one magneto-Rossby mode) are previously known. The other two wave modes are strongly influenced by the magnetic field and rotation, and have substantially lower angular frequencies; as such, we term them "magnetostrophic modes." We obtain analytical functions for the velocity, height, and magnetic field perturbations in the limit that the magnitude of the MHD analogue of Lamb's parameter is large. On a sphere, the magnetostrophic modes reside near the poles, while the other modes are equatorially confined. Magnetostrophic modes may be an ingredient in explaining the frequency drifts observed in Type I X-ray bursts from neutron stars.

Original languageEnglish (US)
Pages (from-to)1819-1831
Number of pages13
JournalAstrophysical Journal
Issue number2
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • MHD
  • Stars: neutron
  • Waves
  • X-rays: bursts


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