STABILITY AND TRAPPING OF SLOW HYDROMAGNETIC-WAVES IN ROTATING CYLINDRICAL GEOMETRY

A multiple-scale asymptotic technique is used to study the propagation of slow hydromagnetic waves in a magnetostrophic regime for an incomp ressible, inviscid; perfectly conducting fluid of constant density in rotating cylindrical geometry. Such waves may play an important role i n both the generation and behavior of the Earth's magnetic field. Know ledge of their behavior may be useful in studying the flows at the cor e-mantle boundary. The equations of motion are linearized about an amb ient state of no motion with respect to rotating cylindrical coordinat es and an azimuthal ambient magnetic field of the form r(n/2) where r is the radial distance in cylindrical coordinates. The waves may be tr apped in a variety of ways while westward travelling modes may be unst able for n > 3. These results extend the local results of ACHESON (197 2) and are consistent with the numerical results of FEARN (1983).