Mathematical Sciences: Hydrodynamic and Hydromagnetic Waves

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The principal investigator will continue her studies of hydrodynamic and hydromagnetic waves of the type that occur in the earth's core. In particular, she will use eigenfunction analysis of the partial differential equations that describe oscillations in stratified, rotating, electrically conducting fluids and Hamiltonian techniques to study the stability of three-dimensional magnetohydrodynamic equilibrium states. The behavior of fluids inside of the earth is a very complicated problem whose solution involves the combined efforts of experimentalists and theoreticians. Essentially both groups study simplified models that regard the earth as a rotating ball of stratified, electrically conducting fluid inside of a magnetic field. The principal investigator is a theoretician who will investigate among other topics whether certain equilibrium states are stable to outside perturbations. Her work has relevance in geophysics and in the study of earthquakes.