CONSTRUCTION OF BASIS VECTORS FOR FLOWS IN THE OUTER CORE OF THE EARTH

Abstract

We demonstrate the use of basis vectors with specific properties in two problems related to flows of an inviscid incompressible fluid in a spherical layer modeling the earth's outer core. The first problem deals with the spectrum of Poincar\'{e}'s operator. We show that this operator has no poloidal eigenvectors, but only toroidal, obtained by restricting toroidal eigenvectors, existing in a sphere, to a spherical layer. The second problem addresses the construction of basis vectors ordered by a measure of their oscillatory behavior. This measure is the functional previously suggested by the authors. We construct a basis ordered by increasing values of this functional. The basis so constructed can be useful for studying flows in spherically symmetric regions.

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Computational Seismology, Vol. 3.