Geophysical models of the surface global vorticity vector

Abstract

Within the framework of Newtonian kinematics the local vorticity vector is introduced and averaged with respect to global earth geometry, namely the ellipsoid of revolution. For a deformable body like the earth the global vorticity vector is defined as the earth rotation. A decomposition of the Lagrangean displacement and of the Lagrangean vorticity vector into vector spherical harmonics, namely into spheroidal and toroidal parts, proves that the global vorticity vector only contains toroidal coefficients of degree and order one (polar motion) and toroidal coefficients of degree one and order zero (length of the day) in the case of an ellipsoidal earth. Once we assume an earth model of type ellipsoid of revolution the earth rotation is also slightly dependent on the ellipsoidal flattening and the radial derivative of the spheroidal coefficients of degree two and order one.