The Free Oscillations

The free oscillations of theWorld Ocean on the rotating Earth consist of gravity and vorticity modes, primarily governed by the gravity of the Earth and by the latitude dependent Coriolis force, respectively. A total of 284 free oscillations is found in the period range of 7.7 h to 165 h. Of these, 169 oscillations are classified as physically relevant, while the remaining 115 are considered to be spurious modes. These spurious modes are characterized by very large amplitudes in both the horizontal mass transport and the sea surface elevation. They are concentrated on small areas and located mainly in bays and gulfs. Although resonances do exist in these regions, they cannot be resolved with this model. In the following, only the physically meaningful modes are considered.

All 56 modes, computed by ZAMU2005 with the parameterized LSA-term and periods between 8.03 h and 133.10 h, correspond to modes that have now been computed with consideration of the full LSA-effect. As expected, the three single modes with the full LSA-effect, computed with a special iteration procedure in ZAMU2005, and the four modes calculated with the Wielandt Method by [29], have been verified in this work with exact match (compare Section 2.2). Additionally, for an analysis of the full LSA-effect and not its parameterization , 107 normal modes with periods between 12h and 120h are computed without the LSA-effect. The accuracy of all these normal modes is of the same order of magnitude as that of those found using the inverse iteration method by ZAMU2005. The residual r ranges from 1.24E-13 to 1.23E-10 for the calculated eigensolutions (equation 2.46), corresponding to a correctness of the first six digits of the mantissa of σk.