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Open Access Publications from the University of California

Singular tidal modes and the regularization of the tidal singularity


Following the work on ray orbits in spatially hyperbolic systems by Mass and Lam (1995) and Rieutord and Valdettaro (1997) we seek to examine the behaviour of the shear layer emitted at the critical latitude in 3D in a spherical shell fllled with rotating fluid. We compare the (previously known) 3D and the 2D solutions for a sphere in an infinite domain to find the major difference being a logarithmic singularity on the rotation axis formed by a cone of shear converging to an apex. We then consider the "split disc" arrangement first considered by Walton to examine this singularity in more detail. We also consider the behaviour of the Moore and Saffman shear layers under the influence of a large-scale forcing; our motivation is primarily the dissipation of tidal energiesin astrophysical binary systems.

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