| Time harmonic inviscid internal wave motions constrained to fully
closed domains generically lead to singular velocity fields. In
spite of this difficulty, several techniques exist to solve such
internal wave boundary value problems. Recently it has been shown
that for a domain with the shape of a trapezium, solutions can be
written in terms of a double sine Fourier series. However, the
solutions were found by a numerical technique and thus not all
coefficients of the series are available. Unfortunately, for
questions related e.g. to regularization of the inviscid {\em
singular} solutions, the knowledge of the asymptotic behavior of the
spectrum for large wave numbers is essential. Here we discuss
solutions of internal wave boundary value problems for which the
spectra are known, at least asymptotically. We further describe
shortcomings of the found solutions that need to be overcome in the
future. Finally, we sketch applications of the solutions in the
context of viscous energy dissipation. |