We study a model of internal waves in an effectively 2D aquarium under periodic
forcing. In the case when the underlying classical dynamics has sufficiently irrational
rotation number, we prove that the energy of the internal waves remains bounded.
This involves studying the spectrum of a related 0-th order pseudodifferential
operator at spectral parameters corresponding to such dynamics. For the special
cases of rectangular and elliptic domains, we give an explicit spectral description of
that operator.
