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We study a model of internal waves in an effectively 2D aquarium underperiodic forcing. In the case when the underlying classical dynamics hassufficiently irrational rotation number, we prove that the energy of theinternal waves remains bounded. This involves studying the spectrum of arelated 0-th order pseudodifferential operator at spectral parameterscorresponding to such dynamics. For the special cases of rectangular andelliptic domains, we give an explicit spectral description of that operator.

Internal waves in 2D domains with ergodic classical dynamics