  The hydrodynamic equations of an ideal fluid formed by a dilute quantum gas
in a parabolic trapping potential are studied analytically and numerically. Due
to the appearance of internal modes in the fluid stratified by the trapping
potential, the spectrum of low-lying modes is found to be dense in the
high-temperature limit, with an infinitely degenerate set of zero-frequency
modes. The spectrum for Bose-fluids and Fermi-fluids is obtained and discussed.
