  The dynamics of toroidal condensates in the presence of condensate flow and
dipole perturbation have been investigated. The Bogoliubov spectrum of
condensate is calculated for an oblate torus using a discrete-variable
representation and a spectral method to high accuracy. The transition from
spheroidal to toroidal geometry of the trap displaces the energy levels into
narrow bands. The lowest-order acoustic modes are quantized with the dispersion
relation $\omega \sim |m| \omega_s $ with $m=0,\pm 1,\pm 2, ...$. A condensate
with toroidal current $\kappa$ splits the $|m|$ co-rotating and
counter-rotating pair by the amount: $\Delta E \approx 2 |m|\hbar^2 \kappa <
r^{-2}>$. Radial dipole excitations are the lowest energy dissipation modes.
For highly occupied condensates the nonlinearity creates an asymmetric mix of
dipole circulation and nonlinear shifts in the spectrum of excitations so that
the center of mass circulates around the axis of symmetry of the trap. We
outline an experimental method to study these excitations.
