  Utilizing a second-order hydrodynamics formalism, the dispersion relations
for the frequencies and damping rates of collective oscillations as well as
spatial structure of these modes up to the decapole oscillation in both two-
and three- dimensional gas geometries are calculated. In addition to
higher-order modes, the formalism also gives rise to purely damped
"non-hydrodynamic" modes. We calculate the amplitude of the various modes for
both symmetric and asymmetric trap quenches, finding excellent agreement with
an exact quantum mechanical calculation. We find that higher-order hydrodynamic
modes are more sensitive to the value of shear viscosity, which may be of
interest for the precision extraction of transport coefficients in Fermi gas
systems.

Quantum Gases;Nuclear Theory