  The hydrodynamic response of the inviscid small shearing box model of a
midplane section of a rotationally supported astrophysical disk is examined. An
energy functional ${\cal E}$ is formulated for the general nonlinear problem.
It is found that the fate of disturbances is related to the conservation of
this quantity which, in turn, depends on the boundary conditions utilized:
${\cal E}$ is conserved for channel boundary conditions while it is not
conserved in general for shearing box conditions. Linearized disturbances
subject to channel boundary conditions have normal-modes described by Bessel
Functions and are qualitatively governed by a quantity $\Sigma$ which is a
measure of the ratio between the azimuthal and vertical wavelengths. Inertial
oscillations ensue if $\Sigma >1$ - otherwise disturbances must in general be
treated as an initial value problem. We reflect upon these results and offer a
speculation.
