  We find a linear instability of non-axisymmetric Rossby waves in a thin
non-magnetized Keplerian disk when there is a local maximum in the radial
profile of a key function ${\cal L}(r) \equiv {\cal F}(r) S^{2/\Gamma}(r)$,
where ${\cal F}^{-1} = \hat {\bf z}\cdot ({\bf \nabla}\times {\bf v}) /\Sigma$
is the potential vorticity, $S = P/\Sigma^\Gamma$ is the entropy, $\Sigma$ is
the surface mass density, $P$ is the vertically integrated pressure, and
$\Gamma$ is the adiabatic index. We consider in detail the special case where
there is a local maximum in the disk entropy profile $S(r)$. This maximum acts
to trap the waves in its vicinity if its height to width ratio ${\rm
max}(S)/\Delta r$ is larger than a threshold value. The pressure gradient
derived from this entropy variation provides the restoring force for the wave
growth. We show that the trapped waves act to transport angular momentum
outward. A plausible way to produce an entropy variation is when an accretion
disk is starting from negligible mass and temperature, therefore negligible
entropy. As mass accumulates by either tidal torquing, magnetic torquing, or
Roche-lobe overflow, confinement of heat will lead to an entropy maximum at the
outer boundary of the disk. Possible nonlinear developments from this
instability include the formation of Rossby vortices and the formation of
spiral shocks. What remains to be determined from hydrodynamic simulations is
whether or not Rossby wave packets (or vortices) ``hold together'' as they
propagate radially inward.
