In an earlier work we identified a global, nonaxisymmetric instability asso
ciated with the presence of an extreme in the radial profile of the key fun
ction L(r) drop (Sigma Omega/k(2))S-2/Gamma in a thin, inviscid, nonmagneti
zed accretion disk. Here Sigma(r) is the surface mass density of the disk,
Omega(r) is the angular rotation rate, S(r) is the specific entropy, Gamma
is the adiabatic index, and kappa(r) is the radial epicyclic frequency. The
dispersion relation of the instability was shown to be similar to that of
Rossby waves in planetary atmospheres. In this paper, we present the detail
ed linear theory of this Rossby wave instability and show that it exists fo
r a wider range of conditions, specifically, for the case where there is a
"jump" over some range of r in Sigma(r) or in the pressure P(r). We elucida
te the physical mechanism of this instability and its dependence on various
parameters, including the magnitude of the "bump" or "jump," the azimuthal
mode number, and the sound speed in the disk. We find a large parameter ra
nge where the disk is stable to axisymmetric perturbations but unstable to
the nonaxisymmetric Rossby waves. We find that growth rates of the Rossby w
ave instability can be high, similar to 0.2 Omega(K) for relative small jum
ps or bumps. We discuss possible conditions which can lead to this instabil
ity and the consequences of the instability.