The nonlinear response to a periodic bar potential in a differentially
rotating gaseous disk is studied. A comprehensive theory, based on th
e work of Shu, Yuan, & Lissauer and Yuan & Cheng, is developed further
. This approach allows us to include the effects af viscosity and self
-gravitation explicitly in the formulation, and calculates directly th
e streamlines of the gas flow distorted by the rotating bar potential.
Using it, we show that a major morphological difference exists among
the spiral waves excited at the three types of Lindblad resonance. Spi
rals associated with the outer Lindblad resonance are tightly wound, w
hile those associated with the inner Lindblad resonances are relativel
y open. In general, spirals are trailing. However, those excited at th
e Inner inner Lindblad resonance are leading. These results help us un
derstand the underlying physics of the spiral structure revealed in th
e recent radio interferometric observations of the central regions of
disk galaxies. The transport of angular momentum between the bar and t
he disk is related directly to these waves. The spiral waves excited a
t the inner Lindblad resonances would induce inflows of disk material
toward the center, while those excited at the outer Lindblad resonance
induce outflows. Formulae to estimate the rates of the inflows and ou
tflows are derived, and they are used to examine the process of fuelin
g of active galactic nuclei and starburst rings.