  In the present work, we explore the Rossby mode instabilities in neutron
stars as sources of gravitational waves. The intensity and time evolution of
the emitted gravitational waves in terms of the amplitude of the strain tensor
are estimated in the slow rotation approximation using $\beta$-equilibrated
neutron star matter obtained from density dependent M3Y effective interaction.
For a wide range of neutron star masses, the fiducial gravitational and various
viscous time scales, the critical frequencies and the time evolutions of the
frequencies are calculated. The dissipative mechanism of the Rossby modes is
considered to be driven by the shear viscosity along the boundary layer of the
solid crust-liquid core interface as well as in the core and the bulk
viscosity. It is found that neutron stars with slower frequency of rotation,
for the same mass, radius and surface temperature, are expected to emit
gravitational waves of higher intensity.
