  We perform a systematic study of the dependence of the r-mode phenomenology
in normal fluid pulsar neutron stars on the symmetry energy slope parameter
$L$. An essential ingredient in this study is the bulk viscosity, which is
evaluated consistently for several equations of state corresponding to
different values of the slope parameter $L$. Direct Urca processes, which are
allowed from a critical $L$-value onwards, enhance the bulk viscosity and have
large influence on the $r$-mode features, such as the instability boundary and
spin-down properties of newborn neutron stars. The magnitude of the changes in
the $r$-mode properties induced by the direct Urca processes are driven by the
$L$-value of the equation of state and the mass of the pulsar. The study has
been done by using a family of equations of state of $\beta$-equilibrated
neutron star matter obtained with the finite range simple effective
interaction, which provides realistic results for nuclear matter and finite
nuclei properties. These equations of state predict the same properties in
symmetric nuclear matter and have the same value of the symmetry energy
parameter, $E_s(\rho_0)$, but differ in the slope parameter $L$. The range
chosen for the variation of $L$ is decided from the tidal deformability data
extracted from the GW170817 event and the maximum mass constraint.
