  We present simulation results of the impulsively generated linear and
non-linear Alfv\'en waves in the weakly curved coronal magnetic flux-tubes
(coronal funnels) and discuss their implications for the coronal heating and
solar wind acceleration. We solve numerically the time-dependent
magnetohydrodynamic (MHD) equations to obtain the temporal signatures of the
small (linear) and large-amplitude (non-linear) Alfv\'en waves in the model
atmosphere of expanding open magnetic field configuration (e.g., coronal
funnels) by considering a realistic temperature distribution. We compute the
maximum transversal velocity of both linear and non-linear Alfv\'en waves at
different heights in the coronal funnel, and study their response in the solar
corona during the time of their propagation. We infer that the pulse-driven
non-linear Alfv\'en waves may carry sufficient wave energy fluxes to heat the
coronal funnels and also to power the solar wind that originates in these
funnels. Our study of linear Alfv\'en waves show that they can contribute only
to the plasma dynamics and heating of the funnel-like magnetic flux-tubes
associated with the polar coronal holes.
