  We study the asymptotic behavior of the quasi-normal modes (QNMs) of w-mode
pulsations of compact stars in the high-frequency regime. We observe that both
the axial and polar w-mode QNMs attain similar asymptotic behaviors in spite of
the fact that they are described by two totally different differential equation
systems. We obtain robust asymptotic formulae relating w-mode QNMs of different
polarities and different angular momenta. To explore the physical reason
underlying such similarity, we first derive a high-frequency approximation for
the polar w-mode oscillations to unify the descriptions for both cases. Then,
we develop WKB-type analyses for them and quantitatively explain the observed
asymptotic behaviors for polytropic stars and quark stars. We also point out
that such asymptotic behaviors for realistic stars are strongly dependent on
the equation of state near the stellar surface.
