  In this paper, we study wave transmission in a rotating fluid with multiple
alternating convectively stable and unstable layers. We have discussed wave
transmissions in two different circumstances: cases where the wave is
propagative in each layer and cases where wave tunneling occurs. We find that
efficient wave transmission can be achieved by `resonant propagation' or
`resonant tunneling', even when stable layers are strongly stratified, and we
call this phenomenon `enhanced wave transmission'. Enhanced wave transmission
only occurs when the total number of layers is odd (embedding stable layers are
alternatingly embedded within clamping convective layers, or vise versa). For
wave propagation, the occurrence of enhanced wave transmission requires that
clamping layers have similar properties, the thickness of each clamping layer
is close to a multiple of the half wavelength of the corresponding propagative
wave, and the total thickness of embedded layers is close to a multiple of the
half wavelength of the corresponding propagating wave (resonant propagation).
For wave tunneling, we have considered two cases: tunneling of gravity waves
and tunneling of inertial waves. In both cases, efficient tunneling requires
that clamping layers have similar properties, the thickness of each embedded
layer is much smaller than the corresponding e-folding decay distance, and the
thickness of each clamping layer is close to a multiple-and-a-half of half
wavelength (resonant tunneling).
