  In underwater acoustic waveguides a pressure field can be decomposed over
three kinds of modes: the propagating modes, the radiating modes and the
evanescent modes. In this paper, we analyze the effects produced by a randomly
perturbed free surface and an uneven bottom topography on the coupling
mechanism between these three kinds of modes. Using an asymptotic analysis
based on a separation of scales technique we derive the asymptotic form of the
distribution of the forward mode amplitudes. We show that the surface and
bottom fluctuations affect the propagating-mode amplitudes mainly in the same
way. We observe an effective amplitude attenuation which is mainly due to the
coupling between the propagating modes themselves. However, for the highest
propagating modes this mechanism is stronger and due to an efficient coupling
with the radiating modes.
