Wave propagation in tropospheric ducts with transverse and longitudinal variations

Propagation in guiding environments with transversely and longitudinally varying properties belong to the class of important and complex problems. Attention paid to these propagation problems has been increased for the last couple of years. In such environments, it is desirable to seek propagation modes, as the basis elements of wavefields which are strongly tied to the separability of the wave equation. Although the mode concept is “ill-defined” for non-separable wave problems it is still possible to construct approximate mode fields in guiding environments with arbitrary transverse but slowly longitudinal variations. Local separability can be applied for these weakly separable wave problems giving local (adiabatic) modes (AM). Like exact modes in longitudinally invariant environments, the AM can be normalized (i.e., they have finite energy) showing that they belong to the class of “proper” modes. These AM adapt themselves to the smoothly changing longitudinal variations. The ability to normalize the AM fails when the longitudinal dependence leads to critical ranges such as local mode cut-off. The failure is due to the spectral deficiency of the AM field in these transition regions and can be repaired by constructing a spectral b-continuum around the longitudinally varying point spectrum β_q(z). The extended spectrum is synthesized from that of the AM modes, and the resulting wave object is the intrinsic modes (IM). The IM spectral integral reduces to the AM solution(s) when evaluated asymptotically at the saddle point(s) and results in a uniform solution through the critical transition regions