Dispersive wave attenuation due to orographic forcing
Andre Nachbin | Munoz Grajales, Juan Carlos
dispersive waves | inhomogeneous medium | asymptotic theory
The O'Doherty-Anstey approximation (ODA) was originally formulated in the seismological literature for acoustic pulse propagation through a disordered stratified medium. It explains the mechanism for amplitude attenuation (and pulse shaping) promoted by the, variable coefficient, conservative hyperbolic model. This work generalizes the one-dimensional ODA theory for linear weakly dispersive water waves forced by a disordered orography. The analysis is performed through the recently formulated terrain-following Boussinesq system. This is achieved by applying the invariant imbedding method. As a result dispersion alters the medium's correlation function which controls the apparent attenuation mechanism. On the other hand, orography affects the dispersive mechanism for the Airy function-like formation. A nonlinear Boussinesq solver was implemented and theoretical results were validated for different values of the parameters of interest. The theoretical results are in very good agreement with the small amplitude simulations. In particular, the approximate theory was able to capture a good part of the forward scattering radiation. Moreover, through numerical experiments the theory is pushed beyond its expected regime and captures the attenuation of small amplitude solitons due to orographic forcing.