Dispersive Wave Attenuation Due to Orographic Forcing

The O'Doherty--Anstey (ODA) approximation was originally formulated in the seismological literature for acoustic pulse propagation through a disordered stratified medium [Geophys. Prospecting, 19 (1971), pp. 430--458]. 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 resul...

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