Abstract
Based on the mild-slope equation derived by Smith and Sprinks and the extended refraction–diffraction equation developed by Massel, a two-layer mild-slope equation is constructed for interfacial waves propagating on the interface of a two-layer ocean model. First, Smith and Sprinks's approach is followed to derive the mild-slope equation for the propagation of interfacial waves, with the higher-order terms proportional to the bottom slope and bottom curvature all being neglected. The extended version of the mild-slope equation is then derived with the higher-order terms included. While it is possible to solve the first equation analytically, a numerical solution is presented for the second equation. As part of a verification process, both solutions are compared with each other and also with the single-layer mild-slope equation when the density of the upper layer tends to zero. The new solution is then used to study the effect of the hump dimensions on the refraction of the interfacial waves over a circular hump.
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