Acoustic diffraction from a semi-infinite elastic plate under arbitrary fluid loading with application to scattering from Arctic ice leads

Abstract

The problem of a low-frequency acoustic plane wave incident upon a free surface coupled to a semi-infinite elastic plate surface, is solved using an analytic approach based on the Wiener-Hopf method. By low-frequency it is meant that the elastic properties of the plate are adequately described by the thin plate equation (kH ≲ 1). The diffraction problem relates to issues in long range sound propagation through partially ice-covered Arctic waters, where open leads or polynya on the surface represent features from which acoustic energy can be diffracted or scattered. This work focusses on ice as the material for the elastic plate surface, and, though the solution methods presented here have applicability to general edge diffraction problems, the results and conclusions are directed toward the ice lead diffraction process. The work begins with the derivation of an exact solution to a canonical problem: a plane wave incident upon a free surface (Dirichlet boundary condition) coupled to a perfectly rigid surface (Neumann boundary condition). Important features of the general edge diffraction problem are included here, with the solution serving as a guideline to the more complicated solutions presented later involving material properties of the boundary. The ice material properties are first addressed using the locally reacting approximation for the input impedance of an ice plate, wherein the effects of elasticity are ignored. This is followed by use of the thin plate equation to describe the input impedance, which incorporates elements of elastic wave propagation. An important issue in working with the thin plate equation is the fluid loading pertaining to sea ice and low-frequency acoustics, which cannot be characterized by simplifying heavy or light fluid loading limits. An approximation to the exact kernel of the Wiener-Hopf functional equation is used here, which is valid in this mid-range fluid loading regime. Use of this approximate kernel allows one to proceed to a complete and readily interpretable solution for the far field diffracted pressure, which includes a subsonic flexural wave in the ice plate. By using Green's theorem, in conjunction with the behavior of the diffracted field along the two-part planar boundary, the functional dependence of ∏D (total diffracted power) in terms of k (wavenumber), H (ice thickness), α (grazing angle) and the combined elastic properties of the ice sheet and ambient medium, is determined. A means to convert ∏D into an estimate of dB loss per bounce is developed using ray theoretical methods, in order to demonstrate a mechanism for acoustic propagation loss attributed directly to ice lead diffraction effects. Data from the 1984 MIZEX (Marginal Ice Zone Experiments) narrow-band acoustic transmission experiments are presented and discussed in this context.