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.
