Variational Low Frequency Scattering by a Rectangular Trough in a Hard Ground Plane

A set of analytical expressions are presented for the diffraction from a rectangular trough when excited by a transverse-electric polarized plane-wave. The final explicit forms are appropriate for applications requiring efficient computation, making minimal use of special functions and requiring no matrix inversions. The solution is arrived at via a quasi-static variational technique wherein the aperture field is represented by a linear combination of three simple functions suggested by the solution to Laplace's equation in the channel geometry. Comparison with an independent moment method indicates that the variational solution to the dynamic problem is highly accurate for troughs of general depth. The upper limit on the frequency corresponds to a total aperture width of one-half of a free-space wavelength.