Water-wave scattering by two submerged thin vertical unequal plates

The problem of water-wave scattering by two thin vertical plates of unequal lengths submerged beneath the free surface of an infinitely deep water is studied here assuming linear theory. The problem is reduced to a pair of vector integral equations of first kind which are solved approximately by using single-term Galerkin approximation. Very accurate numerical estimates for the reflection and transmission coefficients for different values of the wave number and other parameters are obtained. The numerical results for the reflection coefficient are plotted against the wave number in a number of figures for different configurations of the two plates. It is observed from these figures that the reflection coefficient vanishes for a sequence of values of the wave number only for two identical submerged plates. However, for two non-identical plates, the reflection coefficient never becomes zero, although there exists a few wave numbers at which this becomes small for some particular configurations of the plates. When the two plates become very close to each other, known numerical results for a single plate are deduced.