Complementary Approximations to the Solution of a Problem in Water Waves

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Abstract
A surface wave is incident upon two vertical parallel barriers immersed to a given depth beneath the surface of water of infinite depth. The problem has an exact but complicated solution. Simpler complementary approximations to the reflection coefficient are derived which may be computed easily. These approximations are found to be very good for all wavelengths provided the ratio of separation to depth of the barrier is not too small. It is shown that there exist certain wavelengths for each barrier configuration for which total reflection of the incident wave occurs.