Diffraction of Water Waves by Breakwaters

Diffraction is an important factor in the determination of the distribution of wave energy within a harbor, and therefore is of importance in harbor design. Previous investigations in this field have made use of Sommerfeld's solution of the diffraction of waves by a semiinfinite screen to obtain results for semiinfinite breakwaters, and by superposition, approximate results for continuous breakwaters with openings large compared to the wave length. The investigation of this subject by the Hydrodynamics Laboratories of the California Institute of Technology has been guided by the theoretical solutions of Morse and Rubenstein for the diffraction of waves by ribbons and by slits with the two boundary conditions of zero wave function and zero normal gradient. Morse and Rubenstein separate the wave equation in elliptic cylinder coordinates and obtain the total transmission and the angular distribution of the scattered or diffracted waves in terms of Mathieu functions. This method bridges the gap between the method of Rayleigh for very small slits and the approximation based on Sommerfeld's solution, which is applicable for slit widths greater than three or four wave lengths, and is useful for any angle of wave approach. The difficulties of computation of the required Mathieu functions have been overcome in recent years by the use of modern methods of machine computation. The Institute for Numerical Analysis of the National Bureau of Standards has recently completed the computation of the transmission and distribution of wave energy for openings of one-half, one, two, and three wave lengths, with wave approach angles from 0° to 90° in 15° increments. These data, in the form of polar plots of a dimensionless intensity factor, are compared with experimental measurements conducted to verify the theory, and the two results are found to be in good agreement. The experimental procedure has also been used to investigate a number of breakwater configurations for which theoretical solutions are not obtainable