Part I. The diffraction theory of sea waves and the shelter afforded by breakwaters

Abstract

The diffraction of sea waves round the end of a long straight breakwater is investigated, use being made of the solutions of mathematically analogous problems in the diffraction of light. The wave patterns and wave heights are determined on both the leeward and windward sides of the breakwater, and for points quite close to the breakwater. This involves some extension of the calculations previously made for optical phenomena. The conditions obtaining in the lee of a small island are discussed. The penetration of waves through a single gap in a long breakwater is examined, and the result is shown to depend very much on whether the gap is small or not compared with the length of the waves. The investigation was suggested by problems arising in the construction of the Mulberry harbours.

The Evolution of Inhomogeneous Wave Statistics through a Variable Medium

“…In Figs. 8 and 9 we compare simulation results with analytic solutions (Penney and Price 1952) for a monochromatic incident wave field impinging on a semiinfinite breakwater (G 1 5 L y /2 and G 2 5 0, with L y the lateral extent of the domain), and a barrier gap (G 1 5 G 2 5 2.65L p ( L y ). The QC approximation is in excellent agreement with the analytic solution for distances greater than about 4 wavelengths behind the barrier (x/L p .…”

“…However, on continental shelves and in coastal regions, where wave fields travel through shallower water, and medium variations are stronger (both currents and topography), the wave field can develop and maintain inhomogeneities that strongly affect the wave statistics (e.g., Janssen et al 2008;Janssen and Herbers 2009). For instance, the refraction over coastal topography or currents (e.g., Berkhoff et al 1982;Vincent and Briggs 1989;Magne et al 2007;Janssen et al 2008), or diffraction around obstacles such as breakwaters, reefs, or headlands (e.g., Penney and Price 1952), can result in relatively fast variations in wave statistics because of coherent wave interference patterns. The effects of such coherent structures on the wave statistics are not accounted for by the RTE (Vincent and Briggs 1989;O'Reilly and Guza 1991).…”

Efficient Solution of the 3D Laplace Problem for Nonlinear Wave-Structure Interaction

“…The calculations are compared to the theoretical result from [23] which are based on the theory of [24]. A snapshot of the solution after steady-state is shown in the top plot, while the bottom plot shows the contours of the amplification factor in the shadow region behind the breakwater.…”

Water wave scattering by partially reflecting breakwaters

“…The solution of Penney and Price (1952) could be used for a vertical caisson breakwater, whilst those of Yu (1995) and McIver (1999) could be used for a rubble mound breakwater or any other porous breakwaters such as curtain wall or pile breakwaters. Nowadays, to reduce wave reflection from and impulsive wave pressure acting on a vertical caisson breakwater, a horizontally composite breakwater (i.e., a vertical caisson breakwater covered with wave-energydissipating concrete blocks) or a perforated-wall caisson breakwater is often used, which has a partially reflective front and solid back.…”

“…Penney and Price (1952) proposed an analytic solution for diffracted waves around a semi-infinitely long impermeable breakwater based on Sommerfeld's (1896) solution for diffraction of light. They also obtained the solution for the waves transmitted through a gap in a breakwater by superposing the solutions for the semi-infinite breakwaters.…”