A modification of the Miche-Rundgren method as presented in the SPM 

 appears to be applicable to breaking, nonbreaking, and broken waves for situa- 

 tions when waves approach at an oblique angle. 



III. MACH-STEM REFLECTION 



Waves in the vicinity of a vertical wall are comprised of incident waves 

 and superimposed reflected waves. For a perfectly reflecting vertical wall 

 with waves of normal incidence, the reflected wave height equals the incident 

 wave height resulting in wave heights in front of the wall equal to twice the 

 incident height. When waves approach a structure at an angle, reflection is 

 not complete resulting in a wave height less than the sum of the incident and 

 reflected waves. For angles of incidence, a > 45°, a phenomenon termed Mach- 

 stem reflection may occur. Instead of reflecting at the angle of incidence, 

 near the structure the incident wave crest turns so that it intersects the 

 structure at a right angle. This gives rise to three separate parts of the 

 wave — an incident wave, a reflected wave, and a Mach-stem wave propagating 

 along the axis of the structure with its crest perpendicular to the structure 

 face (see Fig. 1). The amplitude of the Mach-stem wave, which is the wave 

 causing the force on the wall, was investigated by Perroud (1957) and Chen 

 (1961). The relative amplitude of tlie ^]ach-stem wave as a function of angle of 

 incidence and Hj/2d is given in Figure 2 (H^ is the incident wave height 

 and d the water depth). A more general relationship for average reflection 

 data, independent of H./2d, is given in Figure 3. For a > 45° the relative 

 amplitude of the wave is about 2.0, i.e., the wave height along the wall is 

 the sum of an incident and reflected wave which has a height equal to twice 

 the incident wave height; for a < 45°, the relative amplitude of the Mach-stem 

 wave is less than 2.0. 



H j = Height of Incident Wave 



Hr = Height of Reflected Wove 



Hm - Height of Mach-Stem Wave 



a - Angle of Incidence (angle between wave crest and 



perpendicular to structure ) 



r = Angle of Reflection 



Wave Crest 



Wave Crests 



Wave Crest 



Vertical Structure 

 a< 20° 



Vertical Structure 

 20°<a<45° 



Vertical Structure 

 a >45° 



Figure 1. Reflection patterns of a solitary wave. 



