On the Mach reflection of a solitary wave: Revisited

Abstract

Reflection of an obliquely incident solitary wave at a vertical wall is studied experimentally in the laboratory wave tank. Precision measurements of water-surface variations are achieved with the aid of laser-induced fluorescent (LIF) technique and detailed features of the Mach reflection are captured. During the development stage of the reflection process, the stem wave is not in the form of a Korteweg-de Vries (KdV) soliton but a forced wave, trailing by a continuously broadening depression. Evolution of stem-wave amplification is in good agreement with the Kadomtsev-Petviashvili (KP) theory. The asymptotic characteristics and behaviours are also in agreement with the theory of Miles (J. Fluid Mech., vol. 79, 1977b, p. 171) except those in the neighbourhood of the transition between the Mach reflection and the regular reflection. The predicted maximum fourfold amplification of the stem wave is not realized in the laboratory environment. On the other hand, the laboratory observations are in excellent agreement with the previous numerical results of the higher-order model of Tanaka (J. Fluid Mech., vol. 248, 1993, p. 637). The present laboratory study is the first to sensibly analyse validation of the theory; note that substantial discrepancies exist from previous (both numerical and laboratory) experimental studies. Agreement between experiments and theory can be partially attributed to the large-distance measurements that the precision laboratory apparatus is capable of. More important, to compare the laboratory results with theory, the corrected interaction parameter is derived from proper interpretation of the theory in consideration of the finite incident wave angle. Our laboratory data indicate that the maximum stem wave can reach higher than the maximum solitary wave height. The wave breaking near the wall results in the substantial increase in wave height and slope away from the wall.