Amplification of solitary waves along a vertical wall Public Deposited


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  • 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 temporal and spatial features of the Mach reflection are captured. During the development stage of the reflection process, the stem wave is formed with the wave crest perpendicular to the wall; this stem wave is not in the form of a Korteweg-de Vries (KdV) soliton but a forced wave, trailing by a continuously broadening depression wave. Evolution of stem-wave amplification is in good agreement with the Kadomtsev-Petviashvili (KP) theory. The asymptotic characteristics and behaviors are also in agreement with the theory of Miles (1977b) except those in the neighborhood of the transition between the Mach reflection and the regular reflection. The maximum fourfold amplification of the stem wave at the transition predicted by Miles is not realized in the laboratory environment: the maximum amplification measured in the laboratory is 2.92, which is however in excellent agreement with the numerical results of Tanaka (1993). The present laboratory study is the first to sensibly analyze 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 along the wall results in the substantial increase in wave height and slope away from the wall. Extending the foregoing study on the reflection of a single solitary wave at a vertical wall, laboratory and numerical experiments are performed on two co-propagating obliquely incident solitary waves with different amplitudes that are reflected at the wall. The larger wave catches up with the smaller wave; hence the two waves collide with the strong interaction. The resulting wave pattern near the wall is complex due to the interaction among the two incident solitons and the two reflected solitons. The numerical predictions of the KP theory are in good agreement with the experimental results. Another comparison of the KP theory with laboratory experiments is demonstrated for one of the exact soliton solutions of the KP equation by Chakravarty and Kodama (2009). This solution is called the T-type solution by Kodama. The theoretically predicted formation of the 'box'-shape wave pattern in the vicinity of two-soliton intersection is realized in the laboratory tank. The agreement between the laboratory observation and the KP theory is found better for the cases with the larger wave amplitude a and smaller oblique angle ψ (i.e. tan ψ/(√3a cos ψ) < 0.6). Subtle and unavoidable differences among the analytical KP solution, the setup of numerical calculation, and the laboratory condition are discussed.
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