Fourfold amplification of solitary-wave Mach reflection at a vertical wall


Recently, several new technologies have been developed to investigate the reflection of solitary waves at vertical walls will oblique incident angles. Unfortunately, no technology has been developed up to date to achieve maximum amplification along a wall in an attempt to validate fourfold predictions.

Generally, solitary waves are caused by special disturbances with the ability to propagate but no disperse owing to the fact that they resemble particles. The study of solitary wave reflection along a vertical wall at oblique incident angles was first demonstrated experimentally by Perroud in the mid-twentieth century. His investigation showed wave configurations similar to Mech reflection patterns. Subsequent studies have resulted in the development of several theories for predicting maximum amplifications along vertical walls at specific parameters such as amplitudes and incident angles. However, regardless of the remarkable improvements as a result of these theories, accurate prediction of the fourfold amplification is still missing.

To this note, Oregon State University researchers Jeffrey Knowles (PhD candidate) and Professor Harry Yeh from the School of Civil and Construction Engineering recently utilized higher-order Euler formulation to investigate the reflection of incident solitary waves along vertical walls. Particularly, they aimed to quantitatively validate Miles theory through accurate prediction of fourfold- amplification. Professor Harry Yeh has a distinguished record of studying the maximum amplification of long waves. Their latest research work is now published in the research journal, Journal of Fluid Mechanics.

In brief, the research work entailed a full-wave model for validating the Miles theory. Next, the higher-order pseudo-spectral tool was implemented to enable experimental simulation of various interaction parameters for small incident angles of 10, 15 and 26 degrees. Fundamentally, the study was partially based on an extension of the Tanaka research work by using the presently available advanced computational methods. Eventually, they compared the obtained results to those initially obtained from theoretical Miles prediction.

The duo recorded a maximum amplification of 3.91 along the wall which was the first to nearly equalize the fourfold Miles predictions, standing at 4. This was attributed to the extension of simulation time due to the advanced computational tools used. It was necessary to convert the obtained results to higher-order Kadomtsev Petviashvili theory to achieve the aforementioned maximum amplification at an incident angle of 100 and the incident wave amplitude of 0.0108.

In summary, the Jeffrey Knowles and Harry Yeh successfully conducted simulations based on the water-wave model to quantitatively validate the Miles theory. In general, they noted that maximum amplification depends more on factors including the angle of incident, maximum wall amplitude and incident wave amplitude. However, the discrepancy between the theoretical fourfold amplification value and that obtained from the simulations was attributed to long simulation time as well as the ambiguity associated with the theory. Despite nearly obtaining the fourfold Miles prediction, the authors pointed out the limitations that may compromise achieving the same results through physical experiments. Altogether, the study provides essential information that will further advance future studies on reflection of incident solitary waves.

Fourfold amplification of solitary-wave Mach reflection at a vertical wall - Advances in Engineering

About the author

Harry Yeh is a Professor of Civil & Construction Engineering at Oregon State University. He was the Miles Lowell and Margaret Watt Edwards Distinguished Chair in Engineering at Oregon State University (2003-2015), and a recipient of the 2018 Hamaguchi Award, given by the Japanese Government for his research on tsunamis.

His expertise includes the areas of water-wave mechanics especially for tsunami generation, propagation, transformation, and runup; soliton theory and its numerical and laboratory realization; density and gravity currents; geotechnical and structural considerations of tsunami effects. His research focuses on closely tying mathematical theories, physical consequences, and engineering applications.

Harry has substantial experience in tsunami disaster field surveys, precision laboratory experiments for fundamental problems in fluid mechanics, organizing several multidisciplinary scientific workshops (for mathematicians, geophysists, engineers, sociologists, and practitioner), and conducting international research collaborations.

About the author

Jeffrey Knowles is a graduate student who has been working with Harry, and is on his way to earning his PhD degree and has already been the instructor of record at Oregon State University. In addition to his PhD research, Jeff has worked on a variety of research projects including ground-water monitoring, video data analysis, design of a hydraulic flume, and pavement studies on asphalt emulsions.

Jeff’s current areas of research focus primarily on the theoretical aspects of long waves and their practical applications to civil engineering.


Knowles, J., & Yeh, H. (2019). Fourfold amplification of solitary-wave Mach reflection at a vertical wall. Journal of Fluid Mechanics, 861, 517-523.

Go To Journal of Fluid Mechanics

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