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

Published online by Cambridge University Press:  03 January 2019

Jeffrey Knowles  and
Harry Yeh Open the ORCID record for Harry Yeh [Opens in a new window]
Jeffrey Knowles
Affiliation:
School of Civil and Construction Engineering, Oregon State University, Corvallis, OR 97331, USA
Harry Yeh*
Affiliation:
School of Civil and Construction Engineering, Oregon State University, Corvallis, OR 97331, USA
*
†Email address for correspondence: [email protected]
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Abstract

With the use of a higher-order Euler formulation, we numerically study the reflection of an obliquely incident solitary wave at a vertical wall and compare results with the higher-order Kadomtsev–Petviashvili theory. A maximum amplification of 3.91 is achieved along the wall, nearly realizing the fourfold prediction by Miles (J. Fluid Mech., vol. 79 (1), 1977, pp. 171–179).

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Solitary waves Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 517 - 523
Copyright
© 2019 Cambridge University Press 

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References

Boyce, W. E. & DiPrima, R. C. 2009 Elementary Differential Equations and Boundary Value Problems, 9th edn. Wiley.Google Scholar
Chakravarty, S. & Kodama, Y. 2009 Soliton solutions of the KP equation and application to shallow water waves. Stud. Appl. Maths 123 (1), 83–151.Google Scholar
Craig, W. & Sulem, C. 1993 Numerical simulation of gravity waves. J. Comput. Phys. 108 (1), 73–83.Google Scholar
Dommermuth, D. G. & Yue, D. K. P. 1987 A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288.Google Scholar
Funakoshi, M. 1980 Reflection of obliquely incident solitary waves. J. Phys. Soc. Japan 49 (6), 2371–2379.Google Scholar
Grimshaw, R. 1971 The solitary wave in water of variable depth. Part 2. J. Fluid Mech. 46 (3), 611–622.Google Scholar
Jia, Y. 2014 Numerical Study of the KP Solitons and Higher Order Miles Theory of the Mach Reflection in Shallow Water. The Ohio State University.Google Scholar
Kodama, Y. & Yeh, H. 2016 The KP theory and Mach reflection. J. Fluid Mech. 800, 766–786.Google Scholar
Li, W., Yeh, H. & Kodama, Y. 2011 On the Mach reflection of a solitary wave: revisited. J. Fluid Mech. 672, 326–357.Google Scholar
Melville, W. K. 1980 On the Mach reflexion of a solitary wave. J. Fluid Mech. 98 (2), 285–297.Google Scholar
Miles, J. W. 1977a Obliquely interacting solitary waves. J. Fluid Mech. 79 (1), 157–169.Google Scholar
Miles, J. W. 1977b Resonantly interacting solitary waves. J. Fluid Mech. 79 (1), 171–179.Google Scholar
von Neumann, J. 1943 Oblique reflection of shocks. John von Neumann Collected Works 6, 238–299.Google Scholar
Perroud, P. H.1957 The solitary wave reflection along a straight vertical wall at oblique incidence. Tech. Rep. California Univ Berkeley Wave Research Lab.Google Scholar
Tanaka, M. 1993 Mach reflection of a large-amplitude solitary wave. J. Fluid Mech. 248, 637–661.Google Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9 (2), 190–194.Google Scholar