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The KP theory and Mach reflection

Published online by Cambridge University Press:  13 July 2016

Yuji Kodama  and
Harry Yeh
Yuji Kodama
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43210, 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

Interactions of two line solitons in the two-dimensional shallow-water field are studied based on the Kadomtsev–Petviashvili (KP) theory. With the use of the normal form, the extended KP equation with higher-order correction is derived. This extended KP theory improves significantly the predictability of the original KP theory for soliton interactions with finite oblique angles. The previously existing discrepancy between the experiments and the theory in the Mach reflection problem is now resolved by the normal form theory.

JFM classification

Mathematical Foundations: Mathematical Foundations Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Solitary waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 800 , 10 August 2016 , pp. 766 - 786
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Copyright
© 2016 Cambridge University Press 

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