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Mach Reflection and Expansion of Two-Dimensional Dispersive Shock Waves
Gino Biondini1,2, Alexander Bivolcic1, Mark A Hoefer3
1State University of New York, Department of Mathematics, Buffalo, New York, USA.
Abstract:
The oblique collisions and dynamical interference patterns of two-dimensional dispersive shock waves are studied numerically and analytically via the temporal dynamics induced by wedge-shaped initial conditions for the Kadomtsev-Petviashvili II equation. Various asymptotic wave patterns are identified, classified, and characterized in terms of the incidence angle and the amplitude of the initial step, which can give rise to either subcritical or supercritical configurations, including the generalization to dispersive shock waves of the Mach reflection and expansion of viscous shocks and line solitons. An eightfold amplification of the amplitude of an obliquely incident flow upon a wall at the critical angle is demonstrated. Applications of the results include bore interactions in geophysical fluid dynamics.
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