Mach reflection and expansion of two-dimensional dispersive shock waves

TL;DR

This paper investigates the complex interactions and patterns of two-dimensional dispersive shock waves, including Mach reflection and expansion phenomena, using numerical and analytical methods based on the KP-II equation.

Contribution

It provides a comprehensive classification and analysis of wave patterns resulting from wedge-shaped initial conditions, extending understanding of dispersive shock wave behavior.

Findings

Identification of various asymptotic wave patterns

Demonstration of eightfold amplitude amplification at critical angles

Generalization of Mach reflection phenomena to dispersive shocks

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.