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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.
Physical Review Letters
|August 27, 2025
Summary
This study numerically and analytically investigates two-dimensional dispersive shock waves, revealing various wave patterns and phenomena like Mach reflection. Results show an eightfold amplitude amplification in oblique flows, with applications in geophysical fluid dynamics.
Area of Science:
- Fluid Dynamics
- Nonlinear Wave Phenomena
Background:
- Dispersive shock waves are fundamental in nonlinear physics.
- Understanding their interactions is crucial for fluid dynamics and other fields.
Purpose of the Study:
- To numerically and analytically study oblique collisions of 2D dispersive shock waves.
- To classify wave patterns based on incidence angle and initial amplitude.
- To explore generalizations of shock wave phenomena.
Main Methods:
- Utilizing the Kadomtsev-Petviashvili II equation.
- Employing wedge-shaped initial conditions to induce temporal dynamics.
- Combining numerical simulations with analytical approaches.
Main Results:
- Identified and classified various asymptotic wave patterns.
- Demonstrated subcritical and supercritical configurations.
- Observed Mach reflection and expansion phenomena for dispersive shock waves.
- Showcased an eightfold amplitude amplification at a critical angle.
Conclusions:
- Oblique shock wave collisions exhibit complex dynamics and predictable patterns.
- The findings generalize known shock wave behaviors to dispersive systems.
- Results have potential applications in geophysical fluid dynamics, such as bore interactions.
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