Irregular scattering of acoustic rays by vortices

Area of Science:

• Acoustics
• Fluid Dynamics
• Chaos Theory

Background:

• Vortex dynamics and sound wave interactions are crucial in fluid acoustics.
• Understanding sound scattering by complex flow structures is an ongoing challenge.
• Geometrical acoustics provides a framework for analyzing wave propagation in inhomogeneous media.

Purpose of the Study:

• To investigate the scattering of high-frequency sound waves by three stationary vortices in a two-dimensional flow.
• To explore the emergence of chaotic scattering phenomena in this system.
• To characterize the scattering dynamics using concepts from chaos theory.

Main Methods:

• Application of geometrical acoustic approximation for sound wave propagation.
• Analysis of high-frequency sound wave scattering by stationary vortices.
• Investigation of vortex flow at sufficiently high Mach numbers.
• Calculation of fractal dimension and analysis of stable/unstable manifolds.

Main Results:

• Irregular scattering of sound rays observed at high Mach numbers.
• Demonstration of chaotic scattering in a time-reversal breaking system.
• Characterization of the scattering dynamics through fractal dimension and manifold analysis.

Conclusions:

• The interaction of sound waves with vortices can lead to complex, chaotic scattering.
• The system provides a novel example of chaotic scattering in a time-reversal breaking scenario.
• Fractal geometry and manifold analysis are effective tools for describing the observed scattering dynamics.