Acoustic diffraction by a half-plane in a viscous fluid medium.

Area of Science:

• Acoustics
• Fluid Dynamics
• Wave Diffraction

Background:

• Acoustic wave propagation in fluids is fundamental.
• Understanding diffraction phenomena is crucial for various applications.
• The effect of fluid viscosity on wave diffraction is complex.

Purpose of the Study:

• To analyze the diffraction of time-harmonic acoustic plane waves by a rigid half-plane.
• To investigate the influence of fluid viscosity on the scattered velocity field.
• To provide analytical and numerical solutions for this specific boundary value problem.

Main Methods:

• Linearized equations for viscous fluid flow.
• No-slip boundary condition on the rigid half-plane.
• Derivation and solution of disjoint Wiener-Hopf equations.
• Padé approximation for the Wiener-Hopf kernel function.

Main Results:

• Analytical expressions for specific wave components of the scattered velocity field.
• Numerical results illustrating the effect of viscosity.
• Demonstration of stress integrability near the half-plane edge.

Conclusions:

• The study provides a comprehensive analysis of acoustic wave diffraction in a viscous medium.
• Viscosity plays a critical role in shaping the velocity field near the diffracting object.
• The developed methods offer insights into wave-structure interactions in viscous fluids.