Curle's equation and acoustic scattering by a sphere.

Area of Science:

• Acoustics
• Fluid Dynamics
• Aeroacoustics

Background:

• Recent research explores connections between aeroacoustic theory and acoustic scattering.
• Acoustic scattering by spheres is a fundamental problem with theoretical and practical implications.

Purpose of the Study:

• To investigate Curle's equation in acoustic scattering by a sphere.
• To analyze the impact of viscosity on acoustic scattering predictions.
• To extend scattering solutions to elastic spheres in viscous fluids.

Main Methods:

• Derivation of Curle's equation for linear acoustic scattering.
• Development of a complete solution for scattering by a rigid sphere in a viscous fluid.
• Extension of the null field solution to include vorticity modes.
• Construction of a solution for an elastic sphere in a viscous fluid.

Main Results:

• Explicit confirmation of Curle's equation for plane wave scattering by a rigid sphere in an inviscid fluid.
• Demonstration that neglecting viscous terms leads to incomplete far-field dipole pressure predictions.
• Recovery of the rigid sphere/null field solution from the elastic sphere solution in a limiting case.

Conclusions:

• Curle's equation is validated for specific inviscid scattering scenarios.
• Viscous effects are crucial for accurate far-field pressure predictions in acoustic scattering.
• The developed framework accommodates both rigid and elastic scatterers in viscous media.