Langevin radiation force as a consequence of linear wave fields

Area of Science:

• Acoustics
• Wave Physics
• Fluid Dynamics

Background:

• The origin of acoustic radiation force (linear vs. nonlinear wave fields) has been debated for over 100 years.
• Rayleigh radiation pressure is linked to the nonlinear equation of state.
• Langevin radiation pressure is traditionally derived from nonlinear equations, despite not depending on the nonlinear state equation.

Purpose of the Study:

• To demonstrate that Langevin radiation force arises from linear wave fields.
• To resolve the long-standing debate on the origins of acoustic radiation force.
• To provide a clear derivation of Langevin radiation force from linearized equations.

Main Methods:

• Derivation of Langevin radiation force using linearized continuity, state, and momentum equations.
• Analysis of the quadratic velocity terms in the force calculation.
• Comparison with radiation forces from electromagnetic waves, surface gravity waves, and string waves.

Main Results:

• The Langevin radiation force is derived from linearized equations, confirming its linear origin.
• The study shows that solving the linear scattering problem is sufficient for calculating the average force up to second-order velocity terms.
• Parallels are drawn with other wave phenomena to elucidate the linear nature of the force.

Conclusions:

• The Langevin radiation force is fundamentally a consequence of linear wave fields.
• This finding clarifies the theoretical basis of acoustic radiation force, resolving a historical debate.
• The derivation provides a simplified approach using linear scattering solutions.