Radiation stress, momentum, angular momentum, and power relationships for axisymmetric objects in acoustic vortex and coaxial wavefields

Abstract

Starting with P. Westervelt’s formulation of the radiation stress tensor and G. Maidanik’s application to angular momentum in the 1950s, some recent theorems concerning acoustic radiation forces, torques, angular momentum, and power flow will be illustrated. Applications include acoustic vortex wavefields, Bessel beams, and other invariant beams. While derivations are simplified for objects surrounded by inviscid fluids [L. Zhang and P. L. Marston, Phys. Rev. E. 84, 035601 (2011); L. Zhang and P. L. Marston, Phys. Rev. E. 84, 065601 (2011); L. Zhang and P. L. Marston, J. Acoust. Soc. Am. 131, EL329–EL335 (2012)], for spheres in slightly viscous liquids limiting approximations are known at long wavelengths that recover results derivable by other approaches [L. Zhang and P. L. Marston, J. Acoust. Soc. Am. 136, 2917–2921 (2014); P. L. Marston, POMA 19, 045005 (2013)]. Theorems obtained are helpful for relating negative radiation forces to the asymmetry of the scattering pattern for spheres in Bessel beams. The relation with extinction theorems is noted [L. Zhang and P. L. Marston, Bio. Opt. Express 4, 1610–1617 (2013); (E) 4, 2988 (2013)] as well as momentum and angular momentum radiated by sources. [Work supported in part by ONR.]