Radiation forces on highly reflecting circular cylinders in two slanted plane waves: Specular-reflection contributions.

Situations arise where it is desirable to understand and estimate the radiation force on large smooth highly reflecting objects in water illuminated by beams of ultrasound. The approach examined here is to extend a formulation experimentally confirmed by Herrey [J. Acoust. Soc. Am. 27, 891-896 (1955)] for tilted reflecting surfaces in fluids that are modeled as being inviscid. The formulation applies Brillouin's analysis of the Langevin-like radiation force on objects in open containers. The specular reflection contributions to the radiation force of two slanted plane waves incident on a rigid cylinder is approximated and compared with a full partial wave series (PWS) solution for an infinitely long cylinder in an inviscid fluid. The availability of the PWS solution gives support to approximations introduced in the geometric analysis, provided ka (the wave number-cylinder-radius product) is sufficiently large. The normalized force projection is plotted as a function of the wave slant angle relative to the symmetry axis. Deviations between the specular and PWS analysis for ka of 7.5 are diminished for ka of 15 and 25. A region of enhanced force associated with constructive interference narrows with increasing ka.