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.

Specular reflection contributions to dynamic radiation forces on highly reflecting spheres (L).

Specular reflection contributions to dynamic radiation forces were recently mentioned for highly reflecting spheres to facilitate comparison with forces on cylinders [Marston, Daniel, Fortuner, Kirsteins, and Abawi, J. Acoust. Soc. Am. 149, 3042-3051 (2021)]. Both shapes of reflectors were taken to be illuminated by short-wavelength plane wave double-sideband suppressed-carrier ultrasound. Here, the geometric method of evaluating dynamic forces on spheres is illustrated along with an analysis of the phase of the modulated radiation force. Comparison with partial wave series solutions supports the relevance of the specular reflection analysis for insight into forces on highly reflecting objects in water.

Specular-reflection contributions to static and dynamic radiation forces on circular cylinders.

Interest in the response of highly reflecting objects in water to modulated acoustical radiation forces makes it appropriate to consider contributions to such forces from perfectly reflecting objects to provide insight into radiation forces. The acoustic illumination can have wavelengths much smaller than the object's size, and objects of interest may have complicated shapes. Here, the specular contribution to the oscillating radiation force on an infinite circular cylinder at normal incidence is considered for double-sideband-suppressed carrier-modulated acoustic illumination. The oscillatory magnitude of the specular force decreases monotonically with increasing modulation frequency, and the phase of the oscillating force depends on the relative phase of the sidebands. The phase dependence on the modulation frequency can be reduced with the appropriate selection of a sideband relative-phase parameter. That is a consequence of the significance of rays that are incident on the cylinder having small impact parameters that are nearly backscattered. For one choice of a relative sideband phase, a prior partial wave series (PWS) solution is available, which supports the specular analysis when the PWS is evaluated for a rigid cylinder. The importance of specular contributions for aluminum cylinders in water is noted. A specular analysis for an analogous spherical reflector is also summarized.