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This analysis reports a formula for torque and viscous power dissipation in scattering of orthogonal waves and vortex beams by a small compressible solid sphere in a slightly viscous fluid. The analysis is based on a viscous correction to far-field scattering, together with beam superposition. The analysis revels the relation between the torque and dissipation. The torque in a heavy sphere limit agrees with a prior analysis by Busse and Wang using boundary flow analysis. The results are applicable to arbitrary sound fields with proper phase distribution, and are extended to other small axisymmetric obstacles such as circular disks and cylinders.


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