It is shown that the third-order differential equations commonly used in connection with acoustic streaming are special approximations to the law of rotational motion for a fluid element. An expression is derived for the torque exerted by stresses on a spherical element of fluid, about its center of gravity. The average torque in a steady-state sound field consists partly of (1) a sonic torque, exerted by the sound field and partly of (2) a viscous torque due to the induced steady flow. Expressions are also derived for the instantaneous rate of increase of moment of momentum of a spherical fluid element, due to angular acceleration, expansion and shearing. Interpretation is given to individual terms in various streaming equations. In general, any field consisting of superposed elementary waves will give rise to a nonzero distribution of sonic torque. In the special case of a directional source the distribution is similar to that of the gradient of the magnitude of radiation pressure.
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Wesley L. Nyborg (1953) studied this question.