Acoustic streaming induced by the non-periodic sound in a viscous medium

Instantaneous radiation force of acoustic streaming in a thermoviscous fluid is the subject
of investigation. Dynamic equation governing the velocity of acoustic streaming is a result of
splitting of the conservative differential equations in partial derivatives basing on the features
of all possible types of a fluid motion. The procedure of deriving does not need averaging over
sound period. It is shown that the radiation force consists of three parts, one corresponding
to the classic result (while averaged over sound period), the second being a small negative
term caused by diffraction, and the third one. This last term equals exactly zero for periodic
sound (after averaging) and differs from zero for other types of sound. Sound itself must
satisfy the well-known Khokhlov–Zabolotskaya–Kuznetsov equation describing the weakly
diffracting nonlinear acoustic beam propagating over viscous thermconducting fluid. The parts
of radiation acoustic force, relating to the sound non-periodicity and diffraction, are discussed
and illustrated.