  The aim of this paper is to derive a new equation (the \emph{acoustic-drift
equation} (ADE)) describing the generation of a flow by an acoustic wave. We
consider acoustic waves of perfect barotropic gas as the zero-order solution
and derive the equation for the averaged flow of the first order. The used
small parameter of our asymptotic study is dimensionless inverse frequency, and
the leading term for a velocity field is chosen to be a purely oscillating
acoustic field. The employed mathematical approach combines the two-timing
method and the notion of a distinguished limit. The properties of commutators
are used to simplify calculations. The derived averaged equation is similar to
the original vorticity equation, where the Reynolds stresses has been
transformed to an additional advection with the drift velocity. Hence ADE can
be seen as a compressible version of the Craik-Leibovich equation. In
particular, ADE shows that if the averaged vorticity is absent in the initial
data, then it will always be equal to zero. This property confirms that the
acoustic streaming is of viscous nature. At the same time ADE can be useful for
the description of secondary motions which take place for `strong' acoustic
streaming flow.
