Starting from the Navier-Stokes equations for a viscous fluid, a general equation governing the generation of vorticity Ris obtained, ∇2R=μ0−1∇×∇⋅〈ρ0uu〉, wherein R is the time independent vorticity in the Eulerian frame and ρ0uu is the first-order Reynolds stress dyadic and the angular brackets indicate time average, while ρ0 and μ0 are the ambient density and viscosity, respectively, of the medium. The solution to the vorticity equation properly transformed to the particle coordinates is shown to be without divergence. A specialization of the vorticity equation to the case of solenoidal first-order motion is shown to lead to the generating term employed by Rayleigh and by Schlichting; a specialization to the case of irrotational first-order motion is shown to lead to the generating term employed by Eckart. The sum of the two specialized driving terms does not equal the general term, indicating that the contributions to vorticity from rotational and compressible effects are not independent of one another. The theory outlined is applied to a problem first investigated by Eckart—namely, the streaming generated by a well-defined beam of sound. Results similar to those recently obtained by Eckart and Markham are verified. When applied to a two-dimensional standing wave problem, first treated by Rayleigh, the configuration and magnitude of the streaming velocity are found to differ from the results obtained by Rayleigh. Finally, the effect on streaming of a time-dependent viscosity is examined.