Starting from the Navier‐Stokes equations, general equation governing the generation of vorticityRis obtained:∇2R = μ0−1∇ × ∇ ⋅ 〈ρ0uu〉, whereinRis the time‐independent vorticity in the Eulerian frame and 〈ρ0uu〉 is the average value of Reynolds' stress dyadic. The solution to this vorticity equation, when properly transformed to the particle coordinates, is shown to be divergence free.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 compression effects are not independent of one another.The theory is applied to find the streaming generated by a well‐defined beam of sound giving results agreeing with Eckart and with Markham. However, when it is applied to a two‐dimensional standing wave problem, the configuration of the streaming velocity in the boundary layer is found to differ from the results obtained by Rayleigh.Finally, the effect on streaming of a time‐dependent viscosity coefficient is examined.