THE DEVELOPMENT OF A SWIRLING ROUND LAMINAR JET

The development of a swirling round laminar jet in an unbounded viscous fluid is investigated in this Brief Communication by applying the unsteady Stokes equations instead of the full Navier-Stokes equations. The solutions corresponding to a constant linear-momentum source, an impulsive linear-momentum source, and constant and impulsive angular-momentum sources are presented. Since the Stokes equations are linear, these results can be superimposed together. For a constant linear-momentum source and a constant angular-momentum source, the present results reduce to the Stokeslet and rotlet solutions, which are the singular solutions of the Stokes equations, respectively, as time approaches infinity. It is also found that the developing flow field due to a linear-momentum source at the initial stage is irrotational and has a dipolelike structure. However, the developing flow field due to an angular-momentum source is immediately rotational and the magnitude of the velocity is exponentially small.