On the relaxation of laminar jets at high Reynolds numbers

In this paper we study several problems involving two dimensional and axisymmetric jets issuing in a medium with negligible dynamical effects: (1) a two-dimensional jet entirely bounded by free surfaces, (2) a two-dimensional jet bounded by a free surface and a wall, (3) an axisymmetric jet and (4) a hollow annular jet in a tube. The theoretical study is based on a new technique in which, on the basis of a boundary layer approximation, the velocity components are expanded into a suitable set of eigenfunctions. The deformation of the jet, that is assumed to be a slow function of the distance from the jet exit, is handled by a scaled coordinate system. For the case of the axisymmetric jet, which is the only one previously considered in the literature, this technique is found to be in excellent agreement with previously published, much more computationally demanding results. An experiment involving a vertical water jet has been carried out to further verify the accuracy of the current technique. In particular the behavior very near the exit was found to be in excellent agreement with the experiment at high Reynolds numbers. The fact that the jet relaxation time is much shorter than the time obtained from dimensional arguments is explained with the aid of the semi-analytical structure of the method. In the case of the annular wall jets, the length of the inner gaseous region is found to be finite depending on the Froude number. (C) 1998 American Institute of Physics.