Contraction of an inviscid swirling liquid jet: Comparison with results for a rotating granular jet.

In honor of the tercentenary of Leonhard Euler, we report a new solution of the Euler equations for the shape of an inviscid rotating liquid jet emanating from a tube of inner radius R$_{0}$ aligned with gravity. Jet contraction is dependent on the exit swirl parameter $\chi_{0}$ = R$_{0}$ $\Omega_{0}$/U$_{0}$ where $\Omega_{0}$ and U$_{0}$ are the uniform rotation rate and axial velocity of the liquid at the exit. The results reveal that rotation reduces the rate of jet contraction. In the limit $\chi_{0} \to$ 0 one recovers the contraction profile for a non-rotating jet and the limit $\chi_{0} \to \infty $ gives a jet of constant radius. In contrast, experiments and a kinematic model for a rotating non-cohesive granular jet show that it expands rather than contracts when a certain small angular velocity is exceeded. The blossoming profiles are parabolic in nature. The model predicts a jet of uniform radius for $\chi_{0} \to$ 0 and a jet with an initially horizontal trajectory in the limit $\chi_{0} \to \infty$.