Pinching solutions of slender cylindrical jets
Abstract
Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and KelvinHelmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The breakups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.
 Publication:

Final Report Institute for Computer Applications in Science and Engineering
 Pub Date:
 June 1993
 Bibcode:
 1993icas.reptS....P
 Keywords:

 Interfacial Tension;
 Inviscid Flow;
 Jet Flow;
 KelvinHelmholtz Instability;
 Momentum Theory;
 Nonlinear Systems;
 Vortex Sheets;
 Fluid Mechanics and Heat Transfer