Document Type : Original Article
Professor, Department of Mathematics, Faculty of Science, Ain-Shams University, Cairo, Egypt.
Engineer, Department of Basic Science, Benha Higher Institute of Technology, Benha, Egypt.
The higher orders instability of a gas cylinder ambient with an incompressible inviscid
liquid endowed with surface tension is analyzed. The perturbation equations up to
third order are derived and solved. The surface displacements, the velocity potentials
and the dispersion relations are derived for each order of axisymmetric perturbation.
It is found that, up to third order, a transition from instability to stability states occurs
when the perturbed wavelength equals the circumference of the gas cylinder. The
stability discussions for the present model have been done and for the nonhollow jet
as well. The hollow jet instability is much larger than that of the nonhollow model. It is
found that the maximum temporal amplification prevailing in the hollow jet is much
higher than that of the full fluid jet. These results are consistent with some data of the
experimental work of Kendall (1986) phys. Fluids 29, 2086, in the first order