Liquid sheet instability

A linear instability analysis is presented for an inviscid liquid sheed emanated into an inviscid gas medium. The influence of Weber number and gas to liquid density ratio on the evolution of two and three dimensional disturbances of symmetrical and antisymmetrical type is studied. It is found that two dimensional disturbances always dominate the instability process at low Weber number. When the Weber number is large, symmetrical three dimensional disturbances become more unstable than two dimensional ones for long waves. The effect of increasing the gas to liquid density ratio is to promote the dominance of long three dimensional symmetrical waves over their two dimensional counterpart. For antisymmetrical waves, two dimensional disturbances always prevail over three dimensional disturbances regardless of Weber number or gas to liquid density ratio especially for long waves. For short waves, both two and three dimensional disturbances grow at approximately the same rate. It is demonstrated that a critical Weber number exists, above which three dimensional disturbances become unstable. Furthermore, a finite wave number is necessary for the onset of three dimensional instability. The wave number range that leads to a higher growth of symmetrical three dimensional disturbances than two dimensional ones is investigated. An explanation of the differences in the behavior of three dimensional symmetrical and antisymmetrical instabilities is provided.