要約

There are three types of linear stability theories that are currently being used to predict the onset of breakup of liquid jets or sheets. Temporal theory, which is most commonly used because of its simplicity, assumes that the disturbance responsible for the breakup grows temporally at the same rate everywhere in space. A less commonly used spatial theory assumes the disturbance grows in space, because the breakup appears to take place in the region downstream of the location where the liquid is introduced. The most complete theory is that of spatiotemporal instability. This theory has not yet been widely applied because of its mathematical and numerical complexity. It is demonstrated here with an example that a flow may be predicted to be neutral according to pure spatial or pure temporal theory, while it is actually stable according to the spatiotemporal theory. The prediction of the latter theory is shown to agree with the numerical solution of the initial value problem.