Instability of Thin Liquid Sheet and Its Break-Up

This paper deals with symmetrical waves of arbitrary amplitude but long wavelength propagating on a thin liquid sheet. These waves are governed by a simple set of two simultaneous equations which allows only periodic wave trains as its steady solutions. From the results obtained in a previous paper, it is highly probable that the steady solutions may be unstable. To conjecture, initial value problems to the set of equations are solved numerically. It is then shown that these waves are remarkably unstable to a subharmonic disturbance. Furthermore, wave energy distributed uniformly at the initial stage is concentrated in a narrow region and at last the solution bursts at a finite time. Thus it is concluded that such a `burst instability' leads to break-up of the liquid sheet.