Nonlinear Stability of a Liquid Jet

Abstract

A nonlinear analysis is presented for the capillary stability of a cylindrical column of liquid, of circular cross section. A second-order expansion is obtained using the method of multiple time scales. It is found that the cutoff wavenumber which separates stable from unstable disturbances is amplitude dependent, in agreement with Yuen, and contrary to the linearized analysis. Axisymmetric disturbances with wavenumbers greater than k′ = (1+3a2/4R2)R−1 where a is the disturbance amplitude and R is the radius of the undisturbed jet, oscillate and are stable. However, the frequency of oscillation is amplitude-dependent, contrary to the linearized results. Below this cutoff wavenumber disturbances grow with time. It is also found that the application of the method of straining of coordinates to this problem leads to erroneous results for wavelengths near the circumference of the jet.