In cylindrical coordinate, the stability for a cylindrical liquid column/ligament can be analysed using perturbation theory by applying small perturbation in radial direction as follow;
$$\rho(z,t)=\rho_0\epsilon e^{(\omega t+ikz)}$$
The physical meaning is quite clear as I can say I am applying small perturbation in radial direction, and the radius is perturbed for at every axial location. However, if I am applying the small perturbation is axial direction, the physical meaning is not very apparent, since the length at each axial location is changing as soon as the initial point (maybe at $z=0$) is perturbed. The expression may looks like this;
$$\zeta(z,t)=\zeta_0\epsilon e^{(\omega t+ikz)}$$
So, can I simply analogously do it this way for axial perturbation?
