A data-driven approach to estimate the global spectrum of gravitational planar liquid jets (sheet or curtain flows) is presented in this work. The investigation is carried out by means of two-dimensional numerical simulations performed through the solver BASILISK, based on the one-fluid formulation and the volume-of-fluid approach. The dynamic mode decomposition technique is applied to extract the underlying linear operator, considering random perturbations of the base flow. The effectiveness of this procedure is first evaluated comparing results with those of a simplified one-dimensional curtain model in terms of spectrum and eigenfunctions. The methodology is then applied to a two-dimensional configuration obtaining the BiGlobal spectra for both supercritical (Weber number We > 1) and subcritical (We < 1) regimes. Results highlight that in supercritical regime, the spectrum presents three branches: the upper and lower ones exhibit a purely sinuous behavior with frequencies quite close to those predicted by the one-dimensional model; the middle branch presents a predominant varicose component, increasing with the frequency. The subcritical spectrum, instead, shows that the first two less stable eigenvalues, sorted by increasing frequency, exhibit, respectively, a sinuous and a varicose behavior, while their growth rate is almost the same. As expected, the subcritical regime does not reveal the slow branch. The effect of the density ratio, r ρ, between the two phases is investigated, revealing that the flow system is unstable for r ρ > 0.05. Topological inspections of the leading modes in this unstable configuration show that the predominance of a varicose behavior is related to the rupture of the curtain.
