The varicose dynamics of a forced gravitational liquid sheet (curtain) issuing into a quiescent gaseous ambient is numerically investigated in this work. The study is relevant for technological applications such as coating deposition, where varicose perturbations of the curtain interfaces can arise due to axial velocity fluctuations coming from the delivering pump placed upstream of the coating die. The investigation is performed in supercritical regime, namely, for Weber number $\mathrm{We}>1$. Two methodologies are employed: a simplified one-dimensional (1D) linear model and two-dimensional (2D) volume-of-fluid simulations. Using harmonic forcing perturbations of the streamwise velocity applied at the inlet section, the curtain varicose dynamics is excited by varying the forcing frequency $f$ and amplitude $A_u$ of the perturbations for different values of $\mathrm{We}$. As a significant result, the 1D analysis reveals that the curtain oscillations amplitude reaches a maximum value for a certain forcing frequency $f=f_{\max }$. In other terms, it is found that the flow manifests a resonance behavior, with the oscillation frequency $f_{\max }$ and corresponding amplitude $A_{h,\max }$ both scaling as ${\mathrm{We}}^{1/3}$, while the average wavelength ${\overline{\lambda }}_{\max }$ scales as ${\mathrm{We}}^{-1/3}$. These scaling laws are confirmed both by theoretical insights and 2D simulations. Moreover, it is found that the 2D curtain breaks up numerically by increasing the forcing amplitude $A_u$. The numerical rupture is determined by a progressive curtain thinning induced by the varicose deformation, which moves upstream by increasing $\mathrm{We}$, i.e., downstream by increasing the surface tension coefficient. In this respect, surface tension is found to play a stabilizing role on the varicose oscillations of the curtain.

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• Instability of free-surface flows
• Interfacial flows
• Surface tension effects