# Frequency selection in a gravitationally stretched capillary jet in the jetting regime

## TL;DR

This study investigates how external periodic forcing affects a gravitationally stretched capillary jet, revealing that the optimal forcing frequency depends on amplitude and can be accurately predicted by resolvent analysis.

## Contribution

It introduces a combined use of nonlinear simulations and resolvent analysis to predict optimal forcing frequencies in a stretching capillary jet, improving understanding of jet breakup dynamics.

## Key findings

- Optimal forcing frequency varies with forcing amplitude.
- Resolvent analysis accurately predicts jet breakup length.
- WKBJ formalism fails to match nonlinear simulation results.

## Abstract

A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency producing the most unstable jet is found to be highly dependent on the forcing amplitude. Taking benefit of the one-dimensional Eggers & Dupont (J. Fluid Mech., vol. 262, 1994, 205-221) equations, we investigate the case through nonlinear simulations and linear stability analysis. In the local framework the WKBJ formalism, established for weakly non-parallel flows, fails to capture the nonlinear simulation results quantitatively. However in the global framework, the resolvent analysis supplemented by a simple approximation of the required response norm inducing breakup, is shown to correctly predict the optimal forcing frequency at a given forcing amplitude and the resulting jet breakup length. The results of the resolvent analysis are found to be in good agreement with those of the nonlinear simulations.