A water bell forms when a fluid jet impacts upon a target and separates into a two-dimensional sheet. Depending on the angle of separation from the target, the sheet can curve into a variety of different geometries. We show analytically that harmonic perturbations of water bells have linear wave solutions with geometry-dependent growth. We test the predictions of this model experimentally with a custom target system, and observe growth in agreement with the model below a critical forcing amplitude. Once the critical forcing amplitude is exceeded, a nonlinear transcritical bifurcation occurs; the response amplitude increases linearly with increasing forcing amplitude, albeit with a fundamentally different spatial form, and distinct nodes appear in the amplitude envelope.
Bibliographical noteFunding Information:
The authors gratefully acknowledge the Naan Dan Jain company for providing the nozzles used to form the jets in these experiments. J.M.K. would like to thank the Fulbright-Israel postdoctoral fellowship for support. H.A. was supported by the National Science Foundation (NSF) Grant No. DMR12-62047. J.F. acknowledges the support of the Israel Science Foundation Grant No. 1523/15.
© 2017 American Physical Society.