A longstanding question on the mechanically forced Faraday instability in rectangular geometries arises from a disparity between theory and experiments (Craik and Armitage in Fluid Dyn Res 15:129–143, 1995). It can be stated as: do corners in a rectangular geometry Faraday experiment cause the disparity between prediction and experiment? This study is an attempt to settle this question by comparing the Faraday instability for two fluids in rectangular geometries where corners must be present with equivalent annular geometries where such corners are necessarily absent. Non-idealities, i.e., damping, arising from a slight meniscus wave motion and induced sidewall damping are observed for thin gaps, causing discrepancies between the predicted instability thresholds and those determined experimentally. However, even for thin-gap geometries, experimental agreement between the tested rectangular geometry and its corresponding annular geometry remains excellent. This suggests that corner effects on the system stability are negligible for rectangular geometries and thus any disparity between theory and experiment is due principally to the damping caused by proximity of the lateral walls.
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Support is acknowledged from the National Science Foundation via a Graduate Research Fellowship under Grant no. DGE-1315138, CASIS NNH11CD70A, NASA NNX17AL27G, and a Chateaubriand Fellowship. RN acknowledges support from the Institute of Advanced Study, Durham University for a Fellowship. FZ acknowledges support from CNES. The authors also acknowledge Dipin Pillai for helpful conversations about the manuscript.
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Ward, K., Zoueshtiagh, F. & Narayanan, R. The Faraday instability in rectangular and annular geometries: comparison of experiments with theory. Exp Fluids 60, 53 (2019). https://doi.org/10.1007/s00348-019-2695-4