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Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation

Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of $0.41\dot{6}η^2$ for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of $η$ much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of $0.42\pm0.08$ consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of $0.415\pm0.010$. Our measurements establish the first experimental observation of Bohr's hydrodynamic theory.