Memory-encoding vibrations in a disconnecting air bubble

Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water

“…As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al (2009) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al (2009b). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off.…”

“…Memory-encoding vibrations induced by a small geometric disturbance have been predicted theoretically for any mode number m, and observed experimentally for cavities with m = 2 and m = 3 disturbances, namely bubbles released underwater from a slotshaped nozzle, by Schmidt et al (2009) and Keim (2011). The theoretical model was derived through a perturbation analysis of an azimuthal distortion to the geometry of a cavity with the behaviour described by equation 3.5.…”

“…Analysis of how the flow is modified by this shape disturbance (Schmidt 2008;Schmidt et al 2009) gives a linear second order ODE for the dependence of time evolution of the amplitudes a m on the mean radial dynamics:…”

“…Part of the information (the mode amplitude) from the initial conditions is encoded and preserved -the cavity 'remembers' the shape that created it-but the chirping of the frequency makes it increasingly difficult to backtrack the evolution of the cavity as the collapse approaches, hence scrambling part of the information at the end (Schmidt et al 2009). …”

“…If axial symmetry is broken by a small azimuthal perturbation, a truly universal system would be expected to converge to the same solution . However, through experiments and simulations of an air bubble disconnecting from an underwater nozzle, Keim, Møller, Zhang & Nagel (2006); Schmidt, Keim, Zhang & Nagel (2009) ;Turitsyn, Lai & Zhang (2009);and Keim (2011) recently showed that a slight azimuthal asymmetry can trigger vibrations that persist in time. The fact that a small perturbation is not smoothed out indicates that the system possesses memory of its initial conditions.…”