The dynamics of periodically driven bubble clouds

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Abstract
An averaged two‐fluid model is used to study the motion of a cloud of bubbles. The linearized equations of motion are shown to be a wave equation with both dissipation and dispersion. The fully nonlinear equations are also examined and it is demonstrated that the cutoff frequency of the cloud is equal to the natural frequency of a single bubble. The steady linear response of a periodically driven bubble cloud is then derived. Resonances are seen to arise when the driving frequency is below the cutoff frequency. The inner core of the cloud is shielded by an outer layer when the driving is above the cutoff frequency. The nonlinear dynamics of periodically driven bubble clouds is studied numerically. It is found that the cutoff frequency is crucial in determining whether or not the cloud will behave like a single bubble. Also, under some conditions the cloud is seen to behave like a damped and driven single‐degree‐of‐freedom Hamiltonian system.