Bubble dynamics in N dimensions

Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the dynamics of a spherical bubble in an N-dimensional fluid are discussed in the hope that examining bubble behavior in N dimensions will add insight to their behavior in three dimensions. Several canonical results in bubble dynamics are re-derived, including the Rayleigh collapse time, the Rayleigh-Plesset equation, and the Minnaert frequency. Recent analytical approximations to the Rayleigh collapse are discussed, and the N-dimensional generalization is used to resolve a known discrepancy. Numerical simulations are used to examine the onset of nonlinear behavior. Overall, the dynamics of bubbles are faster at higher dimensions, with nonlinear behavior occurring at lower strain. Several features are found to be unique to three dimensions, including the trend of nonlinear behavior and apparent coincidences in timescales.