Turbulence and Capillary Waves on Bubbles

TL;DR

This paper establishes a theoretical and numerical connection between deep water wave theory and bubble surface perturbations, demonstrating the applicability of wave turbulence concepts to bubbles and exploring their nonlinear behaviors.

Contribution

It develops second-order perturbation equations for bubble dynamics, links wave turbulence theory to bubble surface phenomena, and provides a publicly available simulation code.

Findings

Recreated the Kolmogorov-Zakharov spectrum on bubble surfaces.

Curvature does not significantly influence turbulent properties.

Qualitative response of bubble surfaces matches low gravity experiments.

Abstract

We present a link between the theory of deep water waves and that of bubble surface perturbations. Theory correspondence is shown analytically for small wavelengths in the linear regime and investigated numerically in the nonlinear regime. To do so, we develop the second-order spatial perturbation equations for the Rayleigh-Plesset equation and solve them numerically. Our code is publicly available. Studying capillary waves on stable bubbles, we recreate the Kolmogorov-Zakharov spectrum predicted by weak turbulence theory, putting wave turbulence theory to use for bubbles. In this investigation, it seems that curvature does not affect turbulent properties. Calculated bubble surface qualitatively responds to low gravity experiments. The link demonstrated opens new possibilities for studying several bubble phenomena, including sonoluminescence and cavitation, using the extensive tools developed in the wave turbulence framework.