  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.
