The homologous contraction of a sonoluminescing bubble

We show that a homologous solution exists for the contraction of a spherical air bubble in water driven by ultrasound. Scaled radial profiles of thermodynamic variables remain time invariant when this solution is valid. For an ideal gas, we show that the homologous solution is stable against linear nonspherical perturbations, which explains partially the remarkable stability of a sonoluminescing bubble. We verified by hydrodynamic simulations that this scaling solution indeed dominates the contraction of a sonoluminescing bubble and remains stable until shock waves are generated.