Dimples, jets and self-similarity in nonlinear capillary waves

Numerical studies of dimple and jet formation from a collapsing cavity often model the initial shape as truncated sphere, mimicking bursting bubble. In this study, we present minimal containing only nonlinear inertial capillary forces, which produces dimples jets wave trough. The trough in our simulation develops smooth perturbation, chosen to be an eigenmode linearised ${O}(\epsilon )$ problem ( $\epsilon$ is non-dimensional amplitude). We explain physical mechanism demonstrate that, for moderate , sharp seen simulations well captured by weakly ^3)$ theory developed here. For $\epsilon \gg 1$ regime strongly nonlinear, spreading surface energy into many modes, precursor now sharply rising jet. Here, reveal novel localised window (in space time) where evolves self-similarly following inviscid (Keller & Miksis, SIAM J. Appl. Maths vol. 43, issue 2, 1983, pp. 268–277) scales. develop analogy self-similar solution first kind, waves. Our first-principles study demonstrates at sufficiently small scales, can form radial inward focusing waves, may described relatively simple employing (nonlinear) effects. Viscosity gravity can, however, significantly influence process, either intensifying singularity or weakening it (Walls et al. Phys. Rev. E 92, 2015, 021002; Gordillo Rodríguez-Rodríguez, Fluid Mech. 867, 2019, 556–571). This leads, particular, critical values Ohnesorge Bond numbers, cannot obtained model.